graph_mining_lab.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "graph_mining_lab.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "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": "3.7.4"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/djambar/courses/blob/master/graph_mining_lab.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "5jlpTuZyRaqn"
      },
      "source": [
        "<center><h2>DSSP<br>Lab: 27/06/2020<br>Graph Mining using Python<br></h2>G. Nikolentzos, C. Xypolopoulos, M. Vazirgiannis</center>\n",
        "\n",
        "## 1. Description\n",
        "The goal of this lab is to work with graph (or network) data using the [NexworkX](http://networkx.github.io/) library of Python. We will use this library to perform data analytics tasks on graphs. The lab is divided into three parts.\n",
        "In the first part, we will analyze a collaboration network. Then, we will implement a well-known algorithm to reveal the community structure of a simple network. Finally, we will use graph kernels to measure the similarity between graphs and to perform graph classification.\n",
        "\n",
        "## 2. Analyzing a Real-World Graph\n",
        "In the first part of the lab, we will analyze the `CA-GrQc` collaboration network, examining several structural properties. Arxiv GR-QC (General Relativity and Quantum Cosmology) collaboration network comes from the e-print arXiv and covers scientific collaborations between authors of papers submitted to General Relativity and Quantum Cosmology category. If an author $i$ co-authored a paper with another author $j$, the graph contains an undirected edge from $i$ to $j$. \n",
        "\n",
        "The graph is stored in the `CA-GrQc.txt` file as an edge list. Below you can see the first lines of the file.\n",
        "\n",
        "``` html\n",
        "# Directed graph (each unordered pair of nodes is saved once): CA-GrQc.txt \n",
        "# Collaboration network of Arxiv General Relativity category (there is an \n",
        "edge if authors coauthored at least one paper)\n",
        "# Nodes: 5242 Edges: 28980\n",
        "# FromNodeId\tToNodeId\n",
        "3466\t937\n",
        "3466\t5233\n",
        "...\n",
        "```\n",
        "\n",
        "Your first task is to load the network data into a *directed* graph $G$, using the [`read_edgelist()`](https://networkx.github.io/documentation/stable/reference/readwrite/generated/networkx.readwrite.edgelist.read_edgelist.html) function of NetworkX. Note that the delimeter used to separate values is the tab character '\\t' and additionaly, the text that follows the '#' character corresponds to comments. The general syntax of the function is the following:\n",
        "\n",
        "    G = read_edgelist(path, comments='#', delimiter='\\t', create_using=nx.Graph())\n",
        "    \n",
        "<u>Tasks</u>:\n",
        "- Load the dataset using the `read_edgelist()` function.\n",
        "- Print the number of nodes and the number of the edges of the dataset (use the [`number_of_nodes()`](https://networkx.github.io/documentation/stable/reference/classes/generated/networkx.DiGraph.number_of_nodes.html#networkx.DiGraph.number_of_nodes) and [`number_of_edges()`](https://networkx.github.io/documentation/stable/reference/classes/generated/networkx.DiGraph.number_of_edges.html#networkx.DiGraph.number_of_edges) functions of NetworkX)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "nqRKLYzURaqp",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 86
        },
        "outputId": "05d09eed-c1cd-4d61-b38f-de314a2f505c"
      },
      "source": [
        "import networkx as nx\n",
        "import urllib\n",
        "\n",
        "G = nx.read_edgelist(urllib.request.urlopen('http://www.db-net.aueb.gr/nikolentzos/dssp/graph_mining/data/CA-GrQc.txt'), comments='#', delimiter='\\t', create_using=nx.Graph())\n",
        "\n",
        "print(\"Number of nodes:\", G.number_of_nodes())\n",
