Big_Data_Digrafos_y_Redes_Clase_octava_Preguntas.ipynb

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      "authorship_tag": "ABX9TyMCyo4Q1lpuERmSJz94YL5s",
      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
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    "language_info": {
      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/sgevatschnaider/Grafos/blob/main/Big_Data_Digrafos_y_Redes_Clase_octava_Preguntas.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import display, HTML\n",
        "\n",
        "# Contenido HTML actualizado\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Material Elaborado por Sergio Gevatschnaider</title>\n",
        "    <link href=\"https://fonts.googleapis.com/css2?family=Roboto:wght@400;700&display=swap\" rel=\"stylesheet\">\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: 'Roboto', Arial, sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "            color: #333;\n",
        "        }\n",
        "        h1 {\n",
        "            color: #2c3e50;\n",
        "            text-align: center;\n",
        "            font-size: 2.5em;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        h2 {\n",
        "            color: #2980b9;\n",
        "            font-size: 1.8em;\n",
        "            margin-top: 30px;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: square;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        ul ul {\n",
        "            list-style-type: disc;\n",
        "            margin-left: 50px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        a {\n",
        "            color: #2980b9;\n",
        "            text-decoration: none;\n",
        "            font-weight: bold;\n",
        "        }\n",
        "        a:hover {\n",
        "            text-decoration: underline;\n",
        "            color: #1b5c8a;\n",
        "        }\n",
        "        .download-link {\n",
        "            background-color: #2980b9;\n",
        "            color: white;\n",
        "            padding: 10px 15px;\n",
        "            text-align: center;\n",
        "            display: inline-block;\n",
        "            border-radius: 5px;\n",
        "            margin-top: 20px;\n",
        "            font-size: 1.1em;\n",
        "            text-decoration: none;\n",
        "        }\n",
        "        .download-link:hover {\n",
        "            background-color: #1b5c8a;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "    <h1>Material Elaborado por Sergio Gevatschnaider</h1>\n",
        "    <p>Clase de Big Data de la Universidad de Palermo</p>\n",
        "    <p>Basado en el libro <em>Introductory Graph Theory with Applications</em> por Fred Buckley y Marty Lewinter</p>\n",
        "\n",
        "    <h2>Índice</h2>\n",
        "    <ul>\n",
        "        <li>Grafos Dirigidos</li>\n",
        "        <li>Redes</li>\n",
        "        <li>Método del Camino Crítico</li>\n",
        "    </ul>\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML mejorado en Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 426
        },
        "id": "2BX8y2Y4JmmM",
        "outputId": "5733ffe7-3364-4bc1-9306-7ba83ca54fdb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Material Elaborado por Sergio Gevatschnaider</title>\n",
              "    <link href=\"https://fonts.googleapis.com/css2?family=Roboto:wght@400;700&display=swap\" rel=\"stylesheet\">\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: 'Roboto', Arial, sans-serif;\n",
              "            line-height: 1.8;\n",
              "            margin: 20px;\n",
              "            padding: 20px;\n",
              "            background-color: #f9f9f9;\n",
              "            color: #333;\n",
              "        }\n",
              "        h1 {\n",
              "            color: #2c3e50;\n",
              "            text-align: center;\n",
              "            font-size: 2.5em;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        h2 {\n",
              "            color: #2980b9;\n",
              "            font-size: 1.8em;\n",
              "            margin-top: 30px;\n",
              "        }\n",
              "        p {\n",
              "            font-size: 1.2em;\n",
              "            margin-bottom: 15px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: square;\n",
              "            margin-left: 30px;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        ul ul {\n",
              "            list-style-type: disc;\n",
              "            margin-left: 50px;\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 10px;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "        a {\n",
              "            color: #2980b9;\n",
              "            text-decoration: none;\n",
              "            font-weight: bold;\n",
              "        }\n",
              "        a:hover {\n",
              "            text-decoration: underline;\n",
              "            color: #1b5c8a;\n",
              "        }\n",
              "        .download-link {\n",
              "            background-color: #2980b9;\n",
              "            color: white;\n",
              "            padding: 10px 15px;\n",
              "            text-align: center;\n",
              "            display: inline-block;\n",
              "            border-radius: 5px;\n",
              "            margin-top: 20px;\n",
              "            font-size: 1.1em;\n",
              "            text-decoration: none;\n",
              "        }\n",
              "        .download-link:hover {\n",
              "            background-color: #1b5c8a;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "    <h1>Material Elaborado por Sergio Gevatschnaider</h1>\n",
              "    <p>Clase de Big Data de la Universidad de Palermo</p>\n",
              "    <p>Basado en el libro <em>Introductory Graph Theory with Applications</em> por Fred Buckley y Marty Lewinter</p>\n",
              "    \n",
              "    <h2>Índice</h2>\n",
              "    <ul>\n",
              "        <li>Grafos Dirigidos</li>\n",
              "        <li>Redes</li>\n",
              "        <li>Método del Camino Crítico</li>\n",
              "    </ul>\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.core.display import display, HTML\n",
        "\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Grafos Dirigidos y No Dirigidos</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: Arial, sans-serif;\n",
        "            line-height: 1.6;\n",
        "            background-color: #f4f4f9;\n",
        "            margin: 20px;\n",
        "        }\n",
        "        h1, h2, h3 {\n",
        "            color: #2c3e50;\n",
        "        }\n",
        "        p {\n",
        "            background: #ffffff;\n",
        "            padding: 10px;\n",
        "            border-radius: 5px;\n",
        "            box-shadow: 0 0 10px rgba(0, 0, 0, 0.1);\n",
        "            margin-bottom: 10px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: disc;\n",
        "            background: #ffffff;\n",
        "            padding: 10px;\n",
        "            border-radius: 5px;\n",
        "            box-shadow: 0 0 10px rgba(0, 0, 0, 0.1);\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 8px;\n",
        "        }\n",
        "        .node {\n",
        "            display: inline-block;\n",
        "            width: 50px;\n",
        "            height: 50px;\n",
        "            background-color: #3498db;\n",
        "            color: white;\n",
        "            font-size: 1.2em;\n",
        "            font-weight: bold;\n",
        "            text-align: center;\n",
        "            line-height: 50px;\n",
        "            border-radius: 50%;\n",
        "            margin: 10px;\n",
        "        }\n",
        "        .arrow {\n",
        "            display: inline-block;\n",
        "            width: 60px;\n",
        "            text-align: center;\n",
        "            font-size: 2em;\n",
        "            color: #000;\n",
        "            vertical-align: middle;\n",
        "        }\n",
        "        .line {\n",
        "            display: inline-block;\n",
        "            width: 60px;\n",
        "            height: 2px;\n",
        "            background-color: #000;\n",
        "            vertical-align: middle;\n",
        "        }\n",
        "        .centered {\n",
        "            text-align: center;\n",
        "            margin: 20px 0;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "\n",
        "    <h1>1. Grafos Dirigidos (Digrafos)</h1>\n",
        "    <p>En un grafo dirigido, las aristas tienen una dirección. Esto significa que si hay una arista entre dos nodos A y B, puede ir de A hacia B o de B hacia A, pero no en ambas direcciones a la vez, a menos que se representen con dos aristas opuestas.</p>\n",
        "\n",
        "    <p>La relación entre los nodos no es simétrica. Si existe una arista de A a B, no necesariamente hay una arista de B a A.</p>\n",
        "\n",
        "    <p>Las aristas suelen representarse con flechas para indicar la dirección.</p>\n",
        "\n",
        "    <h2>Ejemplo de un grafo dirigido:</h2>\n",
        "    <div class=\"centered\">\n",
        "        <div class=\"node\">A</div>\n",
        "        <div class=\"arrow\">&rarr;</div>\n",
        "        <div class=\"node\">B</div>\n",
        "    </div>\n",
        "    <p>Esto significa que hay una conexión de A hacia B, pero no necesariamente de B hacia A.</p>\n",
        "\n",
        "    <h1>2. Grafos No Dirigidos</h1>\n",
        "    <p>En un grafo no dirigido, las aristas no tienen dirección. Si existe una arista entre A y B, esto significa que la conexión es bidireccional; es decir, puedes ir de A a B y de B a A.</p>\n",
        "\n",
        "    <p>La relación entre los nodos es simétrica. Si hay una arista entre A y B, también existe entre B y A.</p>\n",
        "\n",
        "    <p>Las aristas se dibujan como líneas sin flechas.</p>\n",
        "\n",
        "    <h2>Ejemplo de un grafo no dirigido:</h2>\n",
        "    <div class=\"centered\">\n",
        "        <div class=\"node\">A</div>\n",
        "        <div class=\"line\"></div>\n",
        "        <div class=\"node\">B</div>\n",
        "    </div>\n",
        "    <p>Esto indica que hay una conexión entre A y B, y puedes moverte en ambos sentidos.</p>\n",
        "\n",
        "    <h1>Diferencias Clave</h1>\n",
        "    <ul>\n",
        "        <li><strong>Dirección de las conexiones:</strong>\n",
        "            <ul>\n",
        "                <li>En un grafo dirigido, las aristas tienen una dirección específica.</li>\n",
        "                <li>En un grafo no dirigido, las aristas son bidireccionales.</li>\n",
        "            </ul>\n",
        "        </li>\n",
        "        <li><strong>Simetría:</strong>\n",
        "            <ul>\n",
        "                <li>Los grafos dirigidos son asimétricos.</li>\n",
        "                <li>Los grafos no dirigidos son simétricos en cuanto a las conexiones.</li>\n",
        "            </ul>\n",
        "        </li>\n",
        "    </ul>\n",
        "\n",
        "    <h1>Ejemplo de Aplicaciones</h1>\n",
        "    <ul>\n",
        "        <li><strong>Grafos Dirigidos:</strong> Se usan mucho para representar sistemas donde las relaciones tienen direcciones específicas, como las rutas de transporte (puedes ir de una ciudad a otra, pero no siempre de vuelta por la misma ruta) o diagramas de flujo de datos.</li>\n",
        "        <li><strong>Grafos No Dirigidos:</strong> Se aplican comúnmente en redes sociales (amistades son bidireccionales: si eres amigo de alguien, esa persona también es tu amigo) o en modelos de conexiones eléctricas.</li>\n",
        "    </ul>\n",
        "\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML en Google Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "DtHKY9u9JCIT",
        "outputId": "2ccdeb76-a32b-45b8-aedf-771bb6c6154e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Grafos Dirigidos y No Dirigidos</title>\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: Arial, sans-serif;\n",
              "            line-height: 1.6;\n",
              "            background-color: #f4f4f9;\n",
              "            margin: 20px;\n",
              "        }\n",
              "        h1, h2, h3 {\n",
              "            color: #2c3e50;\n",
              "        }\n",
              "        p {\n",
              "            background: #ffffff;\n",
              "            padding: 10px;\n",
              "            border-radius: 5px;\n",
              "            box-shadow: 0 0 10px rgba(0, 0, 0, 0.1);\n",
              "            margin-bottom: 10px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: disc;\n",
              "            background: #ffffff;\n",
              "            padding: 10px;\n",
              "            border-radius: 5px;\n",
              "            box-shadow: 0 0 10px rgba(0, 0, 0, 0.1);\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 8px;\n",
              "        }\n",
              "        .node {\n",
              "            display: inline-block;\n",
              "            width: 50px;\n",
              "            height: 50px;\n",
              "            background-color: #3498db;\n",
              "            color: white;\n",
              "            font-size: 1.2em;\n",
              "            font-weight: bold;\n",
              "            text-align: center;\n",
              "            line-height: 50px;\n",
              "            border-radius: 50%;\n",
              "            margin: 10px;\n",
              "        }\n",
              "        .arrow {\n",
              "            display: inline-block;\n",
              "            width: 60px;\n",
              "            text-align: center;\n",
              "            font-size: 2em;\n",
              "            color: #000;\n",
              "            vertical-align: middle;\n",
              "        }\n",
              "        .line {\n",
              "            display: inline-block;\n",
              "            width: 60px;\n",
              "            height: 2px;\n",
              "            background-color: #000;\n",
              "            vertical-align: middle;\n",
              "        }\n",
              "        .centered {\n",
              "            text-align: center;\n",
              "            margin: 20px 0;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "\n",
              "    <h1>1. Grafos Dirigidos (Digrafos)</h1>\n",
              "    <p>En un grafo dirigido, las aristas tienen una dirección. Esto significa que si hay una arista entre dos nodos A y B, puede ir de A hacia B o de B hacia A, pero no en ambas direcciones a la vez, a menos que se representen con dos aristas opuestas.</p>\n",
              "\n",
              "    <p>La relación entre los nodos no es simétrica. Si existe una arista de A a B, no necesariamente hay una arista de B a A.</p>\n",
              "\n",
              "    <p>Las aristas suelen representarse con flechas para indicar la dirección.</p>\n",
              "\n",
              "    <h2>Ejemplo de un grafo dirigido:</h2>\n",
              "    <div class=\"centered\">\n",
              "        <div class=\"node\">A</div>\n",
              "        <div class=\"arrow\">&rarr;</div>\n",
              "        <div class=\"node\">B</div>\n",
              "    </div>\n",
              "    <p>Esto significa que hay una conexión de A hacia B, pero no necesariamente de B hacia A.</p>\n",
              "\n",
              "    <h1>2. Grafos No Dirigidos</h1>\n",
              "    <p>En un grafo no dirigido, las aristas no tienen dirección. Si existe una arista entre A y B, esto significa que la conexión es bidireccional; es decir, puedes ir de A a B y de B a A.</p>\n",
              "\n",
              "    <p>La relación entre los nodos es simétrica. Si hay una arista entre A y B, también existe entre B y A.</p>\n",
              "\n",
              "    <p>Las aristas se dibujan como líneas sin flechas.</p>\n",
              "\n",
              "    <h2>Ejemplo de un grafo no dirigido:</h2>\n",
              "    <div class=\"centered\">\n",
              "        <div class=\"node\">A</div>\n",
              "        <div class=\"line\"></div>\n",
              "        <div class=\"node\">B</div>\n",
              "    </div>\n",
              "    <p>Esto indica que hay una conexión entre A y B, y puedes moverte en ambos sentidos.</p>\n",
              "\n",
              "    <h1>Diferencias Clave</h1>\n",
              "    <ul>\n",
              "        <li><strong>Dirección de las conexiones:</strong>\n",
              "            <ul>\n",
              "                <li>En un grafo dirigido, las aristas tienen una dirección específica.</li>\n",
              "                <li>En un grafo no dirigido, las aristas son bidireccionales.</li>\n",
              "            </ul>\n",
              "        </li>\n",
              "        <li><strong>Simetría:</strong>\n",
              "            <ul>\n",
              "                <li>Los grafos dirigidos son asimétricos.</li>\n",
              "                <li>Los grafos no dirigidos son simétricos en cuanto a las conexiones.</li>\n",
              "            </ul>\n",
              "        </li>\n",
              "    </ul>\n",
              "\n",
              "    <h1>Ejemplo de Aplicaciones</h1>\n",
              "    <ul>\n",
              "        <li><strong>Grafos Dirigidos:</strong> Se usan mucho para representar sistemas donde las relaciones tienen direcciones específicas, como las rutas de transporte (puedes ir de una ciudad a otra, pero no siempre de vuelta por la misma ruta) o diagramas de flujo de datos.</li>\n",
              "        <li><strong>Grafos No Dirigidos:</strong> Se aplican comúnmente en redes sociales (amistades son bidireccionales: si eres amigo de alguien, esa persona también es tu amigo) o en modelos de conexiones eléctricas.</li>\n",
              "    </ul>\n",
              "\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import display, HTML\n",
        "\n",
        "# Contenido HTML corregido sin barras invertidas\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Ejemplo 10.1: Dibuja el Dígrafo</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: 'Arial', sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1, h2 {\n",
        "            color: #2c3e50;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: square;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        .math {\n",
        "            background: #f4f4f4;\n",
        "            padding: 10px;\n",
        "            border-radius: 5px;\n",
        "            font-family: 'Cambria Math', serif;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "    <h1>Ejemplo 10.1: Dibuja el Dígrafo</h1>\n",
        "    <p>Dibuja el dígrafo D con el conjunto de vértices <strong>V(D) = {a, b, c, d, e}</strong> y el conjunto de aristas <strong>E(D) = {ab, ac, ae, bc, bd, cb, ce, ed}</strong>.</p>\n",
        "\n",
        "    <p>Luego, indica el grado de entrada y el grado de salida de cada vértice.</p>\n",
        "\n",
        "    <p>Finalmente, responde: ¿Cuáles arcos son simétricos?</p>\n",
        "\n",
        "    <h2>Conjuntos Definidos:</h2>\n",
