Introduction_aux_Graphes.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Introduction aux Graphes.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNPe0k7KE4c10FB24IuV0ty",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/GeoLabUniLaSalle/Python/blob/main/Introduction_aux_Graphes.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WmlDDE_uLnZd"
      },
      "source": [
        "# **Introduction aux graphes**\n",
        "\n",
        "Dans ce chapitre, nous allons introduire la notion de graphe et découvrir le vocabulaire associé\n",
        "\n",
        "Afin de représenter nos graphes en Python, nous utiliserons le module networkx que nous détaillerons petit à petit.\n",
        "\n",
        "Un graphe est un ensemble de **sommets** et d'**arêtes** qui relient des sommets entre-eux. Les graphes servent à représenter des relations entre des éléments : villes reliées par des routes, personnes reliées sur un réseau social, etc.\n",
        "\n",
        "Commençons par importer les modules nécessaires"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I_m1i--faaZN"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cRyfikRoahve"
      },
      "source": [
        "En cas d'erreur sur ce bloc d'instructions, lancez l'installation des modules matplotlib et networkx, redémarrez le noyau, puis re-exécutez la dernière cellule de code."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QdSrmBo5aore"
      },
      "source": [
        "import sys  \n",
        "!{sys.executable} -m pip install --user matplotlib\n",
        "!{sys.executable} -m pip install --user networkx"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0HHG2DuHac8v"
      },
      "source": [
        "Voici un exemple de graphe :"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "ljJwevBNLkTn",
        "outputId": "3616289f-e89c-458b-c260-c20f5f3d38c8"
      },
      "source": [
        "G = nx.Graph()\n",
        "G.add_node(\"A\") # Création d'un sommet\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_node(\"E\")\n",
        "G.add_node(\"F\")\n",
        "G.add_node(\"G\")\n",
        "G.add_edge(\"A\",\"B\") # Création d'une arête qui relie les sommets A et B\n",
        "G.add_edge(\"B\",\"F\")\n",
        "G.add_edge(\"C\",\"D\")\n",
        "G.add_edge(\"C\",\"E\")\n",
        "G.add_edge(\"C\",\"F\")\n",
        "G.add_edge(\"D\",\"E\")\n",
        "G.add_edge(\"F\",\"G\")\n",
        "G.add_edge(\"F\",\"A\")\n",
        "G.add_edge(\"G\",\"D\")\n",
        "\n",
        "pos = nx.spring_layout(G) # Génération d'un positionnement des sommets dans l'espace\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos) # Affichage des sommets\n",
        "nx.draw_networkx_edges(G, pos) # Affichage des arêtes\n",
        "\n",
        "plt.show() # Affichage du graphe"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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iC+hCGpF6r5TVoWD+2ScF7lsU2iBPzQS5z2tapjAikyh0idTbHZOLar5wPRp4dXz4x+SKuCIiyyh0iVQrqahG7J3iBudwPwXDAJduF+NZRbVoCyMyi0KXSLWQlMJmH4MDICS1+cchBKDQJVIup6jsrWVhwuDVCZDzmP1OZkQ6UOgSqVbGqxPRcWpFchxCKHSJVFNVFs2qSFVlRZEchxAKXSLV9LurQkmheT/minKAXvcOIqqIyDoKXSLVuIM1UFfXvCmG2tpa+C39HPv27ZPYbeCJ+KDQJVIrLi4Oo20s0PZlHoTtlsDhAI5DNLF76/8hKioK2traWLlyJR48eCDSWonsoNAlUqekpARz587F9OnTsX79ehxaPQPKisK1YFRWkMdXdrqwt7fHyZMnkZSUBD6fDxMTE0yaNAlxcXFghF0ETGQShS6RGgKBAAcOHMCgQYPQsWNHZGVlYdKkSTDS6oQ1LvpQUWzaj7uKohzWuOhjiKZa/ef69u0LX19fPHjwAA4ODvD09ISJiQkOHjwIHo8n6rdEpBCnsf+lzczMmOTk5FYshxDh3Lp1CwsWLEB1dTX27dsHY2Pj977mcGJeo13GXuNw/hnhrnHRxwxL7UZfVyAQ4Ny5c/Dz80NKSgo8PT2xcOFC9OzZs5nviEgyDoeTwjCMWUOP0UiXSLTKykp8++23sLOzg4eHB65evdpg4ALADEttHPO0hKOBBpQU5KD8zqoGZQU5KCnIwdFAA8c8LT8auAAgJycHJycnREZGIi4uDi9evIChoSE8PDxw7do1UbxFImVopEskVkREBL7++mtYW1vD19cX3bt3/+TnPquoRkhqIXIel6OMVwtVZUXo9+iAySYN7xzRFC9fvsSBAwewc+dOdOvWDV5eXpg0aRLtFCxDGhvpUugSiVNYWAgvLy/cvHkT/v7+GD16NNslNYjP5+P06dPw8/NDTk4OFi5ciC+//BLq6upsl0ZaGE0vEKlQV1eHbdu2wcjICEOGDEFGRobYBi4AyMvLg8vl4sKFC4iKisKDBw8wYMAAzJkzB2lpaWyXR1hCoUskwrVr12BmZoaIiAgkJCTgxx9/hLKyMttlfbLBgwcjMDAQd+/exYABA+Dm5gZbW1v89ddfzb55g0gWCl0i1l68eIGFCxdiwoQJWLlyJc6fP48BAwawXZbQunbtitWrV+PevXv46quvsHXrVujq6mLLli148eIF2+WRVkChS8QSwzD4448/YGBgAA6Hg6ysLHh4eEjNTryKior47LPPEB8fj5CQENy8eRP9+vXDggULkJWVxXZ5pAVR6BKxc/v2bYwePRo+Pj4IDQ2Fv78/1NTUPv5ECWVmZoagoCBkZ2ejR48ecHBwwNixY3H69GkIBM3rBUzED4UuERs8Hg8//vgjhg8fDjc3N1y/fh0WFhZsl9Vqunfvjh9//BF5eXmYOXMm1q1bBz09Pfj5+aGsrIzt8oiIUOgSsXD+/HkMHjwYt27dQlpaGpYuXQoFBdH0wpU0SkpKmDlzJq5fv47ff/8d8fHx0NbWhpeXF3JzaZNMSUehS1hVVFQEDw8PeHp6Yvv27QgJCYGmpibbZYkFDocDa2trHDt2DOnp6WjXrh2sra3h5uaG8+fPU6MdCUWhS1jB5/Ph7++PwYMHQ1tbG7du3YKrqyvbZYktLS0t/Pzzz3jw4AG4XC6WL18OQ0ND6vErgSh0SatLTU2FlZUVjh49ipiYGPz8889o27Yt22VJBBUVFcyfPx8ZGRnYtWsXzpw5gz59+lCPXwlCoUtaTVlZGZYuXQpnZ2csXLgQsbGxGDRoENtlSSQOhwN7e3uEhoYiKSkJdXV1MDExweTJk3H58mWaehBjFLqkxTEMg5CQEBgYGKC8vBy3bt3CnDlzpGbNLdv69euHrVu34sGDB7C3t8f8+fNhampKPX7FFDW8IS3q3r17+Prrr5Gfn489e/bAxsaG7ZKknkAgwNmzZ+Hn54fU1FTq8csCanhDWl1NTQ1+/vlnDBs2DLa2tkhNTaXAbSVycnJwdnbGmTNnEBsbi+fPn8PQ0BDTp09HUlIS2+XJPApdInKxsbEwMjJCQkICkpOTsWrVKuolyxJ9fX3s3r0b9+7dg6mpKaZOnQpLS0scOXIEtbW1bJcnk2h6gYhMcXExvvnmG1y4cAF+fn5wd3eneVsx87rH744dO3D79m3q8dtCaHqBtCiBQID9+/fD0NAQXbp0QVZWFiZMmECBK4Ze9/i9ePEizpw5g7y8PAwYMABz586lHr+thEKXNMvNmzcxcuRIBAYG4uzZs/D19UWHDh3YLot8giFDhuDXX3/F3bt30b9///oevydOnKAevy2IQpcIpbKyEqtWrcKoUaMwY8YMJCQkwMjIiO2yiBDe7fHr6+tLPX5bEIUuabJTp05h0KBBePjwITIzM7FgwQLIydGPkqRrqMevjo4OFi5cSD1+RYh+U8gnKygowIQJE+Dt7Y39+/fj8OHD0NDQYLss0gJe9/jNysqChoZGfY/fiIgI6vHbTBS65KNqa2vh6+sLY2NjGBsbIyMjAw4ODmyXRVpB9+7dsW7dOuTl5WHGjBlYu3Yt9fhtJgpd0qjExESYmZkhKioKV69exdq1ayVqQ0giGkpKSpg1axaSk5Nx8OBBXLlyBdra2li6dCn1+G0iCl3SoBcvXmDBggWYOHEiVq9ejXPnzqF///5sl0VYxuFwMHz4cBw/fhzp6elQUVGBlZUV3NzcEB0dTY12PgGFLnkLwzA4fPgwDAwMoKCggKysLEybNo3W3JL3aGlpYdOmTXjw4AHGjx+PZcuW1ff4ffXqFdvliS26I43Ue32HUmlpKfbt2wdzc3O2SyIShGEYXLp0CTt27EBCQgLmzp2LRYsWoU+fPmyX1urojjTSqKqqKqxduxYjRowAl8tFUlISBS5pMg6Hg1GjRiEsLAzXrl1DbW0t9fhtAIWujDt37hwGDx6M7OxspKWlwcvLS2Y3hCSi87rHb15eHuzs7KjH7xtoekFGPX78GMuWLUNSUhJ27doFFxcXtksiUux1j98dO3YgLS2tvsdvjx492C6tRdD0AqnH5/Oxa9cuDBkyBDo6OsjMzKTAJS3udY/fqKgoxMTE4NmzZxg0aJBM9vil0JUhKSkpsLCwQHBwMGJjY7Fx40baEJK0uoZ6/FpZWclMj18KXRnw8uVLLFmyBK6urli8eDFiYmJgYGDAdllExqmpqWH58uXIzc3FqlWrEBAQgL59+2Ljxo0oLi5mu7wWQ6ErxRiGQXBwMAYNGoSqqircunULX3zxBa25JWJFXl4e7u7uuHTpEiIiInD//v36Hr/p6elslydyFLpS6u+//4aLiwvWr1+PY8eOITAwEF26dGG7LEIaNXTo0Poev7q6unB1dYWdnR1OnDgBPp/PdnkiQaErZaqrq7Fx40ZYWFjA3t4eqampGD58ONtlEdIkXbt2xXfffYf79+9j4cKF8PHxgY6ODnx8fCS+xy+FrhSJiYmBkZEREhMTkZycjJUrV0JRUZHtsggRmqKiIqZOnYqEhAQEBwcjPT0d/fr1w8KFC5Gdnc12eUKh0JUCT58+xRdffIFZs2Zh06ZNCA8Ph7a2NttlESJS5ubmOHToELKystCtWzfY29vD0dFR4nr80s0REuz1hpBr1qzBrFmzsG7dOrRv357tsghpFdXV1Th27Bh27NiB8vJyLF68GLNnz27WHn0lFdUISSlETlEZynh1UFVWgH53VUwx1USX9kqffJzGbo6g0JVQGRkZWLBgARiGwd69ezF06FC2SyKEFQzDID4+Hn5+frhw4QJmzpyJxYsXQ0dH55OPkV5Qit0xuYi9889Steq6/0bOygpyYADY6aljka0uhmqpffR4dEeaFKmsrMQ333yD0aNHY/bs2YiPj6fAJTKNw+FgxIgROH78OG7cuAFlZWVYWlp+co/fw4l5mBaYiPPZT1BdJ3grcAGA9+/nzmU9wbTARBxOzGtWvRS6EiQ8PBwGBgZ48uQJbt68CU9PT9oQkpA39O7dG7/88kt9j9+lS5di8ODBCAgIaLDH7+HEPGyMzEZVLR8fa4LGMEBVLR8bI7ObFbz0GysB8vPz4e7ujpUrV+K3335DUFAQbQhJSCPatm2L//3vf7h58yb8/PwQERGBPn36YNWqVcjPzwfwz5TCxsgcVNU27SJcVa0AGyNzkFFYKlRtFLpirLa2Fj4+PjAxMYGpqSnS09MxatQotssiRGK82eM3MTERNTU1MDIywuTJk7H+r2vg1Ql3wwWvjg//GOH2hqPQFVMJCQkwNTXF+fPnkZiYiB9++AFKSp9+9ZQQ8jYdHR1s27YNDx48gLnNKKQ8qvrolMKHMAxw6XYxnlVUN/m5FLpi5vnz5/D09MSUKVOwZs0aREVFQVdXl+2yCJEaHTp0QEcjx2YPYjgAQlILm/w8Cl0xwTAMgoKCYGBgACUlJWRlZWHq1KnUnIaQFpBTVPbeKoWm4tUJkPO4vMnPo31ZxEB2djYWLVqEsrIynD59GmZmDS7vI4SISBmvTkTHaXr/Xxrpsqiqqgrff/89bGxsMHHiRCQlJVHgEtIKVJVFM95UVW56bxMKXZZERUXB0NAQd+/eRUZGBhYvXgx5eXm2yyJEJuh3V4WSQvPiT1lBDvo9mn7LMU0vtLJHjx5h2bJlSE5Oxu7du+Hk5MR2SYTIlJqaGjD3rqK6uj0gL3wXPgbAZBPNJj+PRrqthM/nY+fOnRg6dCj69++PzMxMClxCWlFpaSk2b96Mfv36IeTwbxjaTRHCXqfmcAB7PfUmNcF5jUa6rSA5ORkLFixA+/btERcXh4EDB7JdEiEyIy8vD9u3b0dQUBBcXV1x6tQpGBsbI72gFNMCE1FV2/QbJJQV5LHITrilnBS6n0DYdm8vX77E999/j+DgYGzevBkzZ86kJWCEtJKkpCT4+voiOjoa8+bNQ0ZGBjQ1/5sOGKqlhjUu+v/2Xvj05WMqinJY46KPIZof7zbWEArdRjTe7q0I26LvNNjujWEYHD9+HMuXL4erqyuysrLQuXPnVq+fEFkjEAhw6tQp+Pj4ID8/H8uWLcOvv/76wR67Myy1AQAbI3PAq2u86Q2H888Id42Lfv3zhEGh+wH/dB/68DeC928An8t6grg7JfXfiNzcXHz11Vd4/PgxgoODYW1t3cqVEyJ7Xr16haCgIGzduhUdO3bEihUrMGnSJCgofDziZlhqY4imGvxjcnHpdjE4+O/3G/ivn669njoW2ekKPcJ9jZqYN+C/dm+ffsqhrCgHE9zHOf+1+Pbbb+Hl5UX7kxHSwp48eYLdu3dj7969sLKygre3N2xsbISexntWUY2Q1ELkPC5HGa8WqsqK0O/RAZNNRLdzBI103yFsuzderQBXBT3xZ9QVjDXTb6HqCCHAP3dxbt26FSEhIZg6dSouX74MPT29Zh+3S3slfDny03ecEAYtGXvH7phcodu9QV4RJ3IqRFsQIQTAP9dKLl26hHHjxsHOzg6ampq4c+cO9u7dK5LAbS000n1DSUU1Yu8Ui6TdmzDr9wgh76utrUVwcDB8fX1RWVkJb29vBAcHQ0VFhe3ShEKh+4aQlKa3aXvX63ZvLX2KQoi0e/nyJQIDA+Hn5wcdHR389NNPcHFxkfgtqih038BmuzdCyD/y8/OxY8cOHDx4EI6Ojjh58iRMTU3ZLktkJPu/DBFjs90bIbIuJSUFHh4eMDIyAgDcuHEDf/75p1QFLkCh+xZRtXtrAyEvxBEiYwQCAU6fPg17e3tMmDABJiYmuH//Pnx9fdG7d2+2y2sRNL3whn/avRU1a4qBI6jDiQN+yAjwhru7O7hcLgYMGCDCKgmRfDweD4cOHcLWrVvRtm1beHt7Y8qUKTKxtp1Gum+YbNr0Nm3vatOmDdJO7sMPP/yAe/fuwd7eHgMHDsS3336Lq1evQiBo3pwxIZKsuLgYP/30E7S1tREWFgZ/f38kJyfDw8NDJgIXoNB9S9f2SrAdoN7sdm89OneAk5MT9uzZg4KCAgQFBUFeXh7/+9//0KtXL3h6eiIiIgI8Hk+0b4AQMXX79m0sWLAAAwYMQGFhIS5dulQ/rSBrTaAodN/xlZ2u0B3lG3oxnagAABDbSURBVGr3JicnB3Nzc2zcuBGZmZm4cuUK9PX1sXnzZmhoaGDSpEkICgrCs2fPRFE+IWKDYRjExcWBy+XCxsYG3bp1Q05ODgIDA2W6vSmF7juGaqnBmLkH8Gua9LxPbfemo6OD5cuXIzY2Fn///Tfc3Nxw8uRJ9OvXD/b29ti+fTvu37/fnLdACKvq6upw7NgxDBs2DPPnz4ezszPy8vKwfv16aGhosF0e66jhzTsOHjyI9evXw3tvGHZdedhq7d6qqqoQHR2NsLAwnDp1ChoaGuByueByuTA1NZW5UzAiecrLy/Hrr79ix44d6N27N7y9veHm5ibxNzMIo7GGNxS6bzh37hxmzZqFmJgY6OvrI6OwtNXavb2Jz+cjMTERYWFhCAsLw6tXrzB+/HhwuVzY2dmhTZs2InstQpqrsLAQfn5+OHDgABwcHODt7Y1hw4axXRarKHQ/QXp6OsaMGYMTJ05gxIgRbz0mqnZvwsrJyakP4OzsbDg6OsLd3R3Ozs7o2LFji78+IQ1JS0uDr68vIiIiMGvWLHh5eaFv375slyUWKHQ/oqCgANbW1vD19cVnn33GdjmNKioqwqlTpxAWFoa4uDhYWlqCy+Vi/Pjx0NLSYrs8IuUYhkFUVBR8fHxw+/ZtLFmyBJ6enlBTE92ZnjSg0G1EaWkpbGxsMHv2bHh7e7NdTpNUVFTg3LlzCA0NRUREBLS1tcHlcuHu7o7BgwfTPDARGR6Phz/++ANbt26FoqIivL29MXXqVJrq+gAK3Q+oqamBk5MTDA0NsWPHDokOqbq6Oly5cqV+GoJhmPoLcTY2Np+0bQkh73r27Bn27NmD3bt3w8jICCtWrMCoUaMk+nelNVDoNoBhGMyaNQsVFRUICQmBvLw82yWJDMMwyMzMRGhoKMLCwnD//n24uLjA3d0djo6OaN++PdslEjGXm5uLbdu24ciRI3B3d8fy5cthaGjIdlkSo7HQlb21HP/64YcfkJubiz/++EOqAhcAOBwOBg8ejB9++AHJyclIT0+HlZUVAgIC0LNnT7i6uiIgIACPHz9mu1QiRhiGQXx8PCZOnAgrKyt06tQJWVlZOHDgAAWuCMnkSDcgIABbtmxBQkIC1NXV2S6nVb18+RJRUVEIDQ1FVFQU9PT06ueB9fX16bRRBtXV1eHkyZPw9fVFSUkJli1bhtmzZ6Ndu3ZslyaxaHrhDZGRkZg3bx7i4uLQv39/tsthVU1NDWJjY+vngVVUVOrnga2srKTuDIC8raKiAgcOHMD27dvRo0cPeHt7g8vl0vddBCh0/5WSkgJnZ2eEh4fD0tKS7XLECsMwSE1NrQ/gx48fw83NDVwuF6NHj0bbtm3ZLpGIyKNHj7Bz504EBgbCzs4O3t7esLKyYrssqUJzugDy8vIwfvx47Nu3jwK3ARwOB6ampli/fj3S09Nx7do1DBkyBNu3b0f37t3h7u6O3377DcXFxWyXSoSUkZGB2bNnw9DQEJWVlUhKSkJISAgFbiuTidB98eIFnJ2dsWrVKkyYMIHtciRC37594eXlhYsXLyIvLw+TJk1CREQEdHV1MXLkSPj6+iI3N5ftMslHMAyDc+fOYezYsXBycoKenh5yc3Ph5+eHfv36sV2eTJL66YXq6mqMHTsWZmZm8PX1Zbscicfj8XDx4kWEhobi1KlT6Ny5c/08sLm5uUw2NxFHNTU1OHLkCHx9fcEwDLy9vfH5559DSanlb1snMjynKxAI4OHhAT6fj2PHjlEgiJhAIEBSUlL9PHBpaWl9Y55Ro0bRLzgLnj9/jn379mHXrl0YNGgQvL29MXbsWFqV0spkdk539erVKCwsxKFDhyhwW4CcnBwsLS2xadMmZGVlITY2Frq6uti4cSM0NDQwZcoUHD58GC9evGC7VKl37949LFmyBLq6urh9+zbOnDmDc+fOwdHRkQJXzEhtEu3evbt+BKasrMx2OTKhf//+WLFiBa5cuYI7d+7A2dkZwcHB6NOnD0aNGgU/Pz88ePCA7TKlSmJiIiZPnoxhw4ahXbt2yMzMxMGDBzFkyBC2SyMfIJXTC+Hh4ViwYAGuXLlCFwvEwKtXr3D+/HmEhobi9OnT6NWrV/0NGUZGRjQSayI+n4/w8HD4+Pjg8ePHWLp0KebOnUu3d4sRmZrTTUpKgqurKyIjI2Fubs52OeQdfD4fCQkJCAsLQ2hoKGpra+vngW1tbWVmR1hhVFZW4uDBg9i2bRu6du0Kb29vTJgwgZoZiSGZCd2///4bNjY2CAgIwLhx49guh3wEwzDIysqqnwa6e/cunJycwOVy4ezsDFVVVbZLFAtFRUXYtWsX9u3bBxsbG3h7e8Pa2prOEMSYTFxIKykpgbOzM9auXUuBKyE4HA4GDRqE7777DteuXUNmZiZsbW3x+++/Q1NTs34b+4cPH7JdKitu3bqFefPmwcDAAC9evEBCQgJOnDiB4cOHU+BKMKkY6VZVVWH06NGwsbHBL7/8wnY5RATKy8sRFRWFsLAwREZGQkdHp349sKGhodSGDsMwuHDhAnx9fZGWloavvvoKCxcuRJcuXdgujTSBVE8v8Pn8+g72hw8fpqVhUqi2thaXL1+u7w+soKBQH8DDhw+XijnNmpoaHDt2DL6+vqitrcXy5csxffp0WnkjoaQ6dJctW4YbN27g7NmztBhfBjAMg/T09Pp54Pz8fLi6uoLL5cLR0VHi2hGWlpYiICAAfn5+0NPTw4oVK+Do6EiDBwkntaG7fft2BAYG4sqVK+jUqRPb5RAW5OfnIzw8HKGhoUhKSoKtrS24XC7c3NygoaEh0tcqqahGSEohcorKUMarg6qyAvS7q2KKadN3hc7Ly8OOHTvw+++/w9XVFcuXL4exsbFI6yXskcrQ/euvv+Dl5YX4+Hj06dOH7XKIGCgtLUVkZCTCwsJw9uxZGBgYwN3dHVwuF3p6ekIfN72gFLtjchF7558Oa9V1gvrHlBXkwACw01PHIltdDNVqfFfc69evw9fXF+fPn8e8efOwZMkSaGpqCl0bEU9SF7oJCQngcrk4d+4cjQ5Ig6qrqxETE4PQ0FCEh4ejQ4cO9fPAlpaWn3z6fjgxDxsjc8Cr46ORXxVwOICygjzWuOhjhqX2W48JBAKcPn0aPj4+yM/Px9KlSzFv3jx06NChGe+QiDOpCt07d+5g5MiROHjwIJycnNguh0gAgUCAlJSU+nngp0+fws3NDe7u7nBwcICKikqDz/sncLNRVSto8PGGqCjKYY3LQMyw1MarV68QFBSEbdu2QVVVFStWrMCkSZOk4sIfaZzUhO7Tp09hbW2N1atXY968eWyXQyTU33//XR/AaWlpcHBwAJfLxbhx4+qXZqUXlGJaYCKqavlNPr6yghwccBPB+3xgZWUFb29v2NjYSO0yN/I+qQjdyspKjBo1Co6Ojli/fj3b5RApUVJSgoiICISFheHChQswMjKCu7s7UlRMEJ9f0eiUwocwAgG61xUhyHNks+aSieSS+NDl8/mYOHEi1NTUcPDgQRoxkBZRVVWF6OhoBIefQazaGHAU2gh9LCUFOSSsGtXkVQ1EOkj0bcAMw8DLywuvXr1CYGAgBS5pMSoqKnBzc4P1DO9m35TAARCSWiiawohUEfsZfR8fH8TFxeHy5cto00b4kQchnyqnqOytZWHC4NUJkPO4XEQVEWki1qF77Ngx7Ny5EwkJCejYsSPb5RAp8+rVKxQUFKCgoAD5+fn1/76qOBRQa34f5jJerQiqJNJGbEM3Li4OixcvRnR0NC0eJ01WV1eHR48evRWobwZrfn4+KioqoKWlBS0tLfTu3RtaWlqwsLBAWUVPJD1tfg2qytQbmLxPLEM3OzsbU6ZMwZ9//knbjpD3MAyDkpKSRgP1yZMn6Nat21uB2r9/fzg4ONR/Tl1dvcFrBPzYv5EefadZUwzKCnLQ70E3P5D3iV3oFhUVwcXFBZs3b8bo0aPZLoewoKKiotFALSwshIqKyluB2rt3bxgbG9f/u2fPnkLvQjHZVBPbou806z0wACab0BkaeZ9YhW5FRQVcXV0xd+5cfPHFF2yXQ1pAbW0tHj58+MFALSgoAI/HeytQtbS0MGLEiLc+15LdxLq2V4LtAHWcz34i1DpdDgew11On5WKkQWITunV1dZg6dSqMjY3x/fffs10OEYJAIEBxcfF7gfpmsBYXF6N79+5vBaqBgQEcHR3rP9elSxfWlwZ+ZaeLy3dLhLwjTR6L7HRboCoiDcQidBmGwaJFi8Dn87Fnzx7Wf+FIw8rKyhoN1MLCQnTo0OGtQO3duzfMzc3rP9ejRw+J6D0wVEsNa1z0hey9oI8hmo13GyOySyx++jdt2oTk5GTExsbSbrAsqa6uRmFhYaNzqXw+/71Atbe3r/+cpqYm2rZty/ZbEZnX3cKa22WMkDexHrqHDx9GQEAAEhISqNVdCxEIBCgqKmowUF///eLFC/Ts2fOtQB06dCjc3NzqP1ZTU5O5s5AZltoYoqkG/5hcXLpdDA7+ufHhtdf9dO311LHITpdGuOSjWO29cPHiRXz++ee4ePEiBg0a1GKvI80YhkFpaWmjgfro0SN06tTpvTWpb/6toaEBeXl5tt+OWHtWUY2Q1ELkPC5HGa8WqsqK0O/RAZNNmr5zBJFujfVeYG2km5mZiWnTpuH48eMUuI2oqqpCYWHhBwM1Pz8fcnJy7wXp2LFj6z/u1asXbXAoAl3aK+HLkTpsl0EkHCuh+/DhQ7i4uGD79u2ws7NjowSxwOfz8fjx40YDtby8HL169XorUM3MzDBhwoT6j+kWaUIkh0hD91M27isrK4OrqysWLVoEDw8PUb68WGEYBs+ePXtvDeqbfxcVFaFr165vBWq/fv1ga2tb/3G3bt1oZ1hCpIhIQrfxjfuKsC36Duz01OE5QhurPT1gbW2NVatWieKlWVNZWdlooBYUFEBJSem9udPBgwfXf9yrVy/qnEaIjGn2hbSmbNzH4deh++MExB3YKNZrNWtraz/YLOX1369evYKmpmaDF6VeX7Ci1RiEyKYWu5DWlI37GAZg5BTwXNsOR5MLWVvLyDDMW3dNNRSoT58+Rbdu3d4KUj09PYwZM6Y+UD/ULIUQQhojdOimF5RiY2ROk+7WAQBerQAbI3MwRFOtRdY0lpeXN3pff0FBAdq1a/feyNTU1LT+4x49etBNGoSQFiF06O6OyQWvrun3pQMAr44P/5hc7J3R4Oj7g2pqat67a+rdkWpNTc17gTpy5Mj6EWpLN0shhJDGCBW6JRXViL1TLFQHJuCfqYZLt4vxrKK6flWDQCDAkydPGg3UZ8+eoUePHm8FqqGhIZydnes/17lzZzrtJ4SILaFCNySl+Rvu1dXVYtI3PkD2eeTn5+Phw4fo2LHjexelLCws3jrtp7umCCGSTKjQFcXGfXzIQ7W3HrwmW6J3797Q1NSEiopKs45JCCHiTqjQLePVieTF1Xv2gYODuUiORQghkkCoW51UlUWzxpY27iOEyBqhQle/uyqUFJp3aypt3EcIkUVCJedk0+ZvuEcb9xFCZJFQoft64z5hV2bRxn2EEFkl9BzBV3a6UFYQbvkWbdxHCJFVQofu6437VBSbdgjauI8QIsuatQyBNu4jhJCmafbaL9q4jxBCPp1IFtwO0VTD3hlmtHEfIYR8RKNNzDkcTjGAB61XDiGESIU+DMOoN/RAo6FLCCFEtGjHQ0IIaUUUuoQQ0ooodAkhpBVR6BJCSCui0CWEkFb0/24XwRTdJNLyAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "giE_C33UNduf"