        "print(\"Number of edges:\", G.number_of_edges())\n",
        "\n",
        "to_delete = list()\n",
        "for edge in G.edges():\n",
        "  if edge[0] == edge[1]:\n",
        "    to_delete.append(edge)\n",
        "\n",
        "for edge in to_delete:\n",
        "  G.remove_edge(edge[0], edge[1])\n",
        "\n",
        "print(\"Number of nodes after removing self-loops:\", G.number_of_nodes())\n",
        "print(\"Number of edges after removing self-loops::\", G.number_of_edges())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Number of nodes: 5242\n",
            "Number of edges: 14496\n",
            "Number of nodes after removing self-loops: 5242\n",
            "Number of edges after removing self-loops:: 14484\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Hq1y1g_4Raq2"
      },
      "source": [
        "We will next compute the number of connected components of the graph, and extract the largest connected component. A connected component is a subgraph in which any two vertices are connected to each other by paths.\n",
        "\n",
        "<u>Tasks</u>:\n",
        "- Compute the number of connected components of the graph (use the [`number_connected_components()`](https://networkx.github.io/documentation/stable/reference/algorithms/generated/networkx.algorithms.components.number_connected_components.html#networkx.algorithms.components.number_connected_components) function of NetworkX)\n",
        "- Extract the largest connected component and print its number of nodes and number of the edges (use the [`connected_components()`](https://networkx.github.io/documentation/stable/reference/algorithms/generated/networkx.algorithms.components.connected_components.html#networkx.algorithms.components.connected_components) and [`subgraph()`](https://networkx.github.io/documentation/stable/reference/classes/generated/networkx.Graph.subgraph.html) functions of NetworkX).\n",
        "- What is the proportion of nodes that belong to the largest connected component?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "AUoGRxN3Raq7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 86
        },
        "outputId": "b40c40c4-7749-487f-f31d-8581879f6686"
      },
      "source": [
        "print(\"Number of connected components:\", nx.number_connected_components(G))\n",
        "\n",
        "largest_cc = max(nx.connected_components(G), key=len)\n",
        "print(\"Number of nodes in giant connected component:\", len(largest_cc))\n",
        "\n",
        "GC = G.subgraph(largest_cc)\n",
        "print(\"Number of edges of giant component:\", GC.number_of_edges())\n",
        "print(\"Proportion of nodes in giant connected component:\", len(largest_cc)/G.number_of_nodes())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Number of connected components: 355\n",
            "Number of nodes in giant connected component: 4158\n",
            "Number of edges of giant component: 13422\n",
            "Proportion of nodes in giant connected component: 0.7932086989698588\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "T8Xp0z4mRarE"
      },
      "source": [
        "We will next analyze the degree distribution of the graph.\n",
        "\n",
        "<u>Tasks</u>:\n",
        "- Run the following code to extract the degree sequence of the graph."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "H8FGxz_zRarH",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "504f5e81-fe4d-4923-dc8a-73a3ccabb468"
      },
      "source": [
        "degree_sequence = list(dict(GC.degree()).values())\n",