        "    <p class=\"math\"><strong>V(D) = {a, b, c, d, e}</strong></p>\n",
        "    <p class=\"math\"><strong>E(D) = {ab, ac, ae, bc, bd, cb, ce, ed}</strong></p>\n",
        "\n",
        "    <h2>Preguntas:</h2>\n",
        "    <ul>\n",
        "        <li>¿Cuál es el grado de entrada de cada vértice?</li>\n",
        "        <li>¿Cuál es el grado de salida de cada vértice?</li>\n",
        "        <li>¿Qué arcos son simétricos?</li>\n",
        "    </ul>\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML mejorado en Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 592
        },
        "id": "C0wElgnRNb3q",
        "outputId": "ba80a422-e49b-4383-a11e-cebbc3a51887"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Ejemplo 10.1: Dibuja el Dígrafo</title>\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: 'Arial', sans-serif;\n",
              "            line-height: 1.8;\n",
              "            margin: 20px;\n",
              "            padding: 20px;\n",
              "            background-color: #f9f9f9;\n",
              "        }\n",
              "        h1, h2 {\n",
              "            color: #2c3e50;\n",
              "        }\n",
              "        p {\n",
              "            font-size: 1.2em;\n",
              "            margin-bottom: 15px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: square;\n",
              "            margin-left: 30px;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 10px;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "        .math {\n",
              "            background: #f4f4f4;\n",
              "            padding: 10px;\n",
              "            border-radius: 5px;\n",
              "            font-family: 'Cambria Math', serif;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "    <h1>Ejemplo 10.1: Dibuja el Dígrafo</h1>\n",
              "    <p>Dibuja el dígrafo D con el conjunto de vértices <strong>V(D) = {a, b, c, d, e}</strong> y el conjunto de aristas <strong>E(D) = {ab, ac, ae, bc, bd, cb, ce, ed}</strong>.</p>\n",
              "\n",
              "    <p>Luego, indica el grado de entrada y el grado de salida de cada vértice.</p>\n",
              "    \n",
              "    <p>Finalmente, responde: ¿Cuáles arcos son simétricos?</p>\n",
              "\n",
              "    <h2>Conjuntos Definidos:</h2>\n",
              "    <p class=\"math\"><strong>V(D) = {a, b, c, d, e}</strong></p>\n",
              "    <p class=\"math\"><strong>E(D) = {ab, ac, ae, bc, bd, cb, ce, ed}</strong></p>\n",
              "\n",
              "    <h2>Preguntas:</h2>\n",
              "    <ul>\n",
              "        <li>¿Cuál es el grado de entrada de cada vértice?</li>\n",
              "        <li>¿Cuál es el grado de salida de cada vértice?</li>\n",
              "        <li>¿Qué arcos son simétricos?</li>\n",
              "    </ul>\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Crear el digrafo\n",
        "D = nx.DiGraph()\n",
        "\n",
        "# Definir los nodos (vértices)\n",
        "vertices = ['a', 'b', 'c', 'd', 'e']\n",
        "\n",
        "# Añadir los nodos al grafo\n",
        "D.add_nodes_from(vertices)\n",
        "\n",
        "# Definir los arcos (edges) según el ejemplo\n",
        "edges = [('a', 'b'), ('a', 'c'), ('a', 'e'),\n",
        "         ('b', 'c'), ('b', 'd'),\n",
        "         ('c', 'b'), ('c', 'e'),\n",
        "         ('e', 'd')]\n",
        "\n",
        "# Añadir los arcos al grafo\n",
        "D.add_edges_from(edges)\n",
        "\n",
        "# Función para identificar arcos simétricos\n",
        "def encontrar_arcos_simetricos(grafo):\n",
        "    arcos_simetricos = []\n",
        "    for u, v in grafo.edges():\n",
        "        if grafo.has_edge(v, u):\n",
        "            arcos_simetricos.append((u, v))  # Añadir si ambos arcos existen\n",
        "    return arcos_simetricos\n",
        "\n",
        "# Dibujar el grafo\n",
        "pos = nx.spring_layout(D)  # Posiciones de los nodos\n",
        "\n",
        "# Dibujar nodos y arcos\n",
        "nx.draw(D, pos, with_labels=True, node_color='lightblue', node_size=2000, font_size=16, font_weight='bold', arrows=True)\n",
        "\n",
        "# Dibujar etiquetas de los arcos (dirección de las aristas)\n",
        "labels = {edge: f\"{edge[0]}->{edge[1]}\" for edge in D.edges}\n",
        "nx.draw_networkx_edge_labels(D, pos, edge_labels=labels)\n",
        "\n",
        "# Mostrar el gráfico\n",
        "plt.title(\"Grafo Dirigido del Ejemplo 10.1\")\n",
        "plt.show()\n",
        "\n",
        "# Cálculo de grados de salida y entrada\n",
        "print(\"Grado de salida (outdegree) y entrada (indegree) de cada vértice:\")\n",
        "for v in vertices:\n",
        "    print(f\"Vértice {v}: outdegree = {D.out_degree(v)}, indegree = {D.in_degree(v)}\")\n",
        "\n",
        "# Encontrar e imprimir los arcos simétricos\n",
        "arcos_simetricos = encontrar_arcos_simetricos(D)\n",
        "print(\"\\nArcos simétricos:\")\n",
        "for arco in arcos_simetricos:\n",
        "    print(f\"{arco[0]} <--> {arco[1]}\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 724
        },
        "id": "fRAJJdg2ORit",
        "outputId": "0c3a81e0-f787-4484-e1ce-0cb182459ff5"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Grado de salida (outdegree) y entrada (indegree) de cada vértice:\n",
            "Vértice a: outdegree = 3, indegree = 0\n",
            "Vértice b: outdegree = 2, indegree = 2\n",
            "Vértice c: outdegree = 2, indegree = 2\n",
            "Vértice d: outdegree = 0, indegree = 2\n",
            "Vértice e: outdegree = 1, indegree = 2\n",
            "\n",
            "Arcos simétricos:\n",
            "b <--> c\n",
            "c <--> b\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import display, HTML\n",
        "\n",
        "# Contenido HTML\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Transmisores y Receptores en Diferentes Sistemas</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: 'Arial', sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1, h2 {\n",
        "            color: #2c3e50;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: square;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        .section {\n",
        "            margin-bottom: 40px;\n",
        "        }\n",
        "        .example {\n",
        "            color: #2980b9;\n",
        "            font-weight: bold;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "    <h1>Transmisores y Receptores en Diferentes Sistemas</h1>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>1. Redes de Computadoras (Telecomunicaciones)</h2>\n",
        "        <p>En redes de comunicación, el concepto de transmisor y receptor es fundamental. Imagina una red de computadoras:</p>\n",
        "        <ul>\n",
        "            <li><strong>Transmisor (Transmitter):</strong> Un servidor de archivos en una red que solo envía datos a otros dispositivos (clientes). No recibe datos de ellos, sino que únicamente distribuye la información. <span class=\"example\">Ejemplo: Un servidor web que solo distribuye páginas web a usuarios.</span></li>\n",
        "            <li><strong>Receptor (Receiver):</strong> Un cliente que solo recibe información de un servidor pero no envía datos de vuelta. <span class=\"example\">Ejemplo: Una impresora de red que solo recibe trabajos de impresión pero no envía datos a otras computadoras.</span></li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>2. Cadenas de Suministro</h2>\n",
        "        <p>En una cadena de suministro, los nodos pueden representar fábricas, distribuidores y puntos de venta, mientras que las aristas pueden representar el flujo de productos.</p>\n",
        "        <ul>\n",
        "            <li><strong>Transmisor (Transmitter):</strong> Una fábrica puede actuar como un transmisor, ya que solo envía productos a los distribuidores o tiendas, pero no recibe productos de ellos. <span class=\"example\">Ejemplo: Una fábrica de productos electrónicos que produce teléfonos y los envía a los distribuidores, pero no recibe productos de ellos.</span></li>\n",
        "            <li><strong>Receptor (Receiver):</strong> Una tienda de venta al por menor puede actuar como un receptor, ya que recibe productos de los distribuidores, pero no envía productos de vuelta. <span class=\"example\">Ejemplo: Una tienda que solo recibe productos para vender y no envía productos a otros nodos.</span></li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>3. Sistemas de Energía</h2>\n",
        "        <p>En una red de distribución de electricidad, podemos modelar la transmisión de energía usando grafos dirigidos:</p>\n",
        "        <ul>\n",
        "            <li><strong>Transmisor (Transmitter):</strong> Una planta generadora de energía actúa como un transmisor, porque genera y envía electricidad hacia la red de distribución, pero no recibe electricidad de otras plantas. <span class=\"example\">Ejemplo: Una central hidroeléctrica que suministra electricidad a la red.</span></li>\n",
        "            <li><strong>Receptor (Receiver):</strong> Un hogar o empresa actúa como un receptor, ya que recibe energía de la red eléctrica, pero no devuelve energía a la red. <span class=\"example\">Ejemplo: Una casa que consume electricidad pero no genera energía para otros nodos.</span></li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>4. Flujos de Datos en Redes Sociales</h2>\n",
        "        <p>En una red social dirigida, como Twitter (donde las relaciones no son bidireccionales), se pueden identificar transmisores y receptores de información:</p>\n",
        "        <ul>\n",
        "            <li><strong>Transmisor (Transmitter):</strong> Una cuenta muy influyente (celebridad o figura pública) que tiene muchos seguidores, pero no sigue a otros usuarios. Esta cuenta solo envía información (tweets) pero no recibe información de otras cuentas. <span class=\"example\">Ejemplo: Una cuenta de un influencer con millones de seguidores que no sigue a nadie.</span></li>\n",
        "            <li><strong>Receptor (Receiver):</strong> Una cuenta que solo sigue a otras cuentas pero no tiene seguidores. Esta cuenta recibe información de otras cuentas, pero no genera interacciones que se propaguen hacia otros. <span class=\"example\">Ejemplo: Un usuario de Twitter que sigue a muchas cuentas de noticias pero no tiene seguidores.</span></li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>5. Flujos de Agua en Redes Hidráulicas</h2>\n",
        "        <p>Imagina una red de tuberías en un sistema de distribución de agua:</p>\n",
        "        <ul>\n",
        "            <li><strong>Transmisor (Transmitter):</strong> Un depósito de agua que solo envía agua a otras partes del sistema (como hogares o industrias), pero no recibe agua de otros depósitos. <span class=\"example\">Ejemplo: Un tanque de agua en la parte más alta de una ciudad que distribuye agua a los consumidores.</span></li>\n",
        "            <li><strong>Receptor (Receiver):</strong> Una casa que solo recibe agua del sistema de distribución, pero no la devuelve al sistema. <span class=\"example\">Ejemplo: Un hogar que usa agua para consumo y no la redistribuye.</span></li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>6. Sistemas de Transporte</h2>\n",
        "        <p>En un sistema de transporte, los nodos pueden representar estaciones o puntos de transferencia, y las aristas pueden representar rutas de vehículos (buses, trenes, etc.):</p>\n",
        "        <ul>\n",
        "            <li><strong>Transmisor (Transmitter):</strong> Una estación central de trenes o buses que envía vehículos a múltiples destinos, pero no recibe servicios de otras estaciones. <span class=\"example\">Ejemplo: Una estación de buses en una ciudad grande que actúa como centro de distribución de rutas.</span></li>\n",
        "            <li><strong>Receptor (Receiver):</strong> Un destino final (parada terminal) donde los vehículos llegan pero no parten hacia otros destinos. <span class=\"example\">Ejemplo: Una parada de buses en una localidad lejana que recibe buses de la ciudad, pero no envía buses hacia la ciudad.</span></li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>7. Ecosistemas y Redes Tróficas</h2>\n",
        "        <p>En las redes ecológicas (redes tróficas), los nodos pueden representar diferentes especies y las aristas representan la dirección del flujo de energía (quién se alimenta de quién):</p>\n",
        "        <ul>\n",
        "            <li><strong>Transmisor (Transmitter):</strong> Una especie que se encuentra en el nivel trófico más bajo (como una planta), que solo proporciona energía (al ser consumida), pero no recibe energía de otros organismos. <span class=\"example\">Ejemplo: Plantas que son consumidas por herbívoros, pero no consumen a otros organismos.</span></li>\n",
        "            <li><strong>Receptor (Receiver):</strong> Un depredador ápice (como un león) que se encuentra en la parte superior de la cadena alimenticia y solo recibe energía (al consumir otros organismos), pero no es consumido por otros. <span class=\"example\">Ejemplo: Un tiburón o un águila que consume otros animales, pero no tiene depredadores que lo consuman.</span></li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML en Google Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "tXzH4rSzPiM9",
        "outputId": "97c804b1-1087-4156-ce9d-9ee3923930e0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Transmisores y Receptores en Diferentes Sistemas</title>\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: 'Arial', sans-serif;\n",
              "            line-height: 1.8;\n",
              "            margin: 20px;\n",
              "            padding: 20px;\n",
              "            background-color: #f9f9f9;\n",
              "        }\n",
              "        h1, h2 {\n",
              "            color: #2c3e50;\n",
              "        }\n",
              "        p {\n",
              "            font-size: 1.2em;\n",
              "            margin-bottom: 15px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: square;\n",
              "            margin-left: 30px;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 10px;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "        .section {\n",
              "            margin-bottom: 40px;\n",
              "        }\n",
              "        .example {\n",
              "            color: #2980b9;\n",
              "            font-weight: bold;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "    <h1>Transmisores y Receptores en Diferentes Sistemas</h1>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>1. Redes de Computadoras (Telecomunicaciones)</h2>\n",
              "        <p>En redes de comunicación, el concepto de transmisor y receptor es fundamental. Imagina una red de computadoras:</p>\n",
              "        <ul>\n",
              "            <li><strong>Transmisor (Transmitter):</strong> Un servidor de archivos en una red que solo envía datos a otros dispositivos (clientes). No recibe datos de ellos, sino que únicamente distribuye la información. <span class=\"example\">Ejemplo: Un servidor web que solo distribuye páginas web a usuarios.</span></li>\n",
              "            <li><strong>Receptor (Receiver):</strong> Un cliente que solo recibe información de un servidor pero no envía datos de vuelta. <span class=\"example\">Ejemplo: Una impresora de red que solo recibe trabajos de impresión pero no envía datos a otras computadoras.</span></li>\n",
              "        </ul>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>2. Cadenas de Suministro</h2>\n",
              "        <p>En una cadena de suministro, los nodos pueden representar fábricas, distribuidores y puntos de venta, mientras que las aristas pueden representar el flujo de productos.</p>\n",
              "        <ul>\n",
              "            <li><strong>Transmisor (Transmitter):</strong> Una fábrica puede actuar como un transmisor, ya que solo envía productos a los distribuidores o tiendas, pero no recibe productos de ellos. <span class=\"example\">Ejemplo: Una fábrica de productos electrónicos que produce teléfonos y los envía a los distribuidores, pero no recibe productos de ellos.</span></li>\n",
              "            <li><strong>Receptor (Receiver):</strong> Una tienda de venta al por menor puede actuar como un receptor, ya que recibe productos de los distribuidores, pero no envía productos de vuelta. <span class=\"example\">Ejemplo: Una tienda que solo recibe productos para vender y no envía productos a otros nodos.</span></li>\n",
              "        </ul>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>3. Sistemas de Energía</h2>\n",
              "        <p>En una red de distribución de electricidad, podemos modelar la transmisión de energía usando grafos dirigidos:</p>\n",
              "        <ul>\n",
              "            <li><strong>Transmisor (Transmitter):</strong> Una planta generadora de energía actúa como un transmisor, porque genera y envía electricidad hacia la red de distribución, pero no recibe electricidad de otras plantas. <span class=\"example\">Ejemplo: Una central hidroeléctrica que suministra electricidad a la red.</span></li>\n",
              "            <li><strong>Receptor (Receiver):</strong> Un hogar o empresa actúa como un receptor, ya que recibe energía de la red eléctrica, pero no devuelve energía a la red. <span class=\"example\">Ejemplo: Una casa que consume electricidad pero no genera energía para otros nodos.</span></li>\n",
              "        </ul>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>4. Flujos de Datos en Redes Sociales</h2>\n",
              "        <p>En una red social dirigida, como Twitter (donde las relaciones no son bidireccionales), se pueden identificar transmisores y receptores de información:</p>\n",
              "        <ul>\n",
              "            <li><strong>Transmisor (Transmitter):</strong> Una cuenta muy influyente (celebridad o figura pública) que tiene muchos seguidores, pero no sigue a otros usuarios. Esta cuenta solo envía información (tweets) pero no recibe información de otras cuentas. <span class=\"example\">Ejemplo: Una cuenta de un influencer con millones de seguidores que no sigue a nadie.</span></li>\n",
              "            <li><strong>Receptor (Receiver):</strong> Una cuenta que solo sigue a otras cuentas pero no tiene seguidores. Esta cuenta recibe información de otras cuentas, pero no genera interacciones que se propaguen hacia otros. <span class=\"example\">Ejemplo: Un usuario de Twitter que sigue a muchas cuentas de noticias pero no tiene seguidores.</span></li>\n",
              "        </ul>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>5. Flujos de Agua en Redes Hidráulicas</h2>\n",
              "        <p>Imagina una red de tuberías en un sistema de distribución de agua:</p>\n",
              "        <ul>\n",
              "            <li><strong>Transmisor (Transmitter):</strong> Un depósito de agua que solo envía agua a otras partes del sistema (como hogares o industrias), pero no recibe agua de otros depósitos. <span class=\"example\">Ejemplo: Un tanque de agua en la parte más alta de una ciudad que distribuye agua a los consumidores.</span></li>\n",
              "            <li><strong>Receptor (Receiver):</strong> Una casa que solo recibe agua del sistema de distribución, pero no la devuelve al sistema. <span class=\"example\">Ejemplo: Un hogar que usa agua para consumo y no la redistribuye.</span></li>\n",
