{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "collapsed": true,
        "id": "ekE63q5G6nZk"
      },
      "outputs": [],
      "source": [
        "import warnings\n",
        "warnings.filterwarnings('ignore')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        },
        "id": "kvkvopfY6nZm",
        "outputId": "091d8e1d-b2d3-4a25-c76d-1dfc26f32fe7"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import networkx as nx\n",
        "\n",
        "G = nx.cubical_graph()\n",
        "\n",
        "pos = nx.spring_layout(G)  # positions for all nodes\n",
        "\n",
        "# nodes\n",
        "nx.draw_networkx_nodes(G, pos,\n",
        "                       nodelist=[0, 1, 2, 3],\n",
        "                       node_color='r',\n",
        "                       node_size=500,\n",
        "                       alpha=0.8)\n",
        "nx.draw_networkx_nodes(G, pos,\n",
        "                       nodelist=[4, 5, 6, 7],\n",
        "                       node_color='b',\n",
        "                       node_size=500,\n",
        "                       alpha=0.8)\n",
        "\n",
        "# edges\n",
        "nx.draw_networkx_edges(G, pos, width=0.5, alpha=1)\n",
        "nx.draw_networkx_edges(G, pos,\n",
        "                       edgelist=[(0, 1), (1, 2), (2, 3), (3, 0)],\n",
        "                       width=8, alpha=0.5, edge_color='r')\n",
        "nx.draw_networkx_edges(G, pos,\n",
        "                       edgelist=[(4, 5), (5, 6), (6, 7), (7, 4)],\n",
        "                       width=8, alpha=0.5, edge_color='b')\n",
        "\n",
        "\n",
        "# some math labels\n",
        "labels = {}\n",
        "labels[0] = r'$a$'\n",
        "labels[1] = r'$b$'\n",
        "labels[2] = r'$c$'\n",
        "labels[3] = r'$d$'\n",
        "labels[4] = r'$\\alpha$'\n",
        "labels[5] = r'$\\beta$'\n",
        "labels[6] = r'$\\gamma$'\n",
        "labels[7] = r'$\\delta$'\n",
        "nx.draw_networkx_labels(G, pos, labels, font_size=16)\n",
        "\n",
        "plt.axis('off')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        },
        "id": "r5Tvyih96nZn",
        "outputId": "1dd5c44a-7e9f-40b1-e095-a9e0d02448b7"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import networkx as nx\n",
        "\n",
        "\n",
        "G=nx.DiGraph()\n",
        "# Add nodes by specifying their positions\n",
        "G.add_node('10', pos=(2, 10))\n",
        "G.add_node('9',  pos=(4, 9))\n",
        "G.add_node('8',  pos=(0, 13))\n",
        "G.add_node('7',  pos=(1.5, 4))\n",
        "G.add_node('6',  pos=(4, 4))\n",
        "G.add_node('5',  pos=(6, 11))\n",
        "G.add_node('3',  pos=(6, 6))\n",
        "G.add_node('0',  pos=(0, 0))\n",
        "# Add edges by defining weight and label\n",
        "G.add_edge('10','9',weight=1, label='+')\n",
        "G.add_edge('10','8',weight=1, label='-')\n",
        "G.add_edge('10','7',weight=1, label='-')\n",
        "G.add_edge('9','3', weight=1, label='+')\n",
        "G.add_edge('9','6',weight=1, label='+')\n",
        "G.add_edge('9','5',weight=1, label='+')\n",
        "G.add_edge('7','0',weight=1, label='+')\n",
        "G.add_edge('7','6',weight=0, label='-')\n",
        "G.add_edge('6','3',weight=0, label='-')\n",
        "G.add_edge('5','3',weight=0, label='-')\n",
        "\n",
        "\n",
        "elarge=[(u,v) for (u,v,d) in G.edges(data=True) if d['label'] =='+'] # solid edge\n",
        "esmall=[(u,v) for (u,v,d) in G.edges(data=True) if d['label'] == '-'] # dashed edge\n",
        "\n",
        "# Retrieve the positions from graph nodes and save to a dictionary\n",
        "pos=nx.get_node_attributes(G,'pos')\n",
        "# Draw nodes\n",
        "nx.draw_networkx_nodes(G,pos,node_size=700, node_color='orange')\n",
        "\n",
        "# Draw edges\n",
        "nx.draw_networkx_edges(G,pos,edgelist=elarge, width=2, edge_color='g')\n",
        "nx.draw_networkx_edges(G,pos,edgelist=esmall, width=3,\n",
        "                       alpha=0.5,edge_color='b', arrows=False,style='dashed')\n",
        "\n",
        "# Draw node labels\n",
        "nx.draw_networkx_labels(G,pos,font_size=18,font_family='sans-serif')\n",
        "\n",
        "# Draw edge labels\n",
        "edge_labels =dict([((u, v), d['label']) for u, v, d in G.edges(data=True)])\n",
        "nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels)\n",
        "\n",
        "plt.axis('off')\n",
        "plt.savefig(\"communication_authority_graph.pdf\", format='pdf') # save as eps\n",
        "plt.show() # display"
      ]
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.6.0"
    },
    "colab": {
      "provenance": []
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}