        "print(degree_sequence)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[8, 5, 2, 5, 13, 10, 17, 3, 4, 8, 3, 34, 7, 10, 2, 17, 25, 8, 1, 21, 29, 3, 2, 14, 12, 11, 4, 20, 1, 4, 2, 24, 13, 8, 6, 4, 18, 7, 1, 1, 16, 32, 9, 10, 22, 23, 1, 7, 16, 23, 6, 2, 2, 32, 9, 7, 1, 4, 3, 2, 6, 5, 6, 4, 2, 3, 3, 30, 17, 9, 25, 9, 68, 31, 15, 9, 31, 68, 5, 13, 11, 22, 21, 20, 25, 4, 9, 9, 6, 20, 13, 14, 27, 8, 3, 7, 13, 14, 9, 4, 63, 81, 30, 77, 22, 4, 37, 1, 2, 9, 1, 6, 6, 1, 2, 4, 18, 18, 2, 2, 4, 19, 11, 2, 2, 5, 7, 2, 2, 1, 7, 1, 3, 16, 2, 6, 3, 5, 4, 5, 1, 10, 3, 11, 20, 21, 18, 18, 9, 2, 8, 4, 21, 2, 9, 5, 2, 62, 18, 12, 10, 11, 1, 12, 5, 13, 4, 7, 4, 5, 3, 2, 11, 3, 12, 13, 2, 1, 3, 12, 4, 1, 3, 3, 33, 7, 4, 5, 10, 12, 3, 10, 6, 3, 9, 11, 2, 2, 2, 4, 5, 8, 10, 4, 3, 30, 2, 8, 5, 7, 7, 12, 16, 10, 3, 2, 2, 7, 3, 49, 7, 3, 8, 12, 11, 13, 18, 10, 26, 9, 12, 2, 6, 2, 12, 2, 11, 8, 22, 26, 13, 12, 38, 19, 2, 4, 11, 11, 14, 17, 29, 27, 15, 11, 30, 5, 21, 49, 42, 48, 55, 56, 47, 65, 45, 49, 1, 54, 45, 43, 1, 46, 45, 56, 45, 49, 45, 77, 48, 4, 57, 45, 46, 60, 45, 4, 66, 45, 47, 45, 45, 45, 47, 79, 67, 48, 6, 47, 53, 51, 56, 51, 7, 1, 31, 4, 16, 1, 4, 6, 4, 2, 5, 22, 14, 3, 5, 6, 7, 4, 26, 1, 9, 22, 2, 3, 3, 3, 1, 3, 3, 20, 7, 5, 5, 3, 7, 4, 8, 8, 7, 26, 5, 14, 33, 8, 2, 11, 21, 2, 15, 22, 4, 16, 4, 2, 7, 22, 3, 5, 6, 31, 2, 30, 11, 1, 3, 28, 22, 5, 3, 8, 15, 26, 17, 5, 8, 2, 8, 3, 1, 1, 7, 4, 3, 12, 13, 3, 18, 5, 6, 6, 6, 3, 25, 18, 23, 16, 7, 9, 9, 9, 3, 1, 4, 2, 7, 1, 13, 1, 13, 6, 1, 2, 1, 17, 24, 19, 6, 3, 3, 3, 3, 10, 3, 3, 3, 16, 6, 9, 7, 9, 16, 7, 10, 15, 8, 3, 10, 1, 1, 5, 5, 15, 4, 28, 4, 17, 5, 5, 3, 4, 26, 4, 12, 1, 3, 5, 11, 16, 25, 4, 19, 8, 4, 5, 2, 4, 13, 3, 12, 2, 4, 1, 3, 10, 3, 3, 2, 2, 11, 2, 2, 1, 2, 8, 13, 3, 3, 15, 17, 3, 17, 15, 22, 9, 17, 17, 12, 20, 9, 17, 17, 17, 5, 8, 17, 8, 3, 7, 9, 5, 13, 3, 2, 4, 2, 14, 16, 30, 13, 17, 7, 6, 8, 8, 2, 24, 16, 7, 7, 14, 4, 20, 9, 9, 17, 6, 24, 8, 44, 6, 18, 10, 6, 9, 2, 3, 3, 5, 8, 2, 2, 18, 3, 6, 4, 4, 3, 8, 1, 2, 8, 2, 16, 8, 10, 8, 2, 1, 11, 2, 45, 16, 1, 1, 10, 10, 2, 1, 2, 1, 8, 17, 7, 6, 6, 6, 8, 1, 2, 1, 2, 10, 12, 5, 2, 3, 3, 3, 5, 19, 1, 3, 12, 13, 6, 10, 8, 14, 19, 7, 3, 7, 6, 15, 7, 15, 11, 3, 6, 3, 11, 34, 2, 9, 6, 2, 9, 5, 8, 5, 11, 6, 3, 3, 10, 2, 6, 4, 14, 4, 1, 1, 2, 11, 3, 35, 7, 2, 3, 4, 4, 10, 10, 2, 3, 5, 5, 2, 8, 7, 2, 6, 17, 3, 3, 1, 2, 23, 3, 3, 22, 2, 19, 13, 8, 3, 33, 14, 12, 6, 8, 4, 1, 1, 10, 15, 9, 3, 4, 8, 1, 12, 2, 2, 7, 10, 5, 1, 11, 11, 2, 7, 5, 3, 3, 1, 9, 3, 1, 1, 6, 9, 4, 6, 1, 1, 7, 2, 11, 2, 12, 7, 4, 4, 1, 1, 3, 3, 3, 7, 2, 15, 5, 23, 1, 12, 15, 3, 3, 10, 12, 8, 6, 5, 20, 15, 5, 6, 3, 1, 2, 2, 1, 2, 13, 6, 2, 3, 1, 8, 14, 10, 3, 19, 3, 2, 4, 2, 3, 5, 8, 3, 4, 3, 1, 4, 28, 4, 2, 37, 7, 2, 2, 6, 1, 2, 11, 4, 1, 1, 8, 5, 2, 15, 5, 10, 2, 1, 4, 3, 3, 5, 2, 20, 2, 7, 1, 7, 4, 3, 16, 2, 4, 1, 2, 2, 2, 3, 3, 3, 3, 2, 3, 2, 3, 10, 5, 4, 2, 4, 9, 4, 2, 21, 7, 9, 10, 4, 2, 5, 7, 4, 10, 6, 3, 11, 10, 1, 10, 7, 5, 6, 1, 3, 2, 2, 7, 5, 5, 15, 3, 13, 4, 2, 8, 17, 11, 18, 7, 11, 6, 6, 4, 2, 2, 1, 6, 2, 2, 2, 2, 2, 2, 3, 1, 3, 9, 4, 4, 3, 2, 8, 5, 6, 2, 1, 12, 14, 4, 4, 10, 4, 7, 4, 1, 3, 13, 3, 5, 10, 8, 9, 17, 2, 6, 4, 3, 9, 9, 2, 5, 4, 3, 10, 6, 13, 7, 6, 7, 10, 1, 1, 10, 3, 1, 1, 1, 20, 6, 2, 3, 6, 3, 5, 6, 5, 5, 3, 13, 2, 4, 19, 3, 3, 8, 16, 12, 9, 13, 6, 5, 5, 21, 13, 11, 3, 10, 25, 12, 3, 3, 18, 3, 4, 4, 7, 3, 1, 1, 15, 2, 2, 9, 1, 14, 4, 1, 4, 3, 2, 4, 4, 15, 2, 19, 3, 6, 1, 8, 5, 6, 3, 15, 6, 3, 1, 14, 7, 2, 14, 2, 9, 12, 8, 8, 28, 4, 3, 9, 12, 45, 5, 12, 21, 7, 5, 5, 6, 5, 1, 2, 4, 2, 1, 3, 6, 1, 1, 2, 15, 5, 4, 2, 10, 5, 1, 2, 2, 3, 25, 9, 10, 17, 19, 10, 6, 7, 10, 12, 10, 2, 1, 28, 9, 9, 17, 7, 4, 12, 3, 3, 26, 10, 8, 27, 14, 10, 3, 7, 6, 3, 9, 5, 7, 1, 2, 9, 3, 2, 2, 3, 2, 3, 7, 7, 3, 3, 9, 2, 2, 10, 17, 9, 8, 3, 6, 3, 3, 1, 1, 2, 1, 1, 1, 2, 10, 2, 5, 2, 3, 15, 4, 1, 2, 2, 1, 1, 10, 5, 6, 1, 9, 2, 1, 4, 1, 9, 8, 7, 6, 6, 10, 6, 6, 10, 2, 5, 2, 3, 3, 1, 6, 3, 4, 7, 3, 12, 7, 6, 15, 8, 10, 5, 7, 3, 5, 1, 1, 1, 5, 1, 2, 3, 2, 1, 5, 3, 7, 2, 2, 5, 6, 3, 2, 2, 5, 3, 2, 1, 2, 8, 4, 7, 13, 5, 4, 4, 4, 3, 2, 2, 11, 7, 3, 3, 4, 21, 8, 8, 3, 10, 5, 1, 3, 2, 13, 30, 4, 2, 3, 3, 5, 2, 3, 8, 6, 1, 7, 2, 4, 5, 2, 1, 1, 4, 3, 42, 42, 42, 42, 42, 31, 42, 33, 42, 42, 42, 33, 31, 42, 41, 43, 42, 33, 31, 42, 42, 59, 33, 34, 41, 42, 42, 42, 36, 34, 31, 33, 42, 42, 2, 41, 31, 33, 34, 5, 40, 4, 5, 4, 5, 4, 6, 6, 4, 2, 6, 2, 11, 1, 