              "        </ul>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>6. Sistemas de Transporte</h2>\n",
              "        <p>En un sistema de transporte, los nodos pueden representar estaciones o puntos de transferencia, y las aristas pueden representar rutas de vehículos (buses, trenes, etc.):</p>\n",
              "        <ul>\n",
              "            <li><strong>Transmisor (Transmitter):</strong> Una estación central de trenes o buses que envía vehículos a múltiples destinos, pero no recibe servicios de otras estaciones. <span class=\"example\">Ejemplo: Una estación de buses en una ciudad grande que actúa como centro de distribución de rutas.</span></li>\n",
              "            <li><strong>Receptor (Receiver):</strong> Un destino final (parada terminal) donde los vehículos llegan pero no parten hacia otros destinos. <span class=\"example\">Ejemplo: Una parada de buses en una localidad lejana que recibe buses de la ciudad, pero no envía buses hacia la ciudad.</span></li>\n",
              "        </ul>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>7. Ecosistemas y Redes Tróficas</h2>\n",
              "        <p>En las redes ecológicas (redes tróficas), los nodos pueden representar diferentes especies y las aristas representan la dirección del flujo de energía (quién se alimenta de quién):</p>\n",
              "        <ul>\n",
              "            <li><strong>Transmisor (Transmitter):</strong> Una especie que se encuentra en el nivel trófico más bajo (como una planta), que solo proporciona energía (al ser consumida), pero no recibe energía de otros organismos. <span class=\"example\">Ejemplo: Plantas que son consumidas por herbívoros, pero no consumen a otros organismos.</span></li>\n",
              "            <li><strong>Receptor (Receiver):</strong> Un depredador ápice (como un león) que se encuentra en la parte superior de la cadena alimenticia y solo recibe energía (al consumir otros organismos), pero no es consumido por otros. <span class=\"example\">Ejemplo: Un tiburón o un águila que consume otros animales, pero no tiene depredadores que lo consuman.</span></li>\n",
              "        </ul>\n",
              "    </div>\n",
              "    \n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import display, HTML\n",
        "\n",
        "# Contenido HTML con el Teorema 10.1 y demostración\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Teorema 10.1: Grafos Dirigidos</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: 'Arial', sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1, h2, h3 {\n",
        "            color: #2c3e50;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: square;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        .math {\n",
        "            background: #f4f4f4;\n",
        "            padding: 10px;\n",
        "            border-radius: 5px;\n",
        "            font-family: 'Cambria Math', serif;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "    <h1>Teorema 10.1: Grafos Dirigidos</h1>\n",
        "\n",
        "    <p>El <strong>Teorema 10.1</strong> que aparece en la imagen es un resultado fundamental en grafos dirigidos (o digrafos). Este teorema relaciona el número total de arcos en un digrafo con los grados de entrada (<strong>id(v)</strong>) y grados de salida (<strong>od(v)</strong>) de los vértices.</p>\n",
        "\n",
        "    <h2>Teorema 10.1</h2>\n",
        "    <p>Si <strong>D</strong> es un digrafo con:</p>\n",
        "    <ul>\n",
        "        <li>Conjunto de vértices <strong>V(D) = {v<sub>1</sub>, v<sub>2</sub>, …, v<sub>n</sub>}</strong> (es decir, el digrafo tiene <strong>n</strong> vértices),</li>\n",
        "        <li>Número total de arcos <strong>q</strong> (es decir, las conexiones dirigidas entre vértices),</li>\n",
        "    </ul>\n",
        "    <p>Entonces se cumple que:</p>\n",
        "    <div class=\"math\">\n",
        "        <p>∑<sub>i=1</sub><sup>n</sup> id(v<sub>i</sub>) = q</p>\n",
        "        <p>y</p>\n",
        "        <p>∑<sub>i=1</sub><sup>n</sup> od(v<sub>i</sub>) = q</p>\n",
        "    </div>\n",
        "\n",
        "    <h3>Interpretación del Teorema</h3>\n",
        "    <p><strong>Grado de entrada total (∑ id(v<sub>i</sub>)):</strong> La suma de los grados de entrada de todos los vértices del grafo es igual al número total de arcos <strong>q</strong>.</p>\n",
        "    <p>Es decir, cada arco que entra en un vértice <strong>v<sub>i</sub></strong> contribuye a su grado de entrada <strong>id(v<sub>i</sub>)</strong>, y la suma de los grados de entrada de todos los vértices debe ser igual a <strong>q</strong>, el número total de arcos en el digrafo.</p>\n",
        "\n",
        "    <p><strong>Grado de salida total (∑ od(v<sub>i</sub>)):</strong> La suma de los grados de salida de todos los vértices también es igual al número total de arcos <strong>q</strong>.</p>\n",
        "    <p>Cada arco que sale de un vértice <strong>v<sub>i</sub></strong> contribuye a su grado de salida <strong>od(v<sub>i</sub>)</strong>, y la suma de los grados de salida de todos los vértices debe ser igual a <strong>q</strong>, el número total de arcos en el digrafo.</p>\n",
        "\n",
        "    <h3>Demostración (Proof)</h3>\n",
        "    <p>Cada arco en un digrafo contribuye exactamente a dos vértices:</p>\n",
        "    <ul>\n",
        "        <li>Al grado de entrada de un vértice: el vértice hacia donde apunta el arco.</li>\n",
        "        <li>Al grado de salida de otro vértice: el vértice desde donde sale el arco.</li>\n",
        "    </ul>\n",
        "    <p>Por lo tanto, cada arco incrementa en 1 tanto el grado de salida de un vértice como el grado de entrada de otro vértice. Como consecuencia:</p>\n",
        "    <p class=\"math\">La suma total de los grados de entrada y salida de todos los vértices es igual al número total de arcos q.</p>\n",
        "\n",
        "    <h3>Ejemplo</h3>\n",
        "    <p>Supongamos que tenemos un digrafo con 4 vértices <strong>V(D) = {a, b, c, d}</strong> y 5 arcos:</p>\n",
        "    <div class=\"math\">\n",
        "        <p>E(D) = {(a, b), (a, c), (b, d), (c, b), (d, a)}</p>\n",
        "    </div>\n",
        "\n",
        "    <h3>Grados de entrada id(v)</h3>\n",
        "    <ul>\n",
        "        <li><strong>id(a) = 1</strong> (el arco (d, a))</li>\n",
        "        <li><strong>id(b) = 2</strong> (los arcos (a, b) y (c, b))</li>\n",
        "        <li><strong>id(c) = 1</strong> (el arco (a, c))</li>\n",
        "        <li><strong>id(d) = 1</strong> (el arco (b, d))</li>\n",
        "    </ul>\n",
        "    <p>Suma de los grados de entrada: <strong>1 + 2 + 1 + 1 = 5</strong>.</p>\n",
        "\n",
        "    <h3>Grados de salida od(v)</h3>\n",
        "    <ul>\n",
        "        <li><strong>od(a) = 2</strong> (los arcos (a, b) y (a, c))</li>\n",
        "        <li><strong>od(b) = 1</strong> (el arco (b, d))</li>\n",
        "        <li><strong>od(c) = 1</strong> (el arco (c, b))</li>\n",
        "        <li><strong>od(d) = 1</strong> (el arco (d, a))</li>\n",
        "    </ul>\n",
        "    <p>Suma de los grados de salida: <strong>2 + 1 + 1 + 1 = 5</strong>.</p>\n",
        "\n",
        "    <p>Tanto la suma de los grados de entrada como la de los grados de salida es <strong>5</strong>, que es igual al número total de arcos en el digrafo (q = 5).</p>\n",
        "\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML en Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "g8nRUTzoSyVo",
        "outputId": "c0bffd2e-8e72-4531-b0af-1bef9ae0a236"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Teorema 10.1: Grafos Dirigidos</title>\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: 'Arial', sans-serif;\n",
              "            line-height: 1.8;\n",
              "            margin: 20px;\n",
              "            padding: 20px;\n",
              "            background-color: #f9f9f9;\n",
              "        }\n",
              "        h1, h2, h3 {\n",
              "            color: #2c3e50;\n",
              "        }\n",
              "        p {\n",
              "            font-size: 1.2em;\n",
              "            margin-bottom: 15px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: square;\n",
              "            margin-left: 30px;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 10px;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "        .math {\n",
              "            background: #f4f4f4;\n",
              "            padding: 10px;\n",
              "            border-radius: 5px;\n",
              "            font-family: 'Cambria Math', serif;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "    <h1>Teorema 10.1: Grafos Dirigidos</h1>\n",
              "    \n",
              "    <p>El <strong>Teorema 10.1</strong> que aparece en la imagen es un resultado fundamental en grafos dirigidos (o digrafos). Este teorema relaciona el número total de arcos en un digrafo con los grados de entrada (<strong>id(v)</strong>) y grados de salida (<strong>od(v)</strong>) de los vértices.</p>\n",
              "    \n",
              "    <h2>Teorema 10.1</h2>\n",
              "    <p>Si <strong>D</strong> es un digrafo con:</p>\n",
              "    <ul>\n",
              "        <li>Conjunto de vértices <strong>V(D) = {v<sub>1</sub>, v<sub>2</sub>, …, v<sub>n</sub>}</strong> (es decir, el digrafo tiene <strong>n</strong> vértices),</li>\n",
              "        <li>Número total de arcos <strong>q</strong> (es decir, las conexiones dirigidas entre vértices),</li>\n",
              "    </ul>\n",
              "    <p>Entonces se cumple que:</p>\n",
              "    <div class=\"math\">\n",
              "        <p>∑<sub>i=1</sub><sup>n</sup> id(v<sub>i</sub>) = q</p>\n",
              "        <p>y</p>\n",
              "        <p>∑<sub>i=1</sub><sup>n</sup> od(v<sub>i</sub>) = q</p>\n",
              "    </div>\n",
              "    \n",
              "    <h3>Interpretación del Teorema</h3>\n",
              "    <p><strong>Grado de entrada total (∑ id(v<sub>i</sub>)):</strong> La suma de los grados de entrada de todos los vértices del grafo es igual al número total de arcos <strong>q</strong>.</p>\n",
              "    <p>Es decir, cada arco que entra en un vértice <strong>v<sub>i</sub></strong> contribuye a su grado de entrada <strong>id(v<sub>i</sub>)</strong>, y la suma de los grados de entrada de todos los vértices debe ser igual a <strong>q</strong>, el número total de arcos en el digrafo.</p>\n",
              "\n",
              "    <p><strong>Grado de salida total (∑ od(v<sub>i</sub>)):</strong> La suma de los grados de salida de todos los vértices también es igual al número total de arcos <strong>q</strong>.</p>\n",
              "    <p>Cada arco que sale de un vértice <strong>v<sub>i</sub></strong> contribuye a su grado de salida <strong>od(v<sub>i</sub>)</strong>, y la suma de los grados de salida de todos los vértices debe ser igual a <strong>q</strong>, el número total de arcos en el digrafo.</p>\n",
              "\n",
              "    <h3>Demostración (Proof)</h3>\n",
              "    <p>Cada arco en un digrafo contribuye exactamente a dos vértices:</p>\n",
              "    <ul>\n",
              "        <li>Al grado de entrada de un vértice: el vértice hacia donde apunta el arco.</li>\n",
              "        <li>Al grado de salida de otro vértice: el vértice desde donde sale el arco.</li>\n",
              "    </ul>\n",
              "    <p>Por lo tanto, cada arco incrementa en 1 tanto el grado de salida de un vértice como el grado de entrada de otro vértice. Como consecuencia:</p>\n",
              "    <p class=\"math\">La suma total de los grados de entrada y salida de todos los vértices es igual al número total de arcos q.</p>\n",
              "\n",
              "    <h3>Ejemplo</h3>\n",
              "    <p>Supongamos que tenemos un digrafo con 4 vértices <strong>V(D) = {a, b, c, d}</strong> y 5 arcos:</p>\n",
              "    <div class=\"math\">\n",
              "        <p>E(D) = {(a, b), (a, c), (b, d), (c, b), (d, a)}</p>\n",
              "    </div>\n",
              "    \n",
              "    <h3>Grados de entrada id(v)</h3>\n",
              "    <ul>\n",
              "        <li><strong>id(a) = 1</strong> (el arco (d, a))</li>\n",
              "        <li><strong>id(b) = 2</strong> (los arcos (a, b) y (c, b))</li>\n",
              "        <li><strong>id(c) = 1</strong> (el arco (a, c))</li>\n",
              "        <li><strong>id(d) = 1</strong> (el arco (b, d))</li>\n",
              "    </ul>\n",
              "    <p>Suma de los grados de entrada: <strong>1 + 2 + 1 + 1 = 5</strong>.</p>\n",
              "    \n",
              "    <h3>Grados de salida od(v)</h3>\n",
              "    <ul>\n",
              "        <li><strong>od(a) = 2</strong> (los arcos (a, b) y (a, c))</li>\n",
              "        <li><strong>od(b) = 1</strong> (el arco (b, d))</li>\n",
              "        <li><strong>od(c) = 1</strong> (el arco (c, b))</li>\n",
              "        <li><strong>od(d) = 1</strong> (el arco (d, a))</li>\n",
              "    </ul>\n",
              "    <p>Suma de los grados de salida: <strong>2 + 1 + 1 + 1 = 5</strong>.</p>\n",
              "\n",
              "    <p>Tanto la suma de los grados de entrada como la de los grados de salida es <strong>5</strong>, que es igual al número total de arcos en el digrafo (q = 5).</p>\n",
              "\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Función para crear un digrafo y verificar el Teorema 10.1\n",
        "def verificar_teorema_10_1(arcos):\n",
        "    # Crear el digrafo\n",
        "    D = nx.DiGraph()\n",
        "\n",
        "    # Añadir arcos al grafo\n",
        "    D.add_edges_from(arcos)\n",
        "\n",
        "    # Calcular grados de entrada y salida\n",
        "    grados_entrada = [D.in_degree(v) for v in D.nodes()]\n",
        "    grados_salida = [D.out_degree(v) for v in D.nodes()]\n",
        "\n",
        "    # Calcular el número total de arcos\n",
        "    q = D.number_of_edges()\n",
        "\n",
        "    # Verificar el teorema\n",
        "    suma_grados_entrada = sum(grados_entrada)\n",
        "    suma_grados_salida = sum(grados_salida)\n",
        "\n",
        "    print(\"Suma de los grados de entrada:\", suma_grados_entrada)\n",
        "    print(\"Suma de los grados de salida:\", suma_grados_salida)\n",
        "    print(\"Número total de arcos (q):\", q)\n",
        "\n",
        "    # Verificar si se cumple el teorema\n",
        "    if suma_grados_entrada == q and suma_grados_salida == q:\n",
        "        print(\"Teorema 10.1 verificado: La suma de grados de entrada y salida es igual al número de arcos.\")\n",
        "    else:\n",
        "        print(\"El teorema 10.1 no se cumple.\")\n",
        "\n",
        "    # Dibujar el grafo\n",
        "    pos = nx.spring_layout(D)\n",
        "    nx.draw(D, pos, with_labels=True, node_size=2000, node_color='lightblue', font_size=16, arrows=True)\n",
        "    plt.show()\n",
        "\n",
        "# Ejemplo 1: Grafo dirigido pequeño\n",
        "arcos_ejemplo_1 = [('a', 'b'), ('b', 'c'), ('c', 'a')]\n",
        "print(\"Ejemplo 1:\")\n",
        "verificar_teorema_10_1(arcos_ejemplo_1)\n",
        "\n",
        "# Ejemplo 2: Grafo dirigido más grande\n",
        "arcos_ejemplo_2 = [('a', 'b'), ('a', 'c'), ('b', 'd'), ('c', 'd')]\n",
        "print(\"\\nEjemplo 2:\")\n",
        "verificar_teorema_10_1(arcos_ejemplo_2)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "BFGr8C69TBCQ",
        "outputId": "17cc2ba0-6df0-412a-8888-3097512c6d2a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Ejemplo 1:\n",
            "Suma de los grados de entrada: 3\n",
            "Suma de los grados de salida: 3\n",
            "Número total de arcos (q): 3\n",
            "Teorema 10.1 verificado: La suma de grados de entrada y salida es igual al número de arcos.\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Ejemplo 2:\n",
            "Suma de los grados de entrada: 4\n",
            "Suma de los grados de salida: 4\n",
            "Número total de arcos (q): 4\n",
            "Teorema 10.1 verificado: La suma de grados de entrada y salida es igual al número de arcos.\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import display, HTML\n",
        "\n",
        "# Contenido HTML con definiciones\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Definiciones de Grafos Dirigidos</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: 'Arial', sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1, h2, h3 {\n",
        "            color: #2c3e50;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: square;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        .example {\n",
        "            color: #2980b9;\n",
        "            font-weight: bold;\n",
        "        }\n",
        "        .section {\n",
        "            margin-bottom: 40px;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "    <h1>Definiciones</h1>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Débilmente conectado (Weakly Connected)</h2>\n",
        "        <p>Un grafo dirigido es débilmente conectado si, al ignorar las direcciones de los arcos, existe un camino entre cualquier par de vértices. Es decir, si tratamos todas las aristas como no dirigidas, todos los vértices estarían conectados por algún camino. En un grafo débilmente conectado, puede que no haya caminos dirigidos en ambas direcciones entre ciertos pares de vértices, pero sin tener en cuenta las direcciones, los vértices están conectados.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Unilateral</h2>\n",
        "        <p>Un grafo dirigido es unilateral si, para cada par de vértices <strong>u</strong> y <strong>v</strong>, existe un camino dirigido en una de las dos direcciones, es decir, de <strong>u</strong> a <strong>v</strong> o de <strong>v</strong> a <strong>u</strong>, pero no necesariamente en ambas. Esto implica que siempre hay una conexión en una dirección entre los vértices, aunque puede no haber una ruta de regreso.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Fuertemente conectado (Strongly Connected)</h2>\n",
        "        <p>Un grafo dirigido es fuertemente conectado si, para cada par de vértices <strong>u</strong> y <strong>v</strong>, existe un camino dirigido en ambas direcciones: tanto de <strong>u</strong> a <strong>v</strong> como de <strong>v</strong> a <strong>u</strong>. En un grafo fuertemente conectado, siempre es posible viajar entre cualquier par de vértices y regresar al punto de origen.</p>\n",
        "    </div>\n",
        "\n",
        "    <h2>Aplicaciones</h2>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h3>1. Débilmente conectado</h3>\n",
        "        <ul>\n",
        "            <li><span class=\"example\">Redes de telecomunicaciones:</span> Imagina una red de telecomunicaciones en la que la dirección de los datos importa (por ejemplo, ciertos servidores solo envían datos y otros solo los reciben). Si ignoramos la dirección de la comunicación (como si todos los nodos pudieran intercambiar datos en ambas direcciones), la red podría estar débilmente conectada.</li>\n",
        "            <li><span class=\"example\">Redes sociales:</span> En una red social dirigida como Twitter, si ignoramos las relaciones de seguimiento (quién sigue a quién), los usuarios pueden estar conectados de alguna manera. Esto haría que la red sea débilmente conectada.</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h3>2. Unilateral</h3>\n",