      },
      "source": [
        "Ici, nous avons 7 **sommets** représentés par des ronds bleus, et 9 **arêtes** représentées par des lignes noires.\n",
        "\n",
        "*Remarque : Ce graphe peut être représenté de plusieurs façons, en positionnant les sommets à des endroits différents par exemple, ou avec des arêtes qui se croisent. Cela n'a aucune importance. En exécutant à nouveau le code ci-dessus, vous obtiendrez une autre représentation du même graphe.*\n",
        "\n",
        "Il est possible de donner des noms aux sommets, et de les afficher :"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "B_m4bWaLM9AX",
        "outputId": "6736472b-62ee-4513-d8b0-17ecdf35a677"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.Graph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_node(\"E\")\n",
        "G.add_node(\"F\")\n",
        "G.add_node(\"G\")\n",
        "G.add_edge(\"A\",\"B\")\n",
        "G.add_edge(\"B\",\"F\")\n",
        "G.add_edge(\"C\",\"D\")\n",
        "G.add_edge(\"C\",\"E\")\n",
        "G.add_edge(\"C\",\"F\")\n",
        "G.add_edge(\"D\",\"E\")\n",
        "G.add_edge(\"F\",\"G\")\n",
        "G.add_edge(\"F\",\"A\")\n",
        "G.add_edge(\"G\",\"D\")\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos) # Affichage du nom des sommets\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5lo3qJsGOrsx"
      },
      "source": [
        "Un **chemin** est une suite d'arêtes qui relie deux sommets.\n",
        "\n",
        "Plusieurs chemins peuvent relier deux arêtes. Ici, E et F sont par exemple reliés par un chemin passant par C et par un autre chemin passant par D et G.\n",
        "\n",
        "On dit que le chemin passant par C est de longueur 2 et que celui passant par D et G est de longueur 3. La **longueur** est le nombre d'arrêtes parcourues pour relier deux sommets.\n",
        "\n",
        "On dit qu'un graphe est **connexe** s'il est d'un seul tenant, c'est à dire que tous les sommets du graphe sont reliés par un **chemin**. Le graphe ci-dessus est donc connexe.\n",
        "\n",
        "Cela signifie aussi qu'un graphe peut être non connexe :\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "-2Xv3FpPORoJ",
        "outputId": "bedab5c9-8a62-4e7b-d796-3281f34f23e3"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.Graph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_node(\"E\")\n",
        "G.add_node(\"F\")\n",
        "G.add_node(\"G\")\n",
        "G.add_edge(\"A\",\"B\")\n",
        "G.add_edge(\"B\",\"F\")\n",
        "G.add_edge(\"C\",\"D\")\n",
        "G.add_edge(\"C\",\"E\")\n",
        "G.add_edge(\"D\",\"E\")\n",
        "G.add_edge(\"F\",\"A\")\n",
        "G.add_edge(\"G\",\"D\")\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y61G5XEoQlXf"
      },
      "source": [
        "Un graphe peut même ne pas contenir d'arêtes :"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "whNSnosKQjOb",
        "outputId": "2a16efe5-9ac8-4b78-cf13-68d47c8e2cfc"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.Graph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_node(\"E\")\n",
        "G.add_node(\"F\")\n",