6, 6, 4, 19, 10, 5, 8, 4, 5, 5, 2, 3, 6, 3, 7, 8, 7, 6, 2, 3, 6, 2, 6, 4, 2, 3, 3, 3, 10, 2, 6, 4, 2, 8, 1, 5, 7, 11, 3, 8, 2, 11, 2, 5, 1, 3, 6, 2, 3, 2, 9, 17, 21, 7, 7, 3, 3, 5, 1, 10, 1, 8, 1, 5, 1, 3, 3, 3, 1, 6, 2, 1, 4, 2, 4, 7, 5, 2, 5, 3, 17, 2, 4, 5, 2, 3, 3, 3, 19, 2, 1, 13, 1, 2, 7, 3, 2, 3, 4, 2, 4, 3, 2, 2, 2, 4, 2, 16, 3, 5, 3, 2, 1, 1, 2, 1, 7, 7, 7, 7, 7, 8, 1, 9, 2, 1, 3, 9, 1, 3, 3, 8, 1, 1, 5, 2, 8, 4, 1, 4, 2, 2, 1, 5, 2, 1, 1, 1, 2, 2, 7, 10, 3, 12, 2, 1, 5, 11, 2, 6, 4, 4, 6, 10, 4, 7, 4, 4, 3, 3, 6, 3, 10, 1, 2, 1, 6, 3, 2, 4, 2, 6, 6, 4, 4, 6, 4, 1, 5, 4, 1, 2, 22, 4, 5, 5, 1, 3, 2, 5, 9, 6, 11, 2, 4, 2, 3, 6, 8, 1, 4, 6, 2, 1, 4, 11, 2, 2, 4, 1, 4, 2, 7, 4, 3, 5, 3, 1, 4, 14, 2, 7, 6, 2, 10, 7, 12, 5, 3, 13, 2, 18, 5, 1, 13, 3, 7, 5, 2, 17, 6, 2, 2, 8, 2, 3, 2, 5, 8, 3, 14, 12, 3, 5, 5, 6, 5, 5, 5, 3, 9, 3, 3, 4, 10, 10, 12, 3, 3, 2, 3, 2, 4, 2, 6, 1, 6, 4, 8, 4, 2, 3, 2, 2, 1, 4, 4, 21, 4, 11, 6, 2, 1, 3, 7, 3, 13, 3, 3, 8, 4, 8, 4, 19, 7, 4, 3, 1, 1, 16, 5, 2, 2, 1, 2, 2, 5, 4, 1, 4, 2, 4, 2, 1, 1, 6, 3, 2, 2, 3, 5, 3, 3, 2, 7, 2, 2, 2, 2, 4, 1, 2, 4, 4, 4, 3, 2, 2, 1, 1, 11, 4, 2, 3, 2, 1, 1, 2, 2, 2, 1, 1, 5, 1, 2, 10, 9, 1, 9, 9, 2, 1, 9, 2, 3, 3, 12, 13, 6, 4, 4, 3, 5, 6, 2, 1, 2, 7, 2, 2, 16, 2, 32, 6, 5, 8, 1, 1, 1, 9, 4, 1, 1, 4, 4, 6, 3, 3, 2, 11, 5, 5, 5, 5, 1, 1, 8, 4, 3, 6, 3, 2, 1, 3, 3, 1, 4, 5, 12, 11, 3, 4, 6, 2, 2, 2, 2, 2, 10, 7, 3, 3, 2, 9, 3, 3, 3, 12, 3, 10, 5, 4, 4, 4, 4, 4, 1, 15, 9, 1, 8, 9, 1, 1, 12, 1, 4, 1, 8, 1, 3, 18, 7, 7, 6, 4, 1, 2, 11, 4, 5, 4, 8, 4, 13, 13, 1, 2, 1, 4, 1, 6, 3, 4, 3, 2, 6, 2, 9, 3, 1, 2, 3, 3, 2, 2, 1, 2, 7, 3, 3, 13, 4, 4, 4, 6, 3, 8, 1, 1, 5, 2, 8, 2, 3, 4, 3, 3, 4, 1, 4, 3, 6, 2, 4, 2, 2, 11, 4, 9, 5, 9, 4, 5, 5, 3, 3, 3, 5, 6, 5, 5, 4, 5, 13, 11, 5, 7, 1, 1, 1, 1, 13, 2, 9, 8, 1, 3, 1, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 37, 17, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 1, 2, 2, 2, 6, 3, 5, 6, 2, 2, 2, 3, 6, 3, 2, 2, 3, 3, 2, 2, 3, 2, 6, 1, 2, 6, 3, 2, 2, 3, 4, 5, 3, 1, 2, 2, 1, 5, 2, 2, 6, 11, 5, 4, 3, 3, 4, 6, 3, 6, 1, 2, 1, 1, 5, 24, 3, 3, 3, 13, 3, 5, 6, 5, 4, 5, 15, 5, 2, 3, 3, 10, 8, 6, 6, 23, 3, 7, 1, 8, 5, 3, 3, 2, 4, 4, 2, 7, 3, 2, 6, 6, 2, 1, 1, 1, 2, 1, 4, 3, 1, 7, 12, 2, 2, 23, 9, 4, 2, 2, 4, 2, 3, 2, 1, 1, 2, 4, 1, 1, 4, 1, 3, 4, 3, 2, 7, 2, 2, 2, 2, 2, 1, 1, 2, 3, 2, 1, 7, 2, 7, 4, 5, 1, 2, 3, 5, 2, 2, 4, 1, 3, 2, 4, 3, 1, 6, 4, 3, 5, 5, 3, 15, 1, 9, 1, 8, 1, 24, 18, 2, 10, 8, 3, 2, 5, 5, 2, 2, 3, 2, 1, 2, 3, 13, 2, 2, 2, 1, 3, 3, 2, 4, 5, 1, 1, 2, 2, 1, 2, 1, 2, 1, 13, 1, 6, 11, 1, 19, 2, 5, 1, 1, 3, 1, 1, 4, 4, 4, 7, 3, 7, 6, 6, 1, 7, 1, 1, 1, 1, 1, 2, 2, 1, 1, 6, 8, 1, 1, 1, 2, 1, 1, 5, 1, 2, 3, 2, 1, 25, 2, 2, 1, 5, 4, 6, 1, 4, 4, 2, 11, 1, 2, 9, 4, 4, 4, 6, 3, 6, 14, 2, 3, 3, 4, 3, 2, 2, 5, 2, 2, 2, 1, 5, 13, 6, 8, 3, 3, 3, 3, 2, 4, 3, 1, 1, 3, 6, 12, 3, 12, 2, 1, 1, 14, 8, 2, 2, 1, 3, 3, 2, 3, 2, 1, 6, 1, 3, 3, 2, 1, 1, 6, 18, 6, 6, 5, 5, 7, 3, 3, 3, 1, 4, 10, 6, 3, 2, 8, 8, 1, 1, 2, 1, 1, 2, 3, 3, 3, 3, 4, 1, 1, 3, 2, 3, 5, 2, 1, 3, 5, 8, 3, 2, 3, 2, 2, 7, 4, 5, 2, 2, 6, 5, 3, 3, 3, 2, 1, 3, 5, 2, 1, 1, 10, 4, 4, 3, 4, 3, 1, 1, 1, 1, 3, 2, 7, 4, 3, 7, 3, 9, 3, 3, 2, 5, 3, 4, 1, 2, 3, 5, 1, 5, 8, 2, 5, 4, 3, 1, 3, 4, 10, 4, 7, 10, 2, 2, 4, 4, 3, 3, 10, 1, 2, 1, 1, 1, 8, 2, 2, 4, 4, 6, 4, 4, 4, 1, 3, 2, 4, 3, 3, 2, 3, 4, 5, 6, 6, 4, 3, 3, 3, 3, 1, 5, 3, 3, 7, 2, 2, 2, 5, 14, 4, 9, 4, 4, 1, 2, 2, 4, 2, 2, 2, 2, 3, 8, 3, 4, 10, 4, 1, 5, 1, 3, 3, 3, 2, 3, 1, 3, 4, 2, 4, 2, 2, 2, 4, 8, 1, 2, 6, 8, 6, 1, 3, 2, 3, 13, 3, 3, 1, 6, 11, 13, 4, 2, 2, 7, 10, 9, 3, 9, 4, 7, 4, 4, 4, 2, 2, 9, 9, 9, 3, 3, 7, 4, 3, 9, 12, 3, 3, 3, 6, 1, 2, 2, 2, 3, 5, 11, 1, 12, 3, 1, 1, 2, 2, 1, 3, 2, 1, 2, 1, 3, 3, 5, 2, 4, 2, 3, 2, 1, 4, 2, 2, 1, 3, 2, 4, 1, 1, 2, 2, 4, 2, 9, 13, 9, 9, 9, 4, 5, 3, 6, 2, 2, 2, 2, 2, 7, 11, 3, 10, 2, 1, 2, 1, 4, 8, 4, 3, 8, 6, 6, 3, 2, 2, 3, 2, 14, 14, 8, 14, 18, 14, 14, 14, 14, 14, 2, 14, 2, 14, 14, 14, 14, 4, 4, 1, 1, 9, 2, 7, 5, 4, 4, 2, 4, 4, 6, 4, 4, 4, 1, 5, 7, 1, 4, 2, 