        "        <ul>\n",
        "            <li><span class=\"example\">Sistemas de transporte:</span> En un sistema de transporte, una red podría ser unilateral si hay rutas en una sola dirección entre ciertos puntos, pero no en ambas direcciones.</li>\n",
        "            <li><span class=\"example\">Redes de comunicación:</span> En un sistema de correo electrónico, una red de servidores puede ser unilateral si puedes enviar correos a ciertas direcciones, pero esas direcciones no pueden enviarte correos de vuelta.</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h3>3. Fuertemente conectado</h3>\n",
        "        <ul>\n",
        "            <li><span class=\"example\">Internet y redes de datos:</span> Una red de datos es fuertemente conectada si cualquier dispositivo puede comunicarse con cualquier otro dispositivo y, además, puede recibir una respuesta. Esto es crucial en redes descentralizadas o en mallas de comunicación.</li>\n",
        "            <li><span class=\"example\">Sistemas de transporte público:</span> En una ciudad con un sistema de transporte fuertemente conectado, podrías viajar desde cualquier punto a cualquier otro y también regresar sin problemas.</li>\n",
        "            <li><span class=\"example\">Cadenas de suministro:</span> En una cadena de suministro bien organizada, todos los puntos de la red pueden enviar y recibir productos entre sí, garantizando un flujo constante en ambas direcciones.</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <h2>Resumen de Aplicaciones</h2>\n",
        "    <ul>\n",
        "        <li><strong>Débilmente conectado:</strong> Útil en sistemas donde la conectividad física es suficiente para garantizar la comunicación, pero la dirección no es siempre relevante (ej. redes de telecomunicaciones o redes sociales cuando ignoras las direcciones).</li>\n",
        "        <li><strong>Unilateral:</strong> Útil en situaciones donde es posible que haya rutas unidireccionales (ej. sistemas de transporte o redes de comunicación donde la comunicación fluye en una sola dirección).</li>\n",
        "        <li><strong>Fuertemente conectado:</strong> Es crucial en sistemas donde la bidireccionalidad es clave para el funcionamiento (ej. redes de datos, sistemas de transporte público, o cadenas de suministro).</li>\n",
        "    </ul>\n",
        "\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML en Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "vlT6ve8AWlUJ",
        "outputId": "f912dc48-93dd-4157-a976-98113fef6f2a"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Definiciones de Grafos Dirigidos</title>\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: 'Arial', sans-serif;\n",
              "            line-height: 1.8;\n",
              "            margin: 20px;\n",
              "            padding: 20px;\n",
              "            background-color: #f9f9f9;\n",
              "        }\n",
              "        h1, h2, h3 {\n",
              "            color: #2c3e50;\n",
              "        }\n",
              "        p {\n",
              "            font-size: 1.2em;\n",
              "            margin-bottom: 15px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: square;\n",
              "            margin-left: 30px;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 10px;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "        .example {\n",
              "            color: #2980b9;\n",
              "            font-weight: bold;\n",
              "        }\n",
              "        .section {\n",
              "            margin-bottom: 40px;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "    <h1>Definiciones</h1>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>Débilmente conectado (Weakly Connected)</h2>\n",
              "        <p>Un grafo dirigido es débilmente conectado si, al ignorar las direcciones de los arcos, existe un camino entre cualquier par de vértices. Es decir, si tratamos todas las aristas como no dirigidas, todos los vértices estarían conectados por algún camino. En un grafo débilmente conectado, puede que no haya caminos dirigidos en ambas direcciones entre ciertos pares de vértices, pero sin tener en cuenta las direcciones, los vértices están conectados.</p>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>Unilateral</h2>\n",
              "        <p>Un grafo dirigido es unilateral si, para cada par de vértices <strong>u</strong> y <strong>v</strong>, existe un camino dirigido en una de las dos direcciones, es decir, de <strong>u</strong> a <strong>v</strong> o de <strong>v</strong> a <strong>u</strong>, pero no necesariamente en ambas. Esto implica que siempre hay una conexión en una dirección entre los vértices, aunque puede no haber una ruta de regreso.</p>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>Fuertemente conectado (Strongly Connected)</h2>\n",
              "        <p>Un grafo dirigido es fuertemente conectado si, para cada par de vértices <strong>u</strong> y <strong>v</strong>, existe un camino dirigido en ambas direcciones: tanto de <strong>u</strong> a <strong>v</strong> como de <strong>v</strong> a <strong>u</strong>. En un grafo fuertemente conectado, siempre es posible viajar entre cualquier par de vértices y regresar al punto de origen.</p>\n",
              "    </div>\n",
              "\n",
              "    <h2>Aplicaciones</h2>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h3>1. Débilmente conectado</h3>\n",
              "        <ul>\n",
              "            <li><span class=\"example\">Redes de telecomunicaciones:</span> Imagina una red de telecomunicaciones en la que la dirección de los datos importa (por ejemplo, ciertos servidores solo envían datos y otros solo los reciben). Si ignoramos la dirección de la comunicación (como si todos los nodos pudieran intercambiar datos en ambas direcciones), la red podría estar débilmente conectada.</li>\n",
              "            <li><span class=\"example\">Redes sociales:</span> En una red social dirigida como Twitter, si ignoramos las relaciones de seguimiento (quién sigue a quién), los usuarios pueden estar conectados de alguna manera. Esto haría que la red sea débilmente conectada.</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h3>2. Unilateral</h3>\n",
              "        <ul>\n",
              "            <li><span class=\"example\">Sistemas de transporte:</span> En un sistema de transporte, una red podría ser unilateral si hay rutas en una sola dirección entre ciertos puntos, pero no en ambas direcciones.</li>\n",
              "            <li><span class=\"example\">Redes de comunicación:</span> En un sistema de correo electrónico, una red de servidores puede ser unilateral si puedes enviar correos a ciertas direcciones, pero esas direcciones no pueden enviarte correos de vuelta.</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h3>3. Fuertemente conectado</h3>\n",
              "        <ul>\n",
              "            <li><span class=\"example\">Internet y redes de datos:</span> Una red de datos es fuertemente conectada si cualquier dispositivo puede comunicarse con cualquier otro dispositivo y, además, puede recibir una respuesta. Esto es crucial en redes descentralizadas o en mallas de comunicación.</li>\n",
              "            <li><span class=\"example\">Sistemas de transporte público:</span> En una ciudad con un sistema de transporte fuertemente conectado, podrías viajar desde cualquier punto a cualquier otro y también regresar sin problemas.</li>\n",
              "            <li><span class=\"example\">Cadenas de suministro:</span> En una cadena de suministro bien organizada, todos los puntos de la red pueden enviar y recibir productos entre sí, garantizando un flujo constante en ambas direcciones.</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "\n",
              "    <h2>Resumen de Aplicaciones</h2>\n",
              "    <ul>\n",
              "        <li><strong>Débilmente conectado:</strong> Útil en sistemas donde la conectividad física es suficiente para garantizar la comunicación, pero la dirección no es siempre relevante (ej. redes de telecomunicaciones o redes sociales cuando ignoras las direcciones).</li>\n",
              "        <li><strong>Unilateral:</strong> Útil en situaciones donde es posible que haya rutas unidireccionales (ej. sistemas de transporte o redes de comunicación donde la comunicación fluye en una sola dirección).</li>\n",
              "        <li><strong>Fuertemente conectado:</strong> Es crucial en sistemas donde la bidireccionalidad es clave para el funcionamiento (ej. redes de datos, sistemas de transporte público, o cadenas de suministro).</li>\n",
              "    </ul>\n",
              "\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import display, HTML\n",
        "\n",
        "# Contenido HTML traducido\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Problema de Orientación Fuertemente Conectada</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: 'Arial', sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1, h2 {\n",
        "            color: #2c3e50;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: square;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        .example {\n",
        "            color: #2980b9;\n",
        "            font-weight: bold;\n",
        "        }\n",
        "        .section {\n",
        "            margin-bottom: 40px;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "    <h1>Problema de Orientación Fuertemente Conectada</h1>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Definición</h2>\n",
        "        <p>El problema de orientación fuertemente conectada consiste en encontrar una orientación (dirección) de las aristas de un grafo tal que el grafo dirigido resultante sea fuertemente conectado. Esto significa que, para cada par de vértices <strong>u</strong> y <strong>v</strong>, debe existir un camino dirigido de <strong>u</strong> a <strong>v</strong> y un camino dirigido de <strong>v</strong> a <strong>u</strong>.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Aplicación Práctica</h2>\n",
        "        <ul>\n",
        "            <li><span class=\"example\">Gestión del tráfico urbano:</span> En sistemas de tráfico urbano, donde las calles se hacen de un solo sentido, el objetivo es asegurarse de que cada punto de la ciudad pueda alcanzarse desde cualquier otro punto, y también sea posible regresar sin desvíos innecesarios.</li>\n",
        "            <li><span class=\"example\">Redes de telecomunicaciones:</span> En redes de telecomunicaciones, se busca garantizar que la información pueda fluir en ambas direcciones entre cualquier par de nodos, incluso si los caminos son dirigidos.</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <p>Esta optimización es especialmente útil para optimizar sistemas que dependen de conexiones dirigidas (como las calles de un solo sentido en las ciudades), garantizando que todavía exista accesibilidad bidireccional en términos de flujo o movimiento.</p>\n",
        "\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML en Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 551
        },
        "id": "4zF9oGWkdqHJ",
        "outputId": "0930ccd7-6cc7-432a-ff5b-b7d48f13c01c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Problema de Orientación Fuertemente Conectada</title>\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: 'Arial', sans-serif;\n",
              "            line-height: 1.8;\n",
              "            margin: 20px;\n",
              "            padding: 20px;\n",
              "            background-color: #f9f9f9;\n",
              "        }\n",
              "        h1, h2 {\n",
              "            color: #2c3e50;\n",
              "        }\n",
              "        p {\n",
              "            font-size: 1.2em;\n",
              "            margin-bottom: 15px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: square;\n",
              "            margin-left: 30px;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 10px;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "        .example {\n",
              "            color: #2980b9;\n",
              "            font-weight: bold;\n",
              "        }\n",
              "        .section {\n",
              "            margin-bottom: 40px;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "    <h1>Problema de Orientación Fuertemente Conectada</h1>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>Definición</h2>\n",
              "        <p>El problema de orientación fuertemente conectada consiste en encontrar una orientación (dirección) de las aristas de un grafo tal que el grafo dirigido resultante sea fuertemente conectado. Esto significa que, para cada par de vértices <strong>u</strong> y <strong>v</strong>, debe existir un camino dirigido de <strong>u</strong> a <strong>v</strong> y un camino dirigido de <strong>v</strong> a <strong>u</strong>.</p>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>Aplicación Práctica</h2>\n",
              "        <ul>\n",
              "            <li><span class=\"example\">Gestión del tráfico urbano:</span> En sistemas de tráfico urbano, donde las calles se hacen de un solo sentido, el objetivo es asegurarse de que cada punto de la ciudad pueda alcanzarse desde cualquier otro punto, y también sea posible regresar sin desvíos innecesarios.</li>\n",
              "            <li><span class=\"example\">Redes de telecomunicaciones:</span> En redes de telecomunicaciones, se busca garantizar que la información pueda fluir en ambas direcciones entre cualquier par de nodos, incluso si los caminos son dirigidos.</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "\n",
              "    <p>Esta optimización es especialmente útil para optimizar sistemas que dependen de conexiones dirigidas (como las calles de un solo sentido en las ciudades), garantizando que todavía exista accesibilidad bidireccional en términos de flujo o movimiento.</p>\n",
              "\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import files\n",
        "uploaded = files.upload()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 73
        },
        "outputId": "8f2ba1e3-7285-4642-f410-c1b07e6c1631",
        "id": "2_wqGcxIY8YE"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-b290f5ba-2fa7-4153-bc83-68948b0b3833\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-b290f5ba-2fa7-4153-bc83-68948b0b3833\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script>// Copyright 2017 Google LLC\n",
              "//\n",
              "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
              "// you may not use this file except in compliance with the License.\n",
              "// You may obtain a copy of the License at\n",
              "//\n",
              "//      http://www.apache.org/licenses/LICENSE-2.0\n",
              "//\n",
              "// Unless required by applicable law or agreed to in writing, software\n",
              "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
              "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
              "// See the License for the specific language governing permissions and\n",
              "// limitations under the License.\n",
              "\n",
              "/**\n",
              " * @fileoverview Helpers for google.colab Python module.\n",
              " */\n",
              "(function(scope) {\n",
              "function span(text, styleAttributes = {}) {\n",
              "  const element = document.createElement('span');\n",
              "  element.textContent = text;\n",
              "  for (const key of Object.keys(styleAttributes)) {\n",
              "    element.style[key] = styleAttributes[key];\n",
              "  }\n",
              "  return element;\n",
              "}\n",
              "\n",
              "// Max number of bytes which will be uploaded at a time.\n",
              "const MAX_PAYLOAD_SIZE = 100 * 1024;\n",
              "\n",
              "function _uploadFiles(inputId, outputId) {\n",
              "  const steps = uploadFilesStep(inputId, outputId);\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  // Cache steps on the outputElement to make it available for the next call\n",
              "  // to uploadFilesContinue from Python.\n",
              "  outputElement.steps = steps;\n",
              "\n",
              "  return _uploadFilesContinue(outputId);\n",
              "}\n",
              "\n",
              "// This is roughly an async generator (not supported in the browser yet),\n",
              "// where there are multiple asynchronous steps and the Python side is going\n",
              "// to poll for completion of each step.\n",
              "// This uses a Promise to block the python side on completion of each step,\n",
              "// then passes the result of the previous step as the input to the next step.\n",
              "function _uploadFilesContinue(outputId) {\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  const steps = outputElement.steps;\n",
              "\n",
              "  const next = steps.next(outputElement.lastPromiseValue);\n",
              "  return Promise.resolve(next.value.promise).then((value) => {\n",
              "    // Cache the last promise value to make it available to the next\n",
              "    // step of the generator.\n",
              "    outputElement.lastPromiseValue = value;\n",
              "    return next.value.response;\n",
              "  });\n",
              "}\n",
              "\n",
              "/**\n",
              " * Generator function which is called between each async step of the upload\n",
              " * process.\n",
              " * @param {string} inputId Element ID of the input file picker element.\n",
              " * @param {string} outputId Element ID of the output display.\n",
              " * @return {!Iterable<!Object>} Iterable of next steps.\n",
              " */\n",
              "function* uploadFilesStep(inputId, outputId) {\n",
              "  const inputElement = document.getElementById(inputId);\n",
              "  inputElement.disabled = false;\n",
              "\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  outputElement.innerHTML = '';\n",
              "\n",
              "  const pickedPromise = new Promise((resolve) => {\n",
              "    inputElement.addEventListener('change', (e) => {\n",
              "      resolve(e.target.files);\n",
              "    });\n",
              "  });\n",
              "\n",
              "  const cancel = document.createElement('button');\n",
              "  inputElement.parentElement.appendChild(cancel);\n",
              "  cancel.textContent = 'Cancel upload';\n",
              "  const cancelPromise = new Promise((resolve) => {\n",
              "    cancel.onclick = () => {\n",
              "      resolve(null);\n",
              "    };\n",
              "  });\n",
              "\n",
              "  // Wait for the user to pick the files.\n",
              "  const files = yield {\n",
              "    promise: Promise.race([pickedPromise, cancelPromise]),\n",
              "    response: {\n",
              "      action: 'starting',\n",
              "    }\n",
              "  };\n",
              "\n",
              "  cancel.remove();\n",
              "\n",
              "  // Disable the input element since further picks are not allowed.\n",