        "G.add_node(\"G\")\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lN2OnIi6Qudo"
      },
      "source": [
        "A l'inverse, si tous les sommets d'un graphe sont reliés par un arête, on dit que le graphe est **complet** :"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "7HTNAYHYQrlf",
        "outputId": "ac6aa1d5-bf00-450d-c54e-714dc93b4daf"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.Graph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_edge(\"A\",\"B\")\n",
        "G.add_edge(\"A\",\"C\")\n",
        "G.add_edge(\"A\",\"D\")\n",
        "G.add_edge(\"B\",\"C\")\n",
        "G.add_edge(\"B\",\"D\")\n",
        "G.add_edge(\"C\",\"D\")\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZYhQ7xhnSQaG"
      },
      "source": [
        "On dit que deux sommets sont **voisins** s'ils sont reliés par une arête."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "_S50F5LeSAAJ",
        "outputId": "6ec60e43-f53d-4fde-ec72-757a55413c1b"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.Graph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_edge(\"A\",\"B\")\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s8xrC8qhSaQQ"
      },
      "source": [
        "Les sommets A et B sont **voisins** alors que A et C ne sont pas **voisins**.\n",
        "\n",
        "Le **degré** d'un sommet est égal au nombre de ses voisins. \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "BoH2vQ_fSZVK",
        "outputId": "1c21a496-d7a1-48ca-ea52-fa884dd2ebd3"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.Graph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_edge(\"A\",\"B\")\n",
        "G.add_edge(\"A\",\"C\")\n",
        "G.add_edge(\"A\",\"D\")\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xr8kBRw8S9kQ"
      },
      "source": [
        "On dit que A est de **degré** 3 parce qu'il a 3 voisins (B, C, et D), et on note *deg(A) = 3*.\n",
        "\n",
        "Les sommets B, C, et D sont tous les trois de degré A : *deg(B)=deg(C)=deg(D)=1*.\n",
        "\n",
        "*Remarque : La somme des degrés d'un graphe est égale au nombre d'arêtes du graphe multiplié par 2.*\n",
        "\n",
        "On dit qu'un ensemble de sommets forme un **cycle** s'il contient un chemin dont les deux extrémités sont reliées."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "e5hVKhcqS8nV",
        "outputId": "76145e0a-9df7-4db9-fea1-ba28e6b0ab48"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.Graph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_node(\"E\")\n",
        "G.add_node(\"F\")\n",
        "G.add_node(\"G\")\n",
        "G.add_edge(\"A\",\"B\")\n",
        "G.add_edge(\"B\",\"F\")\n",
        "G.add_edge(\"C\",\"D\")\n",
        "G.add_edge(\"C\",\"E\")\n",
        "G.add_edge(\"C\",\"F\")\n",
        "G.add_edge(\"D\",\"E\")\n",
        "G.add_edge(\"F\",\"G\")\n",
        "G.add_edge(\"F\",\"A\")\n",
        "G.add_edge(\"G\",\"D\")\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pBHXWvIVUvSx"
      },
      "source": [
        "Ici, A, B, F forme un cycle de longueur 3. De même, F, C, D, G forme un cycle de longueur 4.\n",
        "\n",
        "Un **arbre** est un graphe **connexe** qui ne contient pas de **cycle**.\n",
        "\n",
        "Voici un exemple d'arbre :"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "u41YM1cVUt22",
        "outputId": "c3ccba53-dbf7-4ea1-e3d6-02d02864c130"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.Graph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_node(\"E\")\n",
        "G.add_edge(\"A\",\"B\")\n",
        "G.add_edge(\"B\",\"C\")\n",
        "G.add_edge(\"C\",\"D\")\n",