8, 3, 2, 4, 1, 1, 1, 1, 1, 8, 1, 3, 5, 4, 3, 2, 4, 3, 2, 6, 2, 5, 2, 3, 3, 3, 1, 1, 13, 5, 5, 3, 5, 4, 2, 6, 1, 5, 1, 1, 4, 5, 4, 4, 3, 7, 4, 1, 8, 8, 3, 2, 4, 5, 2, 3, 5, 6, 3, 2, 10, 2, 8, 24, 2, 2, 3, 1, 3, 6, 1, 4, 1, 2, 2, 1, 1, 1, 3, 9, 4, 3, 3, 1, 4, 1, 2, 3, 1, 4, 15, 2, 1, 2, 3, 3, 4, 2, 3, 6, 3, 2, 2, 1, 3, 3, 4, 5, 1, 5, 4, 4, 3, 1, 2, 5, 4, 3, 3, 3, 2, 4, 8, 2, 2, 3, 2, 7, 1, 1, 2, 1, 3, 1, 5, 4, 6, 4, 3, 4, 5, 3, 1, 2, 1, 6, 3, 5, 1, 1, 4, 3, 4, 3, 4, 5, 8, 7, 4, 3, 2, 4, 1, 1, 1, 2, 1, 1, 1, 7, 6, 1, 5, 3, 1, 3, 4, 1, 2, 3, 1, 6, 5, 1, 5, 2, 2, 1, 1, 4, 4, 3, 3, 6, 4, 4, 20, 8, 2, 3, 9, 4, 2, 2, 2, 3, 8, 1, 15, 3, 2, 4, 3, 3, 2, 2, 1, 1, 2, 4, 4, 2, 4, 4, 2, 4, 4, 1, 4, 4, 1, 1, 5, 2, 2, 1, 1, 6, 3, 3, 3, 3, 2, 2, 3, 6, 2, 1, 3, 3, 4, 1, 1, 8, 8, 4, 8, 8, 4, 8, 8, 2, 4, 1, 2, 2, 5, 1, 2, 3, 3, 2, 1, 4, 5, 1, 8, 2, 2, 1, 4, 1, 2, 2, 2, 2, 2, 17, 2, 1, 3, 3, 1, 1, 9, 8, 4, 7, 10, 2, 7, 1, 7, 4, 4, 5, 10, 7, 1, 1, 1, 1, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2, 1, 7, 4, 2, 5, 1, 5, 18, 1, 8, 3, 3, 6, 2, 1, 7, 1, 3, 1, 1, 29, 1, 3, 2, 2, 8, 1, 2, 2, 1, 2, 2, 1, 2, 4, 1, 3, 2, 2, 6, 3, 4, 5, 1, 3, 3, 2, 3, 1, 2, 2, 2, 2, 3, 3, 13, 4, 37, 4, 7, 10, 12, 6, 2, 3, 4, 3, 5, 2, 6, 3, 2, 3, 11, 7, 8, 8, 10, 8, 7, 7, 2, 4, 4, 6, 3, 3, 5, 3, 3, 1, 2, 1, 3, 3, 1, 4, 3, 5, 5, 1, 2, 1, 3, 1, 3, 1, 5, 6, 6, 9, 9, 3, 2, 3, 1, 2, 3, 2, 1, 1, 4, 4, 4, 11, 13, 4, 3, 5, 3, 3, 1, 2, 3, 1, 2, 3, 1, 4, 3, 1, 4, 11, 4, 4, 1, 4, 4, 2, 2, 3, 2, 3, 3, 1, 1, 2, 2, 5, 1, 3, 3, 1, 1, 4, 5, 4, 5, 4, 3, 3, 2, 1, 3, 2, 6, 5, 1, 18, 14, 14, 7, 7, 3, 1, 1, 9, 2, 3, 1, 4, 10, 1, 1, 2, 1, 1, 3, 3, 3, 1, 4, 2, 2, 2, 2, 3, 3, 2, 1, 2, 2, 2, 6, 1, 1, 5, 1, 1, 1, 3, 4, 6, 3, 3, 5, 1, 2, 2, 1, 2, 1, 3, 1, 1, 4, 4, 2, 4, 2, 3, 4, 3, 3, 10, 3, 3, 3, 2, 3, 3, 3, 3, 3, 1, 1, 2, 4, 5, 2, 3, 2, 3, 3, 1, 4, 4, 6, 6, 3, 5, 3, 1, 2, 1, 1, 1, 1, 1, 1, 5, 1, 1, 2, 7, 4, 5, 4, 4, 3, 4, 3, 3, 2, 1, 1, 6, 4, 4, 1, 2, 3, 3, 2, 2, 3, 2, 2, 6, 7, 1, 1, 1, 1, 2, 2, 1, 2, 2, 3, 3, 3, 3, 5, 6, 3, 5, 4, 5, 4, 3, 3, 2, 1, 2, 2, 3, 3, 1, 3, 3, 1, 1, 8, 2, 1, 3, 4, 3, 3, 2, 1, 6, 2, 5, 3, 1, 3, 3, 2, 3, 11, 2, 5, 4, 3, 2, 4, 3, 5, 4, 3, 1, 5, 2, 5, 2, 2, 5, 2, 6, 2, 3, 1, 10, 8, 2, 5, 1, 5, 5, 2, 2, 5, 3, 3, 4, 9, 7, 7, 7, 7, 8, 8, 14, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 4, 4, 2, 3, 3, 1, 4, 7, 3, 2, 3, 3, 7, 4, 3, 7, 1, 2, 3, 13, 13, 19, 13, 1, 13, 13, 13, 15, 13, 13, 13, 15, 1, 2, 4, 1, 2, 1, 2, 4, 4, 4, 1, 8, 1, 2, 2, 2, 2, 2, 3, 1, 3, 3, 6, 8, 5, 2, 10, 2, 2, 1, 2, 1, 2, 2, 2, 2, 1, 1, 3, 1, 15, 11, 15, 15, 11, 4, 15, 4, 11, 11, 11, 4, 4, 10, 1, 1, 2, 2, 8, 3, 3, 3, 3, 4, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 4, 1, 1, 1, 2, 6, 5, 4, 4, 6, 4, 1, 2, 4, 3, 1, 1, 2, 2, 6, 5, 4, 30, 10, 16, 23, 23, 23, 19, 23, 23, 23, 21, 23, 23, 23, 23, 4, 23, 21, 24, 23, 23, 3, 21, 21, 19, 23, 3, 3, 1, 2, 2, 1, 1, 6, 3, 1, 3, 1, 3, 3, 3, 1, 8, 5, 1, 2, 2, 3, 1, 3, 3, 2, 7, 3, 2, 3, 7, 6, 3, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 3, 3, 3, 2, 4, 4, 4, 2, 2, 2, 1, 3, 3, 3, 1, 3, 1, 2, 2, 1, 3, 3, 3, 3, 2, 4, 4, 4, 4, 3, 3, 1, 1, 5, 3, 9, 2, 3, 2, 5, 4, 2, 2, 3, 3, 3, 3, 1, 2, 1, 1, 5, 2, 1, 1, 1, 1, 1, 1, 7, 2, 1, 2, 1, 1, 1, 4, 4, 4, 4, 1, 1, 2, 2, 2, 4, 3, 1, 1, 2, 2, 2, 1, 2, 5, 1, 2, 3, 5, 2, 1, 2, 4, 3, 3, 2, 3, 2, 6, 6, 2, 3, 2, 5, 5, 5, 10, 5, 11, 5, 11, 5, 5, 3, 2, 1, 1, 2, 34, 34, 34, 34, 34, 34, 34, 36, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 37, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 3, 3, 3, 2, 1, 1, 3, 6, 2, 4, 1, 1, 3, 2, 1, 3, 2, 1, 5, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 4, 1, 3, 1, 1, 1, 1, 1, 1, 2, 5, 4, 4, 4, 1, 5, 3, 3, 2, 3, 13, 4, 6, 4, 8, 3, 4, 4, 4, 7, 4, 4, 3, 3, 1, 2, 3, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 4, 2, 3, 2, 3, 3, 3, 1, 1, 1, 1, 6, 3, 3, 4, 5, 2, 4, 2, 2, 2, 1, 2, 1, 3, 3, 3, 3, 3, 3, 3, 9, 1, 2, 1, 4, 1, 7, 3, 1, 3, 4, 1, 1, 1, 2, 3, 3, 3, 8, 3, 3, 4, 2, 2, 2, 3, 2, 2, 2, 1, 2, 1, 3, 1, 1, 1, 3, 4, 3, 1, 1, 2, 3, 2, 2, 4, 2, 1, 