              "  inputElement.disabled = true;\n",
              "\n",
              "  if (!files) {\n",
              "    return {\n",
              "      response: {\n",
              "        action: 'complete',\n",
              "      }\n",
              "    };\n",
              "  }\n",
              "\n",
              "  for (const file of files) {\n",
              "    const li = document.createElement('li');\n",
              "    li.append(span(file.name, {fontWeight: 'bold'}));\n",
              "    li.append(span(\n",
              "        `(${file.type || 'n/a'}) - ${file.size} bytes, ` +\n",
              "        `last modified: ${\n",
              "            file.lastModifiedDate ? file.lastModifiedDate.toLocaleDateString() :\n",
              "                                    'n/a'} - `));\n",
              "    const percent = span('0% done');\n",
              "    li.appendChild(percent);\n",
              "\n",
              "    outputElement.appendChild(li);\n",
              "\n",
              "    const fileDataPromise = new Promise((resolve) => {\n",
              "      const reader = new FileReader();\n",
              "      reader.onload = (e) => {\n",
              "        resolve(e.target.result);\n",
              "      };\n",
              "      reader.readAsArrayBuffer(file);\n",
              "    });\n",
              "    // Wait for the data to be ready.\n",
              "    let fileData = yield {\n",
              "      promise: fileDataPromise,\n",
              "      response: {\n",
              "        action: 'continue',\n",
              "      }\n",
              "    };\n",
              "\n",
              "    // Use a chunked sending to avoid message size limits. See b/62115660.\n",
              "    let position = 0;\n",
              "    do {\n",
              "      const length = Math.min(fileData.byteLength - position, MAX_PAYLOAD_SIZE);\n",
              "      const chunk = new Uint8Array(fileData, position, length);\n",
              "      position += length;\n",
              "\n",
              "      const base64 = btoa(String.fromCharCode.apply(null, chunk));\n",
              "      yield {\n",
              "        response: {\n",
              "          action: 'append',\n",
              "          file: file.name,\n",
              "          data: base64,\n",
              "        },\n",
              "      };\n",
              "\n",
              "      let percentDone = fileData.byteLength === 0 ?\n",
              "          100 :\n",
              "          Math.round((position / fileData.byteLength) * 100);\n",
              "      percent.textContent = `${percentDone}% done`;\n",
              "\n",
              "    } while (position < fileData.byteLength);\n",
              "  }\n",
              "\n",
              "  // All done.\n",
              "  yield {\n",
              "    response: {\n",
              "      action: 'complete',\n",
              "    }\n",
              "  };\n",
              "}\n",
              "\n",
              "scope.google = scope.google || {};\n",
              "scope.google.colab = scope.google.colab || {};\n",
              "scope.google.colab._files = {\n",
              "  _uploadFiles,\n",
              "  _uploadFilesContinue,\n",
              "};\n",
              "})(self);\n",
              "</script> "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving conectividad.png to conectividad (1).png\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.image as mpimg\n",
        "\n",
        "# Cargar y mostrar la imagen\n",
        "img = mpimg.imread('conectividad.png')\n",
        "imgplot = plt.imshow(img)\n",
        "plt.axis('off')  # Para ocultar los ejes\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 213
        },
        "outputId": "b86b1248-539c-40cd-d375-d96eb3a46ea1",
        "id": "1yaHzw0dZQac"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import display, HTML\n",
        "\n",
        "# Contenido HTML con la explicación del Teorema de Robbins\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Teorema de Robbins: Orientación Fuerte de Grafos Conectados</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: 'Arial', sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1, h2, h3 {\n",
        "            color: #2c3e50;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: square;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        .example {\n",
        "            color: #2980b9;\n",
        "            font-weight: bold;\n",
        "        }\n",
        "        .section {\n",
        "            margin-bottom: 40px;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "    <h1>Teorema de Robbins (Teorema 10.2): Orientación Fuerte de Grafos Conectados</h1>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Enunciado del Teorema</h2>\n",
        "        <p>Un grafo no dirigido <strong>conectado</strong> (G) puede ser orientado de manera que el grafo resultante sea <strong>fuertemente conectado</strong> si y solo si (G) <strong>no tiene puentes</strong>.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Explicación de los términos</h2>\n",
        "        <ul>\n",
        "            <li><strong>Grafo conectado:</strong> Un grafo no dirigido es <strong>conectado</strong> si hay un camino entre cualquier par de vértices.</li>\n",
        "            <li><strong>Puente (Bridge):</strong> Un <strong>puente</strong> es una arista cuya eliminación desconecta el grafo en dos componentes. Es una arista esencial para mantener la conectividad entre dos partes del grafo.</li>\n",
        "            <li><strong>Orientación fuerte:</strong> En un <strong>grafo dirigido</strong>, un grafo es <strong>fuertemente conectado</strong> si existe un camino dirigido en ambas direcciones entre cualquier par de vértices (u) y (v).</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Intuición detrás del Teorema</h2>\n",
        "        <p>Los <strong>puentes</strong> en un grafo no permiten una <strong>orientación fuerte</strong>. Si una arista es un puente, entonces es el único camino que conecta dos subconjuntos del grafo. Si orientas esta arista en una dirección, no habrá forma de viajar en la dirección opuesta, lo que impide que el grafo sea fuertemente conectado.</p>\n",
        "        <p>Por otro lado, si un grafo <strong>no tiene puentes</strong>, todas las aristas están contenidas en <strong>ciclos</strong>, lo que garantiza que haya caminos alternativos entre los vértices.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Aplicación del Teorema</h2>\n",
        "        <ul>\n",
        "            <li><span class=\"example\">Redes de tráfico:</span> Organizar calles de una ciudad de modo que siempre puedas viajar de un punto a otro y regresar sin desvíos innecesarios.</li>\n",
        "            <li><span class=\"example\">Redes de telecomunicaciones:</span> Asegurar que la información fluya en ambas direcciones entre todos los nodos.</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Ejemplo</h2>\n",
        "        <p>Imagina un grafo no dirigido en forma de cuadrado:</p>\n",
        "        <pre>\n",
        "        A --- B\n",
        "        |     |\n",
        "        C --- D\n",
        "        </pre>\n",
        "        <p>Este grafo no tiene puentes y es posible orientarlo de tal forma que el grafo resultante sea <strong>fuertemente conectado</strong>.</p>\n",
        "        <p>Por ejemplo, podrías orientar las aristas así: <strong>(A → B)</strong>, <strong>(B → D)</strong>, <strong>(D → C)</strong>, <strong>(C → A)</strong>.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Conclusión</h2>\n",
        "        <p>El <strong>Teorema de Robbins</strong> nos dice que para lograr una <strong>orientación fuerte</strong> de un grafo no dirigido, es crucial que el grafo <strong>no tenga puentes</strong>. Si un grafo no tiene puentes, podemos orientarlo de manera que sea <strong>fuertemente conectado</strong>.</p>\n",
        "    </div>\n",
        "\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML en Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "H50O_N6elVxH",
        "outputId": "ba107a53-6581-49cf-bcaf-b9ea124745d2"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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              "\n",
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              "    <title>Teorema de Robbins: Orientación Fuerte de Grafos Conectados</title>\n",
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              "</head>\n",
              "<body>\n",
              "    <h1>Teorema de Robbins (Teorema 10.2): Orientación Fuerte de Grafos Conectados</h1>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>Enunciado del Teorema</h2>\n",
              "        <p>Un grafo no dirigido <strong>conectado</strong> (G) puede ser orientado de manera que el grafo resultante sea <strong>fuertemente conectado</strong> si y solo si (G) <strong>no tiene puentes</strong>.</p>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>Explicación de los términos</h2>\n",
              "        <ul>\n",
              "            <li><strong>Grafo conectado:</strong> Un grafo no dirigido es <strong>conectado</strong> si hay un camino entre cualquier par de vértices.</li>\n",
              "            <li><strong>Puente (Bridge):</strong> Un <strong>puente</strong> es una arista cuya eliminación desconecta el grafo en dos componentes. Es una arista esencial para mantener la conectividad entre dos partes del grafo.</li>\n",
              "            <li><strong>Orientación fuerte:</strong> En un <strong>grafo dirigido</strong>, un grafo es <strong>fuertemente conectado</strong> si existe un camino dirigido en ambas direcciones entre cualquier par de vértices (u) y (v).</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>Intuición detrás del Teorema</h2>\n",
              "        <p>Los <strong>puentes</strong> en un grafo no permiten una <strong>orientación fuerte</strong>. Si una arista es un puente, entonces es el único camino que conecta dos subconjuntos del grafo. Si orientas esta arista en una dirección, no habrá forma de viajar en la dirección opuesta, lo que impide que el grafo sea fuertemente conectado.</p>\n",
              "        <p>Por otro lado, si un grafo <strong>no tiene puentes</strong>, todas las aristas están contenidas en <strong>ciclos</strong>, lo que garantiza que haya caminos alternativos entre los vértices.</p>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>Aplicación del Teorema</h2>\n",
              "        <ul>\n",
              "            <li><span class=\"example\">Redes de tráfico:</span> Organizar calles de una ciudad de modo que siempre puedas viajar de un punto a otro y regresar sin desvíos innecesarios.</li>\n",
              "            <li><span class=\"example\">Redes de telecomunicaciones:</span> Asegurar que la información fluya en ambas direcciones entre todos los nodos.</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>Ejemplo</h2>\n",
              "        <p>Imagina un grafo no dirigido en forma de cuadrado:</p>\n",
              "        <pre>\n",
              "        A --- B\n",
              "        |     |\n",
              "        C --- D\n",
              "        </pre>\n",
              "        <p>Este grafo no tiene puentes y es posible orientarlo de tal forma que el grafo resultante sea <strong>fuertemente conectado</strong>.</p>\n",
              "        <p>Por ejemplo, podrías orientar las aristas así: <strong>(A → B)</strong>, <strong>(B → D)</strong>, <strong>(D → C)</strong>, <strong>(C → A)</strong>.</p>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>Conclusión</h2>\n",
              "        <p>El <strong>Teorema de Robbins</strong> nos dice que para lograr una <strong>orientación fuerte</strong> de un grafo no dirigido, es crucial que el grafo <strong>no tenga puentes</strong>. Si un grafo no tiene puentes, podemos orientarlo de manera que sea <strong>fuertemente conectado</strong>.</p>\n",
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    },
    {
      "cell_type": "code",
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def es_fuertemente_conectado(grafo):\n",
        "    \"\"\" Verifica si el grafo dirigido es fuertemente conectado \"\"\"\n",
        "    return nx.is_strongly_connected(grafo)\n",
        "\n",
        "def tiene_puentes(grafo):\n",
        "    \"\"\" Verifica si el grafo no dirigido tiene puentes \"\"\"\n",
        "    return len(list(nx.bridges(grafo))) > 0\n",
        "\n",
        "def orientar_grafo(grafo):\n",
        "    \"\"\" Orienta un grafo no dirigido sin puentes para hacerlo fuertemente conectado \"\"\"\n",
        "    if tiene_puentes(grafo):\n",
        "        print(\"El grafo tiene puentes, no puede ser orientado para ser fuertemente conectado.\")\n",
        "        return None\n",
        "\n",
        "    # Convertir el grafo no dirigido en un grafo dirigido usando DFS\n",
        "    dirigido = nx.DiGraph()\n",
        "\n",
        "    # Realizamos DFS y orientamos las aristas\n",
        "    dfs_edges = list(nx.dfs_edges(grafo))\n",
        "    dirigido.add_edges_from(dfs_edges)  # Orientamos hacia los nodos alcanzados en el DFS\n",
        "\n",
        "    # Ahora orientamos las aristas restantes\n",
        "    for u, v in grafo.edges():\n",
        "        if not dirigido.has_edge(u, v) and not dirigido.has_edge(v, u):\n",
        "            # Orientamos las aristas que no están en el DFS, hacia el nodo con menor número\n",
        "            if u < v:\n",
        "                dirigido.add_edge(v, u)\n",
        "            else:\n",
        "                dirigido.add_edge(u, v)\n",
        "\n",
        "    return dirigido\n",
        "\n",
        "def dibujar_grafo(grafo, titulo):\n",
        "    \"\"\" Dibuja el grafo con etiquetas y direcciones de las aristas \"\"\"\n",
        "    pos = nx.spring_layout(grafo)\n",
        "    plt.figure(figsize=(8, 6))\n",
        "    nx.draw(grafo, pos, with_labels=True, node_color='lightblue', node_size=2000, font_size=16, font_weight='bold', arrows=True)\n",
        "    edge_labels = {(u, v): f\"{u}->{v}\" for u, v in grafo.edges()}\n",
        "    nx.draw_networkx_edge_labels(grafo, pos, edge_labels=edge_labels)\n",
        "    plt.title(titulo)\n",
        "    plt.show()\n",
        "\n",
        "# Ejemplo 1: Grafo sin puentes\n",
        "grafo1 = nx.Graph()\n",
        "grafo1.add_edges_from([(1, 2), (2, 3), (3, 4), (4, 1), (2, 4)])\n",
        "\n",
        "# Verificar si tiene puentes\n",
        "print(\"Ejemplo 1: Grafo sin puentes\")\n",
        "if tiene_puentes(grafo1):\n",
        "    print(\"El grafo tiene puentes.\")\n",
        "else:\n",
        "    print(\"El grafo no tiene puentes.\")\n",
        "    # Orientar el grafo\n",
        "    grafo_orientado1 = orientar_grafo(grafo1)\n",
        "    if grafo_orientado1:\n",
        "        dibujar_grafo(grafo_orientado1, \"Grafo orientado (fuertemente conectado)\")\n",
        "\n",
        "# Ejemplo 2: Grafo con un puente\n",
        "grafo2 = nx.Graph()\n",
        "grafo2.add_edges_from([(1, 2), (2, 3), (3, 4), (4, 5)])  # El borde (4, 5) es un puente\n",
        "\n",
        "print(\"\\nEjemplo 2: Grafo con puente\")\n",
        "if tiene_puentes(grafo2):\n",
        "    print(\"El grafo tiene puentes.\")\n",
        "else:\n",
        "    print(\"El grafo no tiene puentes.\")\n",
        "    # Orientar el grafo\n",
        "    grafo_orientado2 = orientar_grafo(grafo2)\n",
        "    if grafo_orientado2:\n",
        "        dibujar_grafo(grafo_orientado2, \"Grafo orientado (fuertemente conectado)\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 751
        },
        "id": "rJ524S7Vkx7A",
        "outputId": "f3e2a886-bc86-4991-918a-1154f6cefefd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Ejemplo 1: Grafo sin puentes\n",
            "El grafo no tiene puentes.\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x600 with 1 Axes>"
            ],
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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Ejemplo 2: Grafo con puente\n",
            "El grafo tiene puentes.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import display, HTML\n",
        "\n",
        "# Contenido HTML para Google Colab\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Grafos Dirigidos Acíclicos y Órdenes Parciales</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: 'Arial', sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1, h2, h3 {\n",
        "            color: #2c3e50;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: square;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        .example {\n",
        "            color: #2980b9;\n",
        "            font-weight: bold;\n",
        "        }\n",
        "        .section {\n",
        "            margin-bottom: 40px;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "    <h1>Grafos Dirigidos Acíclicos (DAGs) y Órdenes Parciales</h1>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>1. Grafos Dirigidos Acíclicos (DAGs)</h2>\n",
        "        <p>Un grafo dirigido acíclico, también conocido como <strong>DAG</strong> (por sus siglas en inglés, Directed Acyclic Graph), es un grafo dirigido que no contiene ciclos dirigidos.</p>\n",
        "\n",
        "        <h3>Definiciones Técnicas:</h3>\n",
        "        <ul>\n",
        "            <li><strong>Grafo dirigido (digrafo):</strong> Un grafo donde las aristas tienen una dirección. Si hay una arista entre dos vértices (u) y (v), se representa como (u → v), indicando que la conexión va de (u) hacia (v).</li>\n",
        "            <li><strong>Ciclo dirigido:</strong> Un ciclo dirigido ocurre cuando puedes empezar en un vértice, seguir una secuencia de aristas dirigidas, y regresar al mismo vértice sin repetir ninguna arista.</li>\n",
        "            <li><strong>Acíclico:</strong> Un grafo dirigido es acíclico si no contiene ciclos dirigidos.</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Ejemplo de un Grafo Dirigido Acíclico</h2>\n",
        "        <p>Imagina un grafo con los siguientes vértices y aristas:</p>\n",
        "        <pre>\n",
        "        Vértices: A, B, C, D\n",
        "        Aristas: A → B, B → C, C → D\n",
        "        </pre>\n",
        "        <p>Visualización:</p>\n",
        "        <pre>\n",
        "        A --> B --> C --> D\n",
        "        </pre>\n",
        "        <p>En este grafo, no hay forma de regresar a un vértice previamente visitado siguiendo las direcciones de las aristas. No hay ciclos, por lo tanto, es un DAG.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Propiedades de los DAGs</h2>\n",
        "        <ul>\n",
        "            <li><strong>Ordenación topológica:</strong> Los DAGs permiten ordenar los vértices de manera lineal tal que para cualquier arista (u → v), el vértice (u) aparezca antes que (v) en la ordenación.</li>\n",
        "            <li><strong>Estructura jerárquica:</strong> Los DAGs son ideales para representar dependencias entre tareas o jerarquías donde la relación fluye en una sola dirección.</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>2. Órdenes Parciales (Partial Orders)</h2>\n",
        "        <p>Un orden parcial es una relación binaria sobre un conjunto que es reflexiva, antisimétrica y transitiva.</p>\n",
        "\n",
        "        <h3>Definiciones Técnicas:</h3>\n",
        "        <ul>\n",
        "            <li><strong>Reflexiva:</strong> Para todo elemento (x) ∈ (X), se cumple que (x ≤ x).</li>\n",