        "G.add_edge(\"C\",\"E\")\n",
        "G.add_edge(\"E\",\"F\")\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XXSAdSXGVTRB"
      },
      "source": [
        "On dit qu'un graphe est **connexe** s'il contient un **arbre couvrant**, c'est à dire s'il est possible d'obtenir un arbre inclus dans le graphe qui connecte tous les sommets de ce graphe.\n",
        "\n",
        "L'**arbre couvrant** est obtenu en supprimant les arêtes du graphe qui forment un **cycle**.\n",
        "\n",
        "Prenons un graphe en exemple :"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "BmwKyqi9VSJo",
        "outputId": "d806d5f0-d3bc-45b1-ad7c-14d1af85a9c5"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.Graph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_node(\"E\")\n",
        "G.add_node(\"F\")\n",
        "G.add_node(\"G\")\n",
        "G.add_edge(\"A\",\"B\")\n",
        "G.add_edge(\"B\",\"F\")\n",
        "G.add_edge(\"C\",\"D\")\n",
        "G.add_edge(\"C\",\"E\")\n",
        "G.add_edge(\"C\",\"F\")\n",
        "G.add_edge(\"D\",\"E\")\n",
        "G.add_edge(\"F\",\"G\")\n",
        "G.add_edge(\"F\",\"A\")\n",
        "G.add_edge(\"G\",\"D\")\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F6x2yQ9HWQlA"
      },
      "source": [
        "Par exemple, en supprimant les arêtes (A,B), (D,G), et (D,E), nous obtenons un arbre :"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "8GkKaj6qWPwr",
        "outputId": "d2f7ef05-aafe-477d-99be-bd0db7fbfd16"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.Graph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_node(\"E\")\n",
        "G.add_node(\"F\")\n",
        "G.add_node(\"G\")\n",
        "# G.add_edge(\"A\",\"B\")\n",
        "G.add_edge(\"B\",\"F\")\n",
        "G.add_edge(\"C\",\"D\")\n",
        "G.add_edge(\"C\",\"E\")\n",
        "G.add_edge(\"C\",\"F\")\n",
        "# G.add_edge(\"D\",\"E\")\n",
        "G.add_edge(\"F\",\"G\")\n",
        "G.add_edge(\"F\",\"A\")\n",
        "# G.add_edge(\"G\",\"D\")\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iVI0-qL5ZWyn"
      },
      "source": [
        "Nous avons ici un **arbre couvrant** et notre graphe est donc **connexe**.\n",
        "\n",
        "Si l'on donne une **orientation** aux arêtes, nous obtenons un **graphe orienté**."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "KKL77gHjj7-k",
        "outputId": "513fb55c-5409-4a2a-c346-a4ee033d541f"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.DiGraph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_node(\"E\")\n",
        "G.add_node(\"F\")\n",
        "G.add_node(\"G\")\n",
        "G.add_edge(\"A\",\"B\")\n",
        "G.add_edge(\"B\",\"F\")\n",
        "G.add_edge(\"C\",\"D\")\n",
        "G.add_edge(\"C\",\"E\")\n",
        "G.add_edge(\"C\",\"F\")\n",
        "G.add_edge(\"D\",\"E\")\n",
        "G.add_edge(\"F\",\"G\")\n",
        "G.add_edge(\"F\",\"A\")\n",
        "G.add_edge(\"G\",\"D\")\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gpwylKYxkDkS"
      },
      "source": [
        "Un **graphe orienté** peut contenir des **circuits**."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "ctSRM9pikBQa",
        "outputId": "c6a4b647-277a-435f-85c4-23c539e69e70"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.DiGraph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_edge(\"A\",\"B\")\n",
        "G.add_edge(\"B\",\"C\")\n",
        "G.add_edge(\"C\",\"D\")\n",
        "G.add_edge(\"D\",\"A\")\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vJI879fjkhmZ"
      },
      "source": [