2, 1, 2, 1, 3, 3, 3, 2, 2, 1, 1, 3, 2, 2, 2, 6, 6, 6, 6, 6, 6, 3, 9, 6, 6, 2, 6, 6, 2, 7, 3, 2, 2, 5, 3, 3, 3, 2, 1, 2, 2, 1, 7, 4, 3, 4, 3, 3, 6, 1, 4, 2, 2, 2, 2, 1, 1, 7, 5, 5, 2, 2, 3, 4, 6, 2, 2, 2, 2, 2, 4, 1, 1, 2, 2, 2, 1, 5, 3, 2, 4, 2, 1, 1, 1, 2, 2, 4, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 3, 3, 2, 3, 2, 2, 1, 1, 1, 1, 1, 4, 1, 2, 2, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 2, 2, 2, 7, 7, 7, 7, 7, 1, 1, 1, 5, 1, 1, 1, 1, 3, 4, 1, 2, 1, 1, 2, 1, 4, 2, 2, 2, 2, 1, 1, 5, 1, 2, 1, 3, 3, 3, 2, 2, 1, 1, 2, 2, 1, 3, 3, 1, 1, 2, 2, 2, 2, 1, 1, 4, 2, 3, 1, 1, 2, 1, 2, 2, 2, 4, 11, 16, 16, 11, 11, 16, 16, 11, 11, 16, 10, 10, 10, 10, 10, 3, 3, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 3, 2, 2, 4, 1, 4, 4, 4, 1, 1, 3, 2, 2, 1, 9, 9, 9, 9, 9, 8, 9, 9, 2, 2, 3, 4, 5, 4, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "2-6wjrhhRarO"
      },
      "source": [
        "<u>Tasks</u>:\n",
        "- Find and print the minimum, maximum, median and mean degree of the nodes of the graph (you can use the built-in functions `min, max, median` and `mean` of the `NumPy` library)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "Wgnehlm4RarP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 86
        },
        "outputId": "b2705942-2e92-444a-ffc4-fcf26eeb3581"
      },
      "source": [
        "import numpy as np\n",
        "\n",
        "print(\"Minimum Degree:\", np.min(degree_sequence))\n",
        "print(\"Maximum Degree:\", np.max(degree_sequence))\n",
        "print(\"Median Degree:\", np.median(degree_sequence))\n",
        "print(\"Mean Degree:\", np.mean(degree_sequence))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Minimum Degree: 1\n",
            "Maximum Degree: 81\n",
            "Median Degree: 3.0\n",
            "Mean Degree: 6.455988455988456\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "DbKZYaUzRarX"
      },
      "source": [
        "Let's now compute and plot the degree distribution of the graph.\n",
        "\n",
        "<u>Tasks</u>:\n",
        "- Use the [`degree_histogram()`](https://networkx.github.io/documentation/stable/reference/generated/networkx.classes.function.degree_histogram.html#networkx.classes.function.degree_histogram) function of NetworkX to obtain a list of the frequency of each degree value.\n",
        "- Plot the degree histogram using the [`plot()`](http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.plot) function of matplotlib."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "yORrKzG2RarZ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "fc1b69b1-4a2e-40c8-f29a-c29ec9d9eae1"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "\n",
        "hist = nx.degree_histogram(GC)\n",
        "plt.plot(hist)\n",
        "plt.xlabel('degree')\n",
        "plt.ylabel('frequency')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'frequency')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "QZd91mTNRarh"
      },
      "source": [
        "<u>Tasks</u>:\n",
        "- Produce again the plot using a log-log axis (use the [`loglog()`](http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.loglog) function of matplotlib)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "xXcU2InBRari",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 303
        },
        "outputId": "9d061ac1-35d7-4b05-9590-8728d0edf053"
      },
      "source": [
        "plt.loglog(hist)\n",
        "plt.xlabel('degree')\n",
        "plt.ylabel('frequency')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'frequency')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Qcg14qDSRaro"
      },
      "source": [