        "            <li><strong>Antisimétrica:</strong> Si (x ≤ y) y (y ≤ x), entonces (x = y).</li>\n",
        "            <li><strong>Transitiva:</strong> Si (x ≤ y) y (y ≤ z), entonces (x ≤ z).</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Ejemplo de un Orden Parcial</h2>\n",
        "        <p>Consideremos el conjunto (X = {A, B, C}) con la siguiente relación de orden parcial:</p>\n",
        "        <pre>\n",
        "        A ≤ B\n",
        "        B ≤ C\n",
        "        </pre>\n",
        "        <p>Visualización con un DAG:</p>\n",
        "        <pre>\n",
        "        A --> B --> C\n",
        "        </pre>\n",
        "        <p>Este grafo representa un orden parcial donde (A ≤ B), (B ≤ C), y por transitividad, (A ≤ C).</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Aplicaciones de DAGs y Órdenes Parciales</h2>\n",
        "        <ul>\n",
        "            <li><strong>Gestión de dependencias en proyectos:</strong> Los DAGs se usan para representar dependencias entre tareas. Cada tarea está representada por un nodo, y una arista (u → v) indica que la tarea (u) debe completarse antes de que la tarea (v) pueda comenzar.</li>\n",
        "            <li><strong>Ordenamiento de compilación:</strong> Los compiladores usan DAGs para representar dependencias entre módulos de un programa, asegurando que los archivos se procesen en el orden correcto.</li>\n",
        "            <li><strong>Teoría de órdenes:</strong> Los órdenes parciales se usan para modelar estructuras jerárquicas y relaciones de precedencia.</li>\n",
        "            <li><strong>Análisis de flujo de datos:</strong> Los DAGs se usan para analizar el flujo de datos en programas, garantizando que no haya ciclos de dependencias circulares.</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML en Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "VEMDtvjdruqa",
        "outputId": "45f35fac-d575-4821-d65f-58651936a76d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Grafos Dirigidos Acíclicos y Órdenes Parciales</title>\n",
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              "</head>\n",
              "<body>\n",
              "    <h1>Grafos Dirigidos Acíclicos (DAGs) y Órdenes Parciales</h1>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>1. Grafos Dirigidos Acíclicos (DAGs)</h2>\n",
              "        <p>Un grafo dirigido acíclico, también conocido como <strong>DAG</strong> (por sus siglas en inglés, Directed Acyclic Graph), es un grafo dirigido que no contiene ciclos dirigidos.</p>\n",
              "\n",
              "        <h3>Definiciones Técnicas:</h3>\n",
              "        <ul>\n",
              "            <li><strong>Grafo dirigido (digrafo):</strong> Un grafo donde las aristas tienen una dirección. Si hay una arista entre dos vértices (u) y (v), se representa como (u → v), indicando que la conexión va de (u) hacia (v).</li>\n",
              "            <li><strong>Ciclo dirigido:</strong> Un ciclo dirigido ocurre cuando puedes empezar en un vértice, seguir una secuencia de aristas dirigidas, y regresar al mismo vértice sin repetir ninguna arista.</li>\n",
              "            <li><strong>Acíclico:</strong> Un grafo dirigido es acíclico si no contiene ciclos dirigidos.</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "    \n",
              "    <div class=\"section\">\n",
              "        <h2>Ejemplo de un Grafo Dirigido Acíclico</h2>\n",
              "        <p>Imagina un grafo con los siguientes vértices y aristas:</p>\n",
              "        <pre>\n",
              "        Vértices: A, B, C, D\n",
              "        Aristas: A → B, B → C, C → D\n",
              "        </pre>\n",
              "        <p>Visualización:</p>\n",
              "        <pre>\n",
              "        A --> B --> C --> D\n",
              "        </pre>\n",
              "        <p>En este grafo, no hay forma de regresar a un vértice previamente visitado siguiendo las direcciones de las aristas. No hay ciclos, por lo tanto, es un DAG.</p>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>Propiedades de los DAGs</h2>\n",
              "        <ul>\n",
              "            <li><strong>Ordenación topológica:</strong> Los DAGs permiten ordenar los vértices de manera lineal tal que para cualquier arista (u → v), el vértice (u) aparezca antes que (v) en la ordenación.</li>\n",
              "            <li><strong>Estructura jerárquica:</strong> Los DAGs son ideales para representar dependencias entre tareas o jerarquías donde la relación fluye en una sola dirección.</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>2. Órdenes Parciales (Partial Orders)</h2>\n",
              "        <p>Un orden parcial es una relación binaria sobre un conjunto que es reflexiva, antisimétrica y transitiva.</p>\n",
              "\n",
              "        <h3>Definiciones Técnicas:</h3>\n",
              "        <ul>\n",
              "            <li><strong>Reflexiva:</strong> Para todo elemento (x) ∈ (X), se cumple que (x ≤ x).</li>\n",
              "            <li><strong>Antisimétrica:</strong> Si (x ≤ y) y (y ≤ x), entonces (x = y).</li>\n",
              "            <li><strong>Transitiva:</strong> Si (x ≤ y) y (y ≤ z), entonces (x ≤ z).</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>Ejemplo de un Orden Parcial</h2>\n",
              "        <p>Consideremos el conjunto (X = {A, B, C}) con la siguiente relación de orden parcial:</p>\n",
              "        <pre>\n",
              "        A ≤ B\n",
              "        B ≤ C\n",
              "        </pre>\n",
              "        <p>Visualización con un DAG:</p>\n",
              "        <pre>\n",
              "        A --> B --> C\n",
              "        </pre>\n",
              "        <p>Este grafo representa un orden parcial donde (A ≤ B), (B ≤ C), y por transitividad, (A ≤ C).</p>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>Aplicaciones de DAGs y Órdenes Parciales</h2>\n",
              "        <ul>\n",
              "            <li><strong>Gestión de dependencias en proyectos:</strong> Los DAGs se usan para representar dependencias entre tareas. Cada tarea está representada por un nodo, y una arista (u → v) indica que la tarea (u) debe completarse antes de que la tarea (v) pueda comenzar.</li>\n",
              "            <li><strong>Ordenamiento de compilación:</strong> Los compiladores usan DAGs para representar dependencias entre módulos de un programa, asegurando que los archivos se procesen en el orden correcto.</li>\n",
              "            <li><strong>Teoría de órdenes:</strong> Los órdenes parciales se usan para modelar estructuras jerárquicas y relaciones de precedencia.</li>\n",
              "            <li><strong>Análisis de flujo de datos:</strong> Los DAGs se usan para analizar el flujo de datos en programas, garantizando que no haya ciclos de dependencias circulares.</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def crear_dag():\n",
        "    \"\"\" Crea un DAG (grafo dirigido acíclico) que representa dependencias de tareas \"\"\"\n",
        "    dag = nx.DiGraph()\n",
        "\n",
        "    # Añadimos las tareas como nodos\n",
        "    dag.add_nodes_from(['Tarea 1', 'Tarea 2', 'Tarea 3', 'Tarea 4', 'Tarea 5', 'Tarea 6'])\n",
        "\n",
        "    # Añadimos las dependencias entre las tareas como aristas\n",
        "    # Ejemplo: 'Tarea 1' debe completarse antes que 'Tarea 2', por eso hay una arista 'Tarea 1' -> 'Tarea 2'\n",
        "    dag.add_edges_from([\n",
        "        ('Tarea 1', 'Tarea 2'),\n",
        "        ('Tarea 1', 'Tarea 3'),\n",
        "        ('Tarea 2', 'Tarea 4'),\n",
        "        ('Tarea 3', 'Tarea 4'),\n",
        "        ('Tarea 4', 'Tarea 5'),\n",
        "        ('Tarea 4', 'Tarea 6')\n",
        "    ])\n",
        "\n",
        "    return dag\n",
        "\n",
        "def dibujar_dag(dag, titulo):\n",
        "    \"\"\" Dibuja el DAG con las tareas y sus dependencias \"\"\"\n",
        "    plt.figure(figsize=(10, 7))\n",
        "\n",
        "    # Distribución con más espacio entre nodos\n",
        "    pos = nx.spring_layout(dag, k=1.5, iterations=50)  # k controla la repulsión, mayor k separa más los nodos\n",
        "    nx.draw(dag, pos, with_labels=True, node_size=3000, node_color='lightblue', font_size=14, font_weight='bold', arrows=True, arrowstyle='->', arrowsize=20)\n",
        "\n",
        "    # Mostrar etiquetas de las aristas (dependencias)\n",
        "    edge_labels = {(u, v): f\"{u}->{v}\" for u, v in dag.edges()}\n",
        "    nx.draw_networkx_edge_labels(dag, pos, edge_labels=edge_labels, font_size=10)\n",
        "\n",
        "    plt.title(titulo)\n",
        "    plt.show()\n",
        "\n",
        "def ordenacion_topologica(dag):\n",
        "    \"\"\" Realiza una ordenación topológica de las tareas en el DAG \"\"\"\n",
        "    try:\n",
        "        orden = list(nx.topological_sort(dag))\n",
        "        print(\"Ordenación topológica de las tareas:\")\n",
        "        for i, tarea in enumerate(orden, 1):\n",
        "            print(f\"{i}. {tarea}\")\n",
        "        return orden\n",
        "    except nx.NetworkXUnfeasible:\n",
        "        print(\"El grafo no es un DAG (hay ciclos presentes).\")\n",
        "\n",
        "def verificar_acyclicidad(dag):\n",
        "    \"\"\" Verifica si el grafo es acíclico (DAG) \"\"\"\n",
        "    if nx.is_directed_acyclic_graph(dag):\n",
        "        print(\"El grafo es un DAG (acíclico).\")\n",
        "    else:\n",
        "        print(\"El grafo no es un DAG (hay ciclos).\")\n",
        "\n",
        "# Creación del DAG\n",
        "dag = crear_dag()\n",
        "\n",
        "# Dibujar el DAG con una mejor separación\n",
        "dibujar_dag(dag, \"Dependencias de Tareas en un DAG\")\n",
        "\n",
        "# Verificar si es acíclico\n",
        "verificar_acyclicidad(dag)\n",
        "\n",
        "# Realizar la ordenación topológica\n",
        "orden_topologico = ordenacion_topologica(dag)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 907
        },
        "id": "-SBPszQcsxUh",
        "outputId": "f3afc020-8890-41db-f1f2-ba00b08139e8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x700 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "El grafo es un DAG (acíclico).\n",
            "Ordenación topológica de las tareas:\n",
            "1. Tarea 1\n",
            "2. Tarea 2\n",
            "3. Tarea 3\n",
            "4. Tarea 4\n",
            "5. Tarea 5\n",
            "6. Tarea 6\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import display, HTML\n",
        "\n",
        "# Contenido HTML para Google Colab\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Órdenes Parciales y Aplicaciones</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: 'Arial', sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1, h2, h3 {\n",
        "            color: #2c3e50;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: square;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        pre {\n",
        "            background-color: #ecf0f1;\n",
        "            padding: 10px;\n",
        "            border-radius: 5px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        .example {\n",
        "            color: #2980b9;\n",
        "            font-weight: bold;\n",
        "        }\n",
        "        .section {\n",
        "            margin-bottom: 40px;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "    <h1>Órdenes Parciales y Aplicaciones</h1>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Definición de Orden Parcial</h2>\n",
        "        <p>Un orden parcial es una relación binaria\n",
        "        <strong>&leq;</strong> en un conjunto de elementos\n",
        "        <strong>X</strong> que satisface las siguientes tres propiedades:</p>\n",
        "        <ul>\n",
        "            <li><strong>Reflexiva:</strong> Para todo elemento (x &in; X), se cumple que (x &leq; x) (todo elemento está relacionado consigo mismo).</li>\n",
        "            <li><strong>Antisimétrica:</strong> Si para cualquier par de elementos (x &leq; y) y (y &leq; x), entonces (x = y) (si están relacionados en ambas direcciones, entonces son el mismo elemento).</li>\n",
        "            <li><strong>Transitiva:</strong> Si (x &leq; y) y (y &leq; z), entonces (x &leq; z) (si (x) está relacionado con (y) y (y) con (z), entonces (x) también está relacionado con (z)).</li>\n",
        "        </ul>\n",
        "        <p>Los órdenes parciales se pueden visualizar utilizando <strong>DAGs</strong> (grafos dirigidos acíclicos), donde los elementos son los vértices y las relaciones de orden son las aristas dirigidas.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>1. Aplicación: Planificación de Proyectos</h2>\n",
        "        <p>En la gestión de proyectos, los órdenes parciales se usan para modelar dependencias entre tareas. Si una tarea debe completarse antes de que otra pueda comenzar, estas relaciones pueden ser representadas mediante un orden parcial.</p>\n",
        "        <pre>\n",
        "        A ≤ B ≤ C\n",
        "        </pre>\n",
        "        <p>Esto significa que la tarea A debe completarse antes de la tarea B, y la tarea B antes de la tarea C.</p>\n",
        "        <p class=\"example\">Aplicación práctica: Las herramientas de gestión de proyectos como Microsoft Project usan órdenes parciales para manejar dependencias entre tareas y cronogramas.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>2. Aplicación: Compiladores y Análisis de Programas</h2>\n",
        "        <p>En los compiladores, los órdenes parciales organizan dependencias entre archivos de código. Si un archivo A incluye un archivo B, entonces A debe compilarse después de B.</p>\n",
        "        <pre>\n",
        "        B ≤ A\n",
        "        </pre>\n",
        "        <p class=\"example\">Aplicación práctica: Los compiladores como GCC usan órdenes parciales para compilar archivos en el orden correcto.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>3. Aplicación: Sistemas de Bases de Datos</h2>\n",
        "        <p>En bases de datos, las transacciones que actualizan conjuntos de datos pueden tener dependencias. Un orden parcial puede modelar estas dependencias para evitar conflictos.</p>\n",
        "        <pre>\n",
        "        T₁ ≤ T₂\n",
        "        </pre>\n",
        "        <p class=\"example\">Aplicación práctica: Sistemas como PostgreSQL utilizan órdenes parciales para planificar transacciones y mantener la consistencia de datos.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>4. Aplicación: Jerarquías en Sistemas y Redes</h2>\n",
        "        <p>Las jerarquías en sistemas de control de acceso o redes de computadoras pueden representarse como órdenes parciales. Por ejemplo, en un sistema de control de acceso, los roles están jerárquicamente organizados:</p>\n",
        "        <pre>\n",
        "        Admin ≥ User ≥ Guest\n",
        "        </pre>\n",
        "        <p class=\"example\">Aplicación práctica: Los sistemas operativos utilizan órdenes parciales para organizar los permisos de acceso entre roles de usuarios.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>5. Aplicación: Teoría de Conjuntos</h2>\n",
        "        <p>En la teoría de conjuntos, los órdenes parciales describen la relación de inclusión entre conjuntos.</p>\n",
        "        <pre>\n",
        "        A ⊆ B ⊆ C\n",
        "        </pre>\n",
        "        <p class=\"example\">Aplicación práctica: Los retículos en álgebra usan órdenes parciales para modelar relaciones de inclusión entre conjuntos.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>6. Aplicación: Análisis de Precedencia en Circuitos</h2>\n",
        "        <p>En el diseño de circuitos integrados, las señales eléctricas deben fluir en un orden específico. Esto se representa con un DAG:</p>\n",
        "        <pre>\n",
        "        Input ≤ Compuerta 1 ≤ Compuerta 2 ≤ Output\n",
        "        </pre>\n",
        "        <p class=\"example\">Aplicación práctica: Los ingenieros de hardware usan órdenes parciales para diseñar circuitos que eviten ciclos de retroalimentación.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>7. Aplicación: Sistemas de Control de Versiones</h2>\n",
        "        <p>En sistemas de control de versiones como Git, las dependencias entre commits pueden verse como un orden parcial:</p>\n",
        "        <pre>\n",
        "        Commit B ≤ Commit A\n",
        "        </pre>\n",
        "        <p class=\"example\">Aplicación práctica: Git utiliza un DAG para modelar las dependencias entre commits y garantizar que los cambios se integren en el orden correcto.</p>\n",
        "    </div>\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML en Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "JtxDpBlFvZfa",
        "outputId": "1a2d4d19-efb2-46a8-fdd3-64446afa9999"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Órdenes Parciales y Aplicaciones</title>\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: 'Arial', sans-serif;\n",
              "            line-height: 1.8;\n",
              "            margin: 20px;\n",
              "            padding: 20px;\n",
              "            background-color: #f9f9f9;\n",
              "        }\n",
              "        h1, h2, h3 {\n",
              "            color: #2c3e50;\n",
              "        }\n",
              "        p {\n",
              "            font-size: 1.2em;\n",
              "            margin-bottom: 15px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: square;\n",
              "            margin-left: 30px;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 10px;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "        pre {\n",
              "            background-color: #ecf0f1;\n",
              "            padding: 10px;\n",
              "            border-radius: 5px;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "        .example {\n",
              "            color: #2980b9;\n",
              "            font-weight: bold;\n",
              "        }\n",
              "        .section {\n",
              "            margin-bottom: 40px;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "    <h1>Órdenes Parciales y Aplicaciones</h1>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>Definición de Orden Parcial</h2>\n",
              "        <p>Un orden parcial es una relación binaria \n",
              "        <strong>&leq;</strong> en un conjunto de elementos \n",
              "        <strong>X</strong> que satisface las siguientes tres propiedades:</p>\n",
              "        <ul>\n",
              "            <li><strong>Reflexiva:</strong> Para todo elemento (x &in; X), se cumple que (x &leq; x) (todo elemento está relacionado consigo mismo).</li>\n",
              "            <li><strong>Antisimétrica:</strong> Si para cualquier par de elementos (x &leq; y) y (y &leq; x), entonces (x = y) (si están relacionados en ambas direcciones, entonces son el mismo elemento).</li>\n",
              "            <li><strong>Transitiva:</strong> Si (x &leq; y) y (y &leq; z), entonces (x &leq; z) (si (x) está relacionado con (y) y (y) con (z), entonces (x) también está relacionado con (z)).</li>\n",
              "        </ul>\n",