        "Si un **graphe orienté** ne contient pas de **circuit**, il peut représenter un ordre d'exécution (recette, notice, ...)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "NMdiKoYukcbB",
        "outputId": "625827c3-a9c1-4020-de6d-20a1f36e44a0"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.DiGraph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_edge(\"A\",\"B\")\n",
        "G.add_edge(\"A\",\"C\")\n",
        "G.add_edge(\"B\",\"D\")\n",
        "G.add_edge(\"C\",\"E\")\n",
        "G.add_edge(\"E\",\"D\")\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mf0mSHFS8Y85"
      },
      "source": [
        "Dans le cas des **graphes orientés** :\n",
        "*   Le **degré entrant** d'un sommet est égal au nombre d'arêtes dirigées vers un sommet et est noté D⁻(D) = 2\n",
        "*   Le **degré sortant** d'un sommet est égal au nombre d'arêtes dirigées vers un sommet et est noté D⁺(D) = 0\n",
        "De manière générale, pour un somme x, on a deg(x) = D⁻(x) + D⁺(x)\n",
        "\n",
        "Il est possible d'affecter un **poids** aux arêtes. Ce poids peut par exemple représenter une distance entre deux sommets. Nous obtenons alors un graphe pondéré."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "2PzovC6nk1w6",
        "outputId": "f40266f8-c70c-4a89-9279-d01b9c07f1a7"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.Graph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_node(\"E\")\n",
        "G.add_node(\"F\")\n",
        "G.add_node(\"G\")\n",
        "G.add_edge(\"A\",\"B\", weight = 12.3)\n",
        "G.add_edge(\"B\",\"F\", weight = 6.1)\n",
        "G.add_edge(\"C\",\"D\", weight = 4.2)\n",
        "G.add_edge(\"C\",\"E\", weight = 17.0)\n",
        "G.add_edge(\"C\",\"F\", weight = 9.8)\n",
        "G.add_edge(\"D\",\"E\", weight = 3.3)\n",
        "G.add_edge(\"F\",\"G\", weight = 6.2)\n",
        "G.add_edge(\"F\",\"A\", weight = 14.5)\n",
        "G.add_edge(\"G\",\"D\", weight = 10.6)\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "labels = nx.get_edge_attributes(G,'weight')\n",
        "nx.draw_networkx_edge_labels(G,pos,edge_labels=labels)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1HdXYq7Pln3p"
      },
      "source": [
        "Enfin, un graphe peut être à la fois **orienté** et **pondéré**."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "id": "BhKMS5LHlmio",
        "outputId": "ef6f90e3-8822-44e4-81fb-9bb5cb3ff183"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = nx.DiGraph() # Nous avons remplacé Graph() par DiGraph()\n",
        "G.add_node(\"A\")\n",
        "G.add_node(\"B\")\n",
        "G.add_node(\"C\")\n",
        "G.add_node(\"D\")\n",
        "G.add_node(\"E\")\n",
        "G.add_node(\"F\")\n",
        "G.add_node(\"G\")\n",
        "G.add_edge(\"A\",\"B\", weight = 12.3)\n",
        "G.add_edge(\"B\",\"F\", weight = 6.1)\n",
        "G.add_edge(\"C\",\"D\", weight = 4.2)\n",
        "G.add_edge(\"C\",\"E\", weight = 17.0)\n",
        "G.add_edge(\"C\",\"F\", weight = 9.8)\n",
        "G.add_edge(\"D\",\"E\", weight = 3.3)\n",
        "G.add_edge(\"F\",\"G\", weight = 6.2)\n",
        "G.add_edge(\"F\",\"A\", weight = 14.5)\n",
        "G.add_edge(\"G\",\"D\", weight = 10.6)\n",
        "\n",
        "pos = nx.spring_layout(G)\n",
        "\n",
        "nx.draw_networkx_nodes(G, pos)\n",
        "nx.draw_networkx_labels(G, pos)\n",
        "nx.draw_networkx_edges(G, pos)\n",
        "\n",
        "labels = nx.get_edge_attributes(G,'weight')\n",
        "nx.draw_networkx_edge_labels(G,pos,edge_labels=labels)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}