        "Next, we will compute the average clustering coefficient of the graph, which is a measure of the degree to which nodes in a graph tend to cluster together, i.e., to create tightly knit groups characterized by a relatively high density of ties. The *global clustering coefficient* is based on triplets of nodes. A triplet consists of three nodes that are connected by either two (open triplet) or three (closed triplet) undirected ties. A triangle consists of three closed triplets, one centered on each of the nodes. The global clustering coefficient is the number of closed triplets (or $3$ $\\times$ triangles) over the total number of triplets (both open and closed).\n",
        "\n",
        "<u>Tasks</u>:\n",
        "- Use the [`average_clustering()`](https://networkx.github.io/documentation/stable/reference/algorithms/generated/networkx.algorithms.cluster.average_clustering.html#networkx.algorithms.cluster.average_clustering) function of NetworkX to compute the average clustering coefficient of the graph."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "4XbhWZ5jRarp",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "6bea5688-ff3d-44d1-8a0d-81b4aef94fdc"
      },
      "source": [
        "print(\"Clustering coefficient:\", nx.average_clustering(GC))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Clustering coefficient: 0.5568782161697923\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "KmBVVSNmRarv"
      },
      "source": [
        "Let's now repeat some parts of the above experiment for a random graph. A *random graph* is obtained by starting with a set of $n$ isolated vertices and adding successive edges between them at random. In our case, we will create a random graph using the Erdos-Renyi $G(n,p)$ random graph model, where the graph contains $n$ nodes and each of the edges is included with probability $p$.\n",
        "\n",
        "<u>Tasks</u>:\n",
        "- Create a random graph $R$ using the $G(1000, 0.1)$ model (i.e. 1000 nodes and $p=0.1$) (use the [`fast_gnp_random_graph()`](https://networkx.github.io/documentation/networkx-1.9.1/reference/generated/networkx.generators.random_graphs.fast_gnp_random_graph.html#networkx.generators.random_graphs.fast_gnp_random_graph) function of NetworkX)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "AYHZPRKVRarx",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "a308422c-ce78-489b-ac0a-4e8ec2ca533e"
      },
      "source": [
        "R = nx.fast_gnp_random_graph(1000, 0.01)\n",
        "\n",
        "print('Number of nodes:', R.number_of_nodes())\n",
        "print('Number of edges:', R.number_of_edges())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Number of nodes: 1000\n",
            "Number of edges: 5001\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "zNPCsNcaRar3"
      },
      "source": [
        "<u>Tasks</u>:\n",
        "- Compute again the minimum, maximum, median and mean degree of the nodes of the graph.\n",
        "- Plot the degree histogram of the graph."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "o4hMZLIqRar3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 366
        },
        "outputId": "6f14bb26-cdcc-4137-94a7-73965bd9fe25"
      },
      "source": [
        "degree_sequence = list(dict(R.degree()).values())\n",
        "\n",
        "print(\"Minimum Degree:\", np.min(degree_sequence))\n",
        "print(\"Maximum Degree:\", np.max(degree_sequence))\n",
        "print(\"Median Degree:\", np.median(degree_sequence))\n",
        "print(\"Mean Degree:\", np.mean(degree_sequence))\n",
        "\n",
        "hist = nx.degree_histogram(R)\n",
        "plt.plot(hist)\n",
        "plt.xlabel('degree')\n",
        "plt.ylabel('frequency')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Minimum Degree: 2\n",
            "Maximum Degree: 23\n",
            "Median Degree: 10.0\n",
            "Mean Degree: 9.98\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'frequency')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "9BJ439LmRar-"
      },
      "source": [
        "In order to make more clear the difference of the structural properties between real-world (e.g. social networks, collaboration networks) and random networks, we can examine additional properties similar to the case of `CA-GrQc` previously. We will focus on the clustering properties, trying to stress out that random graphs do not inherently show a clustering structure.\n",