              "        <p>Los órdenes parciales se pueden visualizar utilizando <strong>DAGs</strong> (grafos dirigidos acíclicos), donde los elementos son los vértices y las relaciones de orden son las aristas dirigidas.</p>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>1. Aplicación: Planificación de Proyectos</h2>\n",
              "        <p>En la gestión de proyectos, los órdenes parciales se usan para modelar dependencias entre tareas. Si una tarea debe completarse antes de que otra pueda comenzar, estas relaciones pueden ser representadas mediante un orden parcial.</p>\n",
              "        <pre>\n",
              "        A ≤ B ≤ C\n",
              "        </pre>\n",
              "        <p>Esto significa que la tarea A debe completarse antes de la tarea B, y la tarea B antes de la tarea C.</p>\n",
              "        <p class=\"example\">Aplicación práctica: Las herramientas de gestión de proyectos como Microsoft Project usan órdenes parciales para manejar dependencias entre tareas y cronogramas.</p>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>2. Aplicación: Compiladores y Análisis de Programas</h2>\n",
              "        <p>En los compiladores, los órdenes parciales organizan dependencias entre archivos de código. Si un archivo A incluye un archivo B, entonces A debe compilarse después de B.</p>\n",
              "        <pre>\n",
              "        B ≤ A\n",
              "        </pre>\n",
              "        <p class=\"example\">Aplicación práctica: Los compiladores como GCC usan órdenes parciales para compilar archivos en el orden correcto.</p>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>3. Aplicación: Sistemas de Bases de Datos</h2>\n",
              "        <p>En bases de datos, las transacciones que actualizan conjuntos de datos pueden tener dependencias. Un orden parcial puede modelar estas dependencias para evitar conflictos.</p>\n",
              "        <pre>\n",
              "        T₁ ≤ T₂\n",
              "        </pre>\n",
              "        <p class=\"example\">Aplicación práctica: Sistemas como PostgreSQL utilizan órdenes parciales para planificar transacciones y mantener la consistencia de datos.</p>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>4. Aplicación: Jerarquías en Sistemas y Redes</h2>\n",
              "        <p>Las jerarquías en sistemas de control de acceso o redes de computadoras pueden representarse como órdenes parciales. Por ejemplo, en un sistema de control de acceso, los roles están jerárquicamente organizados:</p>\n",
              "        <pre>\n",
              "        Admin ≥ User ≥ Guest\n",
              "        </pre>\n",
              "        <p class=\"example\">Aplicación práctica: Los sistemas operativos utilizan órdenes parciales para organizar los permisos de acceso entre roles de usuarios.</p>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>5. Aplicación: Teoría de Conjuntos</h2>\n",
              "        <p>En la teoría de conjuntos, los órdenes parciales describen la relación de inclusión entre conjuntos.</p>\n",
              "        <pre>\n",
              "        A ⊆ B ⊆ C\n",
              "        </pre>\n",
              "        <p class=\"example\">Aplicación práctica: Los retículos en álgebra usan órdenes parciales para modelar relaciones de inclusión entre conjuntos.</p>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>6. Aplicación: Análisis de Precedencia en Circuitos</h2>\n",
              "        <p>En el diseño de circuitos integrados, las señales eléctricas deben fluir en un orden específico. Esto se representa con un DAG:</p>\n",
              "        <pre>\n",
              "        Input ≤ Compuerta 1 ≤ Compuerta 2 ≤ Output\n",
              "        </pre>\n",
              "        <p class=\"example\">Aplicación práctica: Los ingenieros de hardware usan órdenes parciales para diseñar circuitos que eviten ciclos de retroalimentación.</p>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>7. Aplicación: Sistemas de Control de Versiones</h2>\n",
              "        <p>En sistemas de control de versiones como Git, las dependencias entre commits pueden verse como un orden parcial:</p>\n",
              "        <pre>\n",
              "        Commit B ≤ Commit A\n",
              "        </pre>\n",
              "        <p class=\"example\">Aplicación práctica: Git utiliza un DAG para modelar las dependencias entre commits y garantizar que los cambios se integren en el orden correcto.</p>\n",
              "    </div>\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import display, HTML\n",
        "\n",
        "# Contenido HTML para Google Colab\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Teorema 10.3 - Grafos Dirigidos Acíclicos</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: 'Arial', sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1, h2 {\n",
        "            color: #2c3e50;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: square;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        pre {\n",
        "            background-color: #ecf0f1;\n",
        "            padding: 10px;\n",
        "            border-radius: 5px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        .section {\n",
        "            margin-bottom: 40px;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "    <h1>Teorema 10.3 - Grafos Dirigidos Acíclicos (DAG)</h1>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Enunciado del Teorema 10.3</h2>\n",
        "        <p>El <strong>Teorema 10.3</strong> establece que en todo <strong>grafo dirigido acíclico (DAG)</strong> existen:</p>\n",
        "        <ul>\n",
        "            <li>Al menos un vértice con <strong>grado de salida cero</strong> (outdegree 0).</li>\n",
        "            <li>Al menos un vértice con <strong>grado de entrada cero</strong> (indegree 0).</li>\n",
        "        </ul>\n",
        "        <p>Este teorema asegura que siempre habrá vértices sin aristas entrantes o salientes en todo DAG.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Grado de Salida e Indegree</h2>\n",
        "        <ul>\n",
        "            <li><strong>Grado de salida (outdegree):</strong> Es el número de aristas que salen de un vértice. Si un vértice tiene outdegree 0, significa que no hay aristas que salgan de él.</li>\n",
        "            <li><strong>Grado de entrada (indegree):</strong> Es el número de aristas que entran en un vértice. Si un vértice tiene indegree 0, significa que no hay aristas que entren en él.</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Demostración del Teorema</h2>\n",
        "        <p>El razonamiento de la demostración se basa en el hecho de que un camino en un DAG es finito (debido a que no hay ciclos). Veamos los pasos:</p>\n",
        "        <ul>\n",
        "            <li><strong>Paso 1:</strong> Encuentra un vértice con outdegree 0 tomando el camino más largo en el DAG. El último vértice en ese camino no tiene aristas salientes, pues de lo contrario se podría extender el camino.</li>\n",
        "            <li><strong>Paso 2:</strong> Encuentra un vértice con indegree 0. El primer vértice en el camino más largo no tiene aristas entrantes, porque de lo contrario podrías extender el camino hacia atrás.</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Ejemplo de un DAG</h2>\n",
        "        <p>Consideremos un DAG con los siguientes vértices y aristas:</p>\n",
        "        <ul>\n",
        "            <li>Vértices: A, B, C, D</li>\n",
        "            <li>Aristas: A → B, A → C, B → D, C → D</li>\n",
        "        </ul>\n",
        "        <h3>Visualización:</h3>\n",
        "        <pre>\n",
        "        A --> B --> D\n",
        "         \\\\     /\n",
        "          \\\\--> C\n",
        "        </pre>\n",
        "        <p>En este ejemplo, podemos ver que:</p>\n",
        "        <ul>\n",
        "            <li>El vértice D tiene <strong>outdegree 0</strong> (no tiene aristas salientes).</li>\n",
        "            <li>El vértice A tiene <strong>indegree 0</strong> (no tiene aristas entrantes).</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Aplicaciones del Teorema</h2>\n",
        "        <p>El Teorema 10.3 tiene aplicaciones clave en varias áreas, incluyendo:</p>\n",
        "        <ul>\n",
        "            <li><strong>Ordenación Topológica:</strong> Garantiza que siempre existe un vértice inicial y uno final en un DAG, facilitando la ordenación de tareas o dependencias.</li>\n",
        "            <li><strong>Gestión de Dependencias:</strong> Permite identificar tareas iniciales (indegree 0) y tareas finales (outdegree 0) en cronogramas o compiladores.</li>\n",
        "            <li><strong>Análisis de Flujos:</strong> Ayuda a determinar los puntos de entrada y salida en sistemas de flujo como redes industriales o de información.</li>\n",
        "        </ul>\n",
        "    </div>\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML en Google Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "83808c3c-4507-423c-8c07-f25dd8b00346",
        "id": "uqT18bWN9NTd"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Teorema 10.3 - Grafos Dirigidos Acíclicos</title>\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: 'Arial', sans-serif;\n",
              "            line-height: 1.8;\n",
              "            margin: 20px;\n",
              "            padding: 20px;\n",
              "            background-color: #f9f9f9;\n",
              "        }\n",
              "        h1, h2 {\n",
              "            color: #2c3e50;\n",
              "        }\n",
              "        p {\n",
              "            font-size: 1.2em;\n",
              "            margin-bottom: 15px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: square;\n",
              "            margin-left: 30px;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 10px;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "        pre {\n",
              "            background-color: #ecf0f1;\n",
              "            padding: 10px;\n",
              "            border-radius: 5px;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "        .section {\n",
              "            margin-bottom: 40px;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "    <h1>Teorema 10.3 - Grafos Dirigidos Acíclicos (DAG)</h1>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>Enunciado del Teorema 10.3</h2>\n",
              "        <p>El <strong>Teorema 10.3</strong> establece que en todo <strong>grafo dirigido acíclico (DAG)</strong> existen:</p>\n",
              "        <ul>\n",
              "            <li>Al menos un vértice con <strong>grado de salida cero</strong> (outdegree 0).</li>\n",
              "            <li>Al menos un vértice con <strong>grado de entrada cero</strong> (indegree 0).</li>\n",
              "        </ul>\n",
              "        <p>Este teorema asegura que siempre habrá vértices sin aristas entrantes o salientes en todo DAG.</p>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>Grado de Salida e Indegree</h2>\n",
              "        <ul>\n",
              "            <li><strong>Grado de salida (outdegree):</strong> Es el número de aristas que salen de un vértice. Si un vértice tiene outdegree 0, significa que no hay aristas que salgan de él.</li>\n",
              "            <li><strong>Grado de entrada (indegree):</strong> Es el número de aristas que entran en un vértice. Si un vértice tiene indegree 0, significa que no hay aristas que entren en él.</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>Demostración del Teorema</h2>\n",
              "        <p>El razonamiento de la demostración se basa en el hecho de que un camino en un DAG es finito (debido a que no hay ciclos). Veamos los pasos:</p>\n",
              "        <ul>\n",
              "            <li><strong>Paso 1:</strong> Encuentra un vértice con outdegree 0 tomando el camino más largo en el DAG. El último vértice en ese camino no tiene aristas salientes, pues de lo contrario se podría extender el camino.</li>\n",
              "            <li><strong>Paso 2:</strong> Encuentra un vértice con indegree 0. El primer vértice en el camino más largo no tiene aristas entrantes, porque de lo contrario podrías extender el camino hacia atrás.</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>Ejemplo de un DAG</h2>\n",
              "        <p>Consideremos un DAG con los siguientes vértices y aristas:</p>\n",
              "        <ul>\n",
              "            <li>Vértices: A, B, C, D</li>\n",
              "            <li>Aristas: A → B, A → C, B → D, C → D</li>\n",
              "        </ul>\n",
              "        <h3>Visualización:</h3>\n",
              "        <pre>\n",
              "        A --> B --> D\n",
              "         \\     /\n",
              "          \\--> C\n",
              "        </pre>\n",
              "        <p>En este ejemplo, podemos ver que:</p>\n",
              "        <ul>\n",
              "            <li>El vértice D tiene <strong>outdegree 0</strong> (no tiene aristas salientes).</li>\n",
              "            <li>El vértice A tiene <strong>indegree 0</strong> (no tiene aristas entrantes).</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>Aplicaciones del Teorema</h2>\n",
              "        <p>El Teorema 10.3 tiene aplicaciones clave en varias áreas, incluyendo:</p>\n",
              "        <ul>\n",
              "            <li><strong>Ordenación Topológica:</strong> Garantiza que siempre existe un vértice inicial y uno final en un DAG, facilitando la ordenación de tareas o dependencias.</li>\n",
              "            <li><strong>Gestión de Dependencias:</strong> Permite identificar tareas iniciales (indegree 0) y tareas finales (outdegree 0) en cronogramas o compiladores.</li>\n",
              "            <li><strong>Análisis de Flujos:</strong> Ayuda a determinar los puntos de entrada y salida en sistemas de flujo como redes industriales o de información.</li>\n",
              "        </ul>\n",
              "    </div>\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import display, HTML\n",
        "\n",
        "# Contenido HTML para Google Colab\n",
        "html_content = \"\"\"\n",
        "<!DOCTYPE html>\n",
        "<html lang=\"es\">\n",
        "<head>\n",
        "    <meta charset=\"UTF-8\">\n",
        "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
        "    <title>Ejemplo 10.3 - Orden Parcial y Grafo Acíclico</title>\n",
        "    <style>\n",
        "        body {\n",
        "            font-family: 'Arial', sans-serif;\n",
        "            line-height: 1.8;\n",
        "            margin: 20px;\n",
        "            padding: 20px;\n",
        "            background-color: #f9f9f9;\n",
        "        }\n",
        "        h1, h2 {\n",
        "            color: #2c3e50;\n",
        "        }\n",
        "        p {\n",
        "            font-size: 1.2em;\n",
        "            margin-bottom: 15px;\n",
        "        }\n",
        "        ul {\n",
        "            list-style-type: square;\n",
        "            margin-left: 30px;\n",
        "            margin-bottom: 20px;\n",
        "        }\n",
        "        li {\n",
        "            margin-bottom: 10px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        pre {\n",
        "            background-color: #ecf0f1;\n",
        "            padding: 10px;\n",
        "            border-radius: 5px;\n",
        "            font-size: 1.1em;\n",
        "        }\n",
        "        .section {\n",
        "            margin-bottom: 40px;\n",
        "        }\n",
        "    </style>\n",
        "</head>\n",
        "<body>\n",
        "    <h1>Ejemplo 10.3 - Relación de Divisibilidad como Orden Parcial</h1>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>Conjunto y Relación</h2>\n",
        "        <p>Consideremos el conjunto (A = {2, 3, 5, 6, 10, 12, 15, 30}) con la relación \"divida\", denotada como <strong>|</strong>. Esto significa que (x | y) indica que el número (x) divide al número (y) sin residuo.</p>\n",
        "\n",
        "        <h3>a. Mostrar que la relación \"|\" es un orden parcial</h3>\n",
        "        <p>Para que esta relación sea un <strong>orden parcial</strong>, debe cumplir con las siguientes propiedades:</p>\n",
        "        <ul>\n",
        "            <li><strong>Reflexiva:</strong> Para cualquier elemento (x) en el conjunto (A), se cumple que (x | x). Todo número divide a sí mismo.</li>\n",
        "            <li><strong>Antisimétrica:</strong> Si (x | y) y (y | x), entonces (x = y). Esto significa que si dos números se dividen mutuamente, entonces deben ser iguales.</li>\n",
        "            <li><strong>Transitiva:</strong> Si (x | y) y (y | z), entonces (x | z). Esto significa que si un número divide a otro, y este a un tercero, el primero también divide al tercero.</li>\n",
        "        </ul>\n",
        "        <p>Por lo tanto, la relación \"divida\" en el conjunto (A) es un <strong>orden parcial</strong>.</p>\n",
        "    </div>\n",
        "\n",
        "    <div class=\"section\">\n",
        "        <h2>b. Dibujar el poset (A, |) como un Grafo Dirigido Acíclico (DAG)</h2>\n",
        "        <p>El conjunto (A) con la relación de divisibilidad se puede representar como un <strong>grafo dirigido acíclico (DAG)</strong>, donde los elementos del conjunto son los vértices, y hay una arista dirigida de (x) a (y) si (x) divide a (y).</p>\n",
        "\n",
        "        <h3>Visualización:</h3>\n",
        "        <pre>\n",
        "        2 --> 6 --> 30\n",
        "        |     |      |\n",
        "        v     v      v\n",
        "        3 --> 12     15\n",
        "        |            |\n",
        "        v            v\n",
        "        5 --> 10\n",
        "        </pre>\n",
        "        <p>En este grafo:</p>\n",
        "        <ul>\n",
        "            <li>El número 2 divide a 6 y 10.</li>\n",
        "            <li>El número 3 divide a 6, 12 y 15.</li>\n",
        "            <li>El número 5 divide a 10 y 15.</li>\n",
        "            <li>El número 6 divide a 12 y 30.</li>\n",
        "            <li>El número 10 divide a 30.</li>\n",
        "        </ul>\n",
        "        <p>Este grafo es <strong>acíclico</strong>, ya que no existe un camino dirigido que regrese al mismo vértice, y representa las relaciones de divisibilidad en el conjunto.</p>\n",
        "    </div>\n",
        "</body>\n",
        "</html>\n",
        "\"\"\"\n",
        "\n",
        "# Mostrar el contenido HTML en Colab\n",
        "display(HTML(html_content))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "fU2rMJS6w1hO",
        "outputId": "eb1059d1-53ee-49ac-9fc9-baca5b44b3f8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "<!DOCTYPE html>\n",
              "<html lang=\"es\">\n",
              "<head>\n",
              "    <meta charset=\"UTF-8\">\n",
              "    <meta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\">\n",
              "    <title>Ejemplo 10.3 - Orden Parcial y Grafo Acíclico</title>\n",
              "    <style>\n",
              "        body {\n",
              "            font-family: 'Arial', sans-serif;\n",
              "            line-height: 1.8;\n",
              "            margin: 20px;\n",
              "            padding: 20px;\n",
              "            background-color: #f9f9f9;\n",
              "        }\n",
              "        h1, h2 {\n",
              "            color: #2c3e50;\n",
              "        }\n",
              "        p {\n",
              "            font-size: 1.2em;\n",
              "            margin-bottom: 15px;\n",
              "        }\n",
              "        ul {\n",
              "            list-style-type: square;\n",
              "            margin-left: 30px;\n",
              "            margin-bottom: 20px;\n",
              "        }\n",
              "        li {\n",
              "            margin-bottom: 10px;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "        pre {\n",
              "            background-color: #ecf0f1;\n",
              "            padding: 10px;\n",
              "            border-radius: 5px;\n",
              "            font-size: 1.1em;\n",
              "        }\n",
              "        .section {\n",
              "            margin-bottom: 40px;\n",
              "        }\n",
              "    </style>\n",
              "</head>\n",
              "<body>\n",
              "    <h1>Ejemplo 10.3 - Relación de Divisibilidad como Orden Parcial</h1>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>Conjunto y Relación</h2>\n",
              "        <p>Consideremos el conjunto (A = {2, 3, 5, 6, 10, 12, 15, 30}) con la relación \"divida\", denotada como <strong>|</strong>. Esto significa que (x | y) indica que el número (x) divide al número (y) sin residuo.</p>\n",
              "        \n",
              "        <h3>a. Mostrar que la relación \"|\" es un orden parcial</h3>\n",
              "        <p>Para que esta relación sea un <strong>orden parcial</strong>, debe cumplir con las siguientes propiedades:</p>\n",
              "        <ul>\n",
              "            <li><strong>Reflexiva:</strong> Para cualquier elemento (x) en el conjunto (A), se cumple que (x | x). Todo número divide a sí mismo.</li>\n",
              "            <li><strong>Antisimétrica:</strong> Si (x | y) y (y | x), entonces (x = y). Esto significa que si dos números se dividen mutuamente, entonces deben ser iguales.</li>\n",
              "            <li><strong>Transitiva:</strong> Si (x | y) y (y | z), entonces (x | z). Esto significa que si un número divide a otro, y este a un tercero, el primero también divide al tercero.</li>\n",
              "        </ul>\n",
              "        <p>Por lo tanto, la relación \"divida\" en el conjunto (A) es un <strong>orden parcial</strong>.</p>\n",
              "    </div>\n",
              "\n",
              "    <div class=\"section\">\n",
              "        <h2>b. Dibujar el poset (A, |) como un Grafo Dirigido Acíclico (DAG)</h2>\n",
              "        <p>El conjunto (A) con la relación de divisibilidad se puede representar como un <strong>grafo dirigido acíclico (DAG)</strong>, donde los elementos del conjunto son los vértices, y hay una arista dirigida de (x) a (y) si (x) divide a (y).</p>\n",
              "        \n",
              "        <h3>Visualización:</h3>\n",
              "        <pre>\n",
              "        2 --> 6 --> 30\n",
              "        |     |      |\n",
              "        v     v      v\n",
              "        3 --> 12     15\n",
              "        |            |\n",
              "        v            v\n",
              "        5 --> 10\n",
              "        </pre>\n",
              "        <p>En este grafo:</p>\n",
              "        <ul>\n",
              "            <li>El número 2 divide a 6 y 10.</li>\n",
              "            <li>El número 3 divide a 6, 12 y 15.</li>\n",
              "            <li>El número 5 divide a 10 y 15.</li>\n",
              "            <li>El número 6 divide a 12 y 30.</li>\n",
              "            <li>El número 10 divide a 30.</li>\n",
              "        </ul>\n",
              "        <p>Este grafo es <strong>acíclico</strong>, ya que no existe un camino dirigido que regrese al mismo vértice, y representa las relaciones de divisibilidad en el conjunto.</p>\n",
              "    </div>\n",
              "</body>\n",
              "</html>\n"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import files\n",
        "uploaded = files.upload()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 73
        },
        "outputId": "c219c103-8733-43ae-f877-fdad613fde4b",
        "id": "Jq7NTGwsxgMB"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-040fbcf1-2eb8-4e35-a6c4-3b36cf525006\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-040fbcf1-2eb8-4e35-a6c4-3b36cf525006\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script>// Copyright 2017 Google LLC\n",
              "//\n",
              "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
              "// you may not use this file except in compliance with the License.\n",
              "// You may obtain a copy of the License at\n",
              "//\n",
              "//      http://www.apache.org/licenses/LICENSE-2.0\n",
              "//\n",
              "// Unless required by applicable law or agreed to in writing, software\n",
              "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
              "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
              "// See the License for the specific language governing permissions and\n",
              "// limitations under the License.\n",
              "\n",
              "/**\n",
              " * @fileoverview Helpers for google.colab Python module.\n",
              " */\n",
              "(function(scope) {\n",
              "function span(text, styleAttributes = {}) {\n",
              "  const element = document.createElement('span');\n",
              "  element.textContent = text;\n",
              "  for (const key of Object.keys(styleAttributes)) {\n",
              "    element.style[key] = styleAttributes[key];\n",
              "  }\n",
              "  return element;\n",
              "}\n",
              "\n",
              "// Max number of bytes which will be uploaded at a time.\n",
              "const MAX_PAYLOAD_SIZE = 100 * 1024;\n",
              "\n",
              "function _uploadFiles(inputId, outputId) {\n",
              "  const steps = uploadFilesStep(inputId, outputId);\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  // Cache steps on the outputElement to make it available for the next call\n",
              "  // to uploadFilesContinue from Python.\n",
              "  outputElement.steps = steps;\n",
              "\n",
              "  return _uploadFilesContinue(outputId);\n",
              "}\n",
              "\n",
              "// This is roughly an async generator (not supported in the browser yet),\n",
              "// where there are multiple asynchronous steps and the Python side is going\n",
              "// to poll for completion of each step.\n",
              "// This uses a Promise to block the python side on completion of each step,\n",
              "// then passes the result of the previous step as the input to the next step.\n",
              "function _uploadFilesContinue(outputId) {\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  const steps = outputElement.steps;\n",
              "\n",
              "  const next = steps.next(outputElement.lastPromiseValue);\n",
              "  return Promise.resolve(next.value.promise).then((value) => {\n",
              "    // Cache the last promise value to make it available to the next\n",
              "    // step of the generator.\n",
              "    outputElement.lastPromiseValue = value;\n",
              "    return next.value.response;\n",
              "  });\n",
              "}\n",
              "\n",
              "/**\n",
              " * Generator function which is called between each async step of the upload\n",
              " * process.\n",
              " * @param {string} inputId Element ID of the input file picker element.\n",
              " * @param {string} outputId Element ID of the output display.\n",
              " * @return {!Iterable<!Object>} Iterable of next steps.\n",
              " */\n",
              "function* uploadFilesStep(inputId, outputId) {\n",
              "  const inputElement = document.getElementById(inputId);\n",
              "  inputElement.disabled = false;\n",
              "\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  outputElement.innerHTML = '';\n",
              "\n",
              "  const pickedPromise = new Promise((resolve) => {\n",
              "    inputElement.addEventListener('change', (e) => {\n",
              "      resolve(e.target.files);\n",
              "    });\n",
              "  });\n",
              "\n",
              "  const cancel = document.createElement('button');\n",
              "  inputElement.parentElement.appendChild(cancel);\n",
              "  cancel.textContent = 'Cancel upload';\n",
              "  const cancelPromise = new Promise((resolve) => {\n",
              "    cancel.onclick = () => {\n",
              "      resolve(null);\n",
              "    };\n",
              "  });\n",
              "\n",
              "  // Wait for the user to pick the files.\n",
              "  const files = yield {\n",
              "    promise: Promise.race([pickedPromise, cancelPromise]),\n",
              "    response: {\n",
              "      action: 'starting',\n",
              "    }\n",
              "  };\n",
              "\n",
              "  cancel.remove();\n",
              "\n",
              "  // Disable the input element since further picks are not allowed.\n",
              "  inputElement.disabled = true;\n",
              "\n",
              "  if (!files) {\n",
              "    return {\n",
              "      response: {\n",
              "        action: 'complete',\n",
              "      }\n",
              "    };\n",
              "  }\n",
              "\n",
              "  for (const file of files) {\n",
              "    const li = document.createElement('li');\n",
              "    li.append(span(file.name, {fontWeight: 'bold'}));\n",
              "    li.append(span(\n",
              "        `(${file.type || 'n/a'}) - ${file.size} bytes, ` +\n",
              "        `last modified: ${\n",
              "            file.lastModifiedDate ? file.lastModifiedDate.toLocaleDateString() :\n",
              "                                    'n/a'} - `));\n",
              "    const percent = span('0% done');\n",
              "    li.appendChild(percent);\n",
              "\n",
              "    outputElement.appendChild(li);\n",
              "\n",
              "    const fileDataPromise = new Promise((resolve) => {\n",
              "      const reader = new FileReader();\n",
              "      reader.onload = (e) => {\n",
              "        resolve(e.target.result);\n",
              "      };\n",
              "      reader.readAsArrayBuffer(file);\n",
              "    });\n",
              "    // Wait for the data to be ready.\n",
              "    let fileData = yield {\n",
              "      promise: fileDataPromise,\n",
              "      response: {\n",
              "        action: 'continue',\n",
              "      }\n",
              "    };\n",
              "\n",
              "    // Use a chunked sending to avoid message size limits. See b/62115660.\n",
              "    let position = 0;\n",
              "    do {\n",
              "      const length = Math.min(fileData.byteLength - position, MAX_PAYLOAD_SIZE);\n",
              "      const chunk = new Uint8Array(fileData, position, length);\n",
              "      position += length;\n",
              "\n",
              "      const base64 = btoa(String.fromCharCode.apply(null, chunk));\n",
              "      yield {\n",
              "        response: {\n",
              "          action: 'append',\n",
              "          file: file.name,\n",
              "          data: base64,\n",
              "        },\n",
              "      };\n",
              "\n",
              "      let percentDone = fileData.byteLength === 0 ?\n",
              "          100 :\n",
              "          Math.round((position / fileData.byteLength) * 100);\n",
              "      percent.textContent = `${percentDone}% done`;\n",
              "\n",
              "    } while (position < fileData.byteLength);\n",
              "  }\n",
              "\n",
              "  // All done.\n",
              "  yield {\n",
              "    response: {\n",
              "      action: 'complete',\n",
              "    }\n",
              "  };\n",
              "}\n",
              "\n",
              "scope.google = scope.google || {};\n",
              "scope.google.colab = scope.google.colab || {};\n",
              "scope.google.colab._files = {\n",
              "  _uploadFiles,\n",
              "  _uploadFilesContinue,\n",
              "};\n",
              "})(self);\n",
              "</script> "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving dag.png to dag.png\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.image as mpimg\n",
        "\n",
        "# Cargar y mostrar la imagen\n",
        "img = mpimg.imread('dag.png')\n",
        "imgplot = plt.imshow(img)\n",
        "plt.axis('off')  # Para ocultar los ejes\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 244
        },
        "outputId": "68fd6ff9-2bf7-417a-e7c8-6c64aee61e7b",
        "id": "Ip5O_fWcx_8T"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## 1. ¿Qué es un dígrafo?\n",
        "Un **dígrafo** es un grafo donde las aristas tienen una **dirección**, es decir, cada conexión entre dos vértices tiene un sentido, representado por flechas. En un dígrafo, si hay una arista desde el vértice \\( A \\) hacia \\( B \\), no necesariamente existe una arista de \\( B \\) hacia \\( A \\).\n",
        "\n",
        "## 2. ¿Qué es un grafo no dirigido?\n",
        "Un **grafo no dirigido** es aquel en el que las aristas no tienen dirección. Si existe una arista entre dos vértices \\( A \\) y \\( B \\), esta representa una conexión **bidireccional**. Las aristas se dibujan como líneas sin flechas y los vértices están conectados en ambas direcciones.\n",
        "\n",
        "## 3. ¿Cuál es la diferencia entre un grafo dirigido y uno no dirigido?\n",
        "La diferencia clave es la **dirección de las aristas**:\n",
        "- En los **grafos dirigidos**, las conexiones entre vértices tienen una dirección específica.\n",
        "- En los **grafos no dirigidos**, las conexiones son **simétricas** y no tienen dirección.\n",
        "\n",
        "## 4. ¿Qué es un camino crítico en una red?\n",
        "El **camino crítico** en una red es la secuencia de actividades que determina el **tiempo mínimo necesario** para completar un proyecto. En un diagrama de red, es el conjunto de tareas que, si se retrasan, retrasan todo el proyecto.\n",
        "\n",
        "## 5. ¿Qué es un puente en un grafo?\n",
        "Un **puente** es una arista cuya eliminación **desconecta** el grafo, dividiéndolo en dos componentes disjuntos. Los puentes son esenciales para mantener la conectividad en el grafo.\n",
        "\n",
        "## 6. ¿Qué significa que un grafo es fuertemente conectado?\n",
        "Un grafo **fuertemente conectado** es un grafo dirigido en el que existe un **camino dirigido** entre cada par de vértices, en ambas direcciones. Es decir, puedes ir de cualquier vértice \\( u \\) a otro \\( v \\), y también regresar de \\( v \\) a \\( u \\).\n",
        "\n",
        "## 7. ¿Qué es un grafo débilmente conectado?\n",
        "Un grafo **débilmente conectado** es un grafo dirigido en el que, si se ignoran las direcciones de las aristas, existe un camino entre todos los vértices. Sin embargo, con las direcciones presentes, puede que no haya caminos en ambas direcciones entre ciertos pares de vértices.\n",
        "\n",
        "## 8. ¿Qué es un grafo unilateral?\n",
        "Un **grafo unilateral** es un grafo dirigido en el que existe un **camino dirigido** entre cada par de vértices, pero solo en **una dirección**. Es decir, puede que exista un camino de \\( u \\) a \\( v \\), pero no necesariamente uno de \\( v \\) a \\( u \\).\n",
        "\n",
        "## 9. ¿Qué establece el Teorema de Robbins?\n",
        "El **Teorema de Robbins** establece que un grafo no dirigido puede ser orientado de manera que el grafo resultante sea **fuertemente conectado** si y solo si el grafo original no contiene puentes.\n",
        "\n",
        "## 10. ¿Qué es el grado de entrada de un vértice en un dígrafo?\n",
        "El **grado de entrada** de un vértice es el número de aristas que **llegan a ese vértice** desde otros vértices. En un dígrafo, este grado representa cuántos caminos llegan a ese nodo.\n",
        "\n",
        "## 11. ¿Qué es el grado de salida de un vértice en un dígrafo?\n",
        "El **grado de salida** de un vértice es el número de aristas que **salen de ese vértice** hacia otros vértices. Representa cuántos caminos parten desde ese nodo.\n",
        "\n",
        "## 12. ¿Qué es un ciclo en un grafo?\n",
        "Un **ciclo** en un grafo es un camino que **empieza y termina** en el mismo vértice, pasando por otros vértices una sola vez antes de regresar al vértice inicial.\n",
        "\n",
        "## 13. ¿Qué es un camino hamiltoniano?\n",
        "Un **camino hamiltoniano** es un camino que pasa **una vez por cada vértice** de un grafo, sin repetir vértices, pero que no necesariamente regresa al vértice de inicio.\n",
        "\n",
        "## 14. ¿Qué es un ciclo hamiltoniano?\n",
        "Un **ciclo hamiltoniano** es un ciclo que pasa por **cada vértice de un grafo exactamente una vez** y regresa al vértice de inicio.\n",
        "\n",
        "## 15. ¿Qué establece el Teorema de Dirac sobre grafos hamiltonianos?\n",
        "El **Teorema de Dirac** establece que si en un grafo con \\( n \\geq 3 \\) vértices, cada vértice tiene un grado de al menos \\( \\frac{n}{2} \\), entonces el grafo contiene un **ciclo hamiltoniano**.\n",
        "\n",
        "## 16. ¿Qué es el Teorema de Ore?\n",
        "El **Teorema de Ore** establece que si en un grafo con \\( n \\) vértices, la suma de los grados de cualquier par de vértices no adyacentes es al menos \\( n \\), entonces el grafo contiene un **ciclo hamiltoniano**.\n",
        "\n",
        "## 17. ¿Cómo se aplica el método del camino crítico en grafos?\n",
        "El **método del camino crítico** en grafos se usa para identificar las actividades que no pueden retrasarse sin afectar el **tiempo total** de un proyecto. En un grafo, el camino crítico es la ruta que toma más tiempo en completarse.\n",
        "\n",
        "## 18. ¿Qué son los arcos simétricos en un dígrafo?\n",
        "Los **arcos simétricos** son pares de aristas entre dos vértices \\( u \\) y \\( v \\) tales que existe una arista de \\( u \\) a \\( v \\) y otra de \\( v \\) a \\( u \\). Los arcos simétricos implican que hay un **camino en ambas direcciones** entre esos vértices.\n",
        "\n",
        "## 19. ¿Qué es la centralidad en una red?\n",
        "La **centralidad** mide la **importancia** de un vértice dentro de una red. Existen varios tipos de centralidad:\n",
        "- **Centralidad de grado**: Cuántas conexiones tiene un vértice.\n",
        "- **Centralidad de cercanía**: Cuán cerca está un vértice de los demás.\n",
        "- **Centralidad de intermediación**: Cuántos caminos más cortos pasan por un vértice.\n",
        "\n",
        "## 20. ¿Qué es la conectividad en un grafo?\n",
        "La **conectividad** se refiere a la capacidad de un grafo de **permanecer conectado** incluso después de la eliminación de ciertos vértices o aristas. Un grafo es **k-conexo** si se necesita eliminar al menos \\( k \\) vértices para desconectarlo.\n"
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