        "\n",
        "<u>Tasks</u>:\n",
        "- Compute the average clustering coefficient of the randomly generated graph."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "_wOeul5JRar_",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "71d1b688-412a-4724-b7c1-061f107811cb"
      },
      "source": [
        "print(\"Clustering coefficient:\", nx.average_clustering(R))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Clustering coefficient: 0.009180242633183807\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VsKDE0ruxsJV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "346f8e25-0e7e-4bfb-aaa5-da6332ac63e6"
      },
      "source": [
        "Q = nx.barabasi_albert_graph(1000, 5)\n",
        "hist = nx.degree_histogram(Q)\n",
        "plt.plot(hist)\n",
        "plt.xlabel('degree')\n",
        "plt.ylabel('frequency')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'frequency')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "oULyHPRNRasd"
      },
      "source": [
        "## 3. Community Detection\n",
        "In the second part of the lab, we will focus on the community detection (or clustering) problem in graphs. Typically, a community corresponds to a set of nodes that highly interact among each other, compared to the intensity of interactions (as expressed by the number of edges) with the rest nodes of the graph. The experiments for this part will be performed in the *karate* dataset, a small dataset that has been used as a benchmark in several community detection algorithms. This dataset is a friendship social network between 34 members of a karate club at a US university in the 1970.\n",
        "\n",
        "<u>Tasks</u>:\n",
        "- Load the graph using the NetworkX library.\n",
        "- Print the number of nodes and the number of edges of the network."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "4k57PuNnRasf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "4ae76b85-f5f9-4a99-cf64-5e553213c4d8"
      },
      "source": [
        "G = nx.read_edgelist(urllib.request.urlopen('http://www.db-net.aueb.gr/nikolentzos/dssp/graph_mining/data/karate.edgelist'), comments='#', delimiter=' ', create_using=nx.Graph())\n",
        "\n",
        "print(\"Number of nodes:\", G.number_of_nodes())\n",
        "print(\"Number of edges:\", G.number_of_edges())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Number of nodes: 34\n",
            "Number of edges: 78\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "JLrTajpFRasj"
      },
      "source": [
        "We will first implement and apply a very popular graph clustering algorithm, called Spectral Clustering. The basic idea of the algorithm is to utilize information associated to the spectrum of the graph, in order to identify well-separated clusters. The pseudocode of Spectral Clustering is shown below:\n",
        "\n",
        "1. Let $\\mathbf{A}$ be the adjacency matrix of the graph\n",
        "2. Compute the Laplacian matrix $\\mathbf{L} = \\mathbf{D}−\\mathbf{A}$. Matrix $\\mathbf{D}$ corresponds to the diagonal degree matrix of graph $G$ (i.e., degree of each node $v$ (= number of neighbors) in the main diagonal)\n",
        "3. Apply eigenvalue decomposition to the Laplacian matrix $\\mathbf{L}$ and compute the eigenvectors that correspond to $k$ smallest eigenvalues. Let $\\mathbf{U} = [\\mathbf{u}_1|\\mathbf{u}_2| \\ldots |\\mathbf{u}_k] \\in \\mathbb{R}^{n \\times k}$ be the matrix containing these eigenvectors as columns\n",
        "4. For $i = 1,\\ldots,n$, let $y_i \\in \\mathbb{R}^k$ be the vector corresponding to the $i$-th row of $\\mathbf{U}$. Apply $k$-means to the points $(y_i)_{i=1,\\ldots,n}$ (i.e., the rows of $\\mathbf{U}$) and find clusters $C_1, C_2, \\ldots, C_k$\n",
        "\n",
        "<u>Tasks</u>:\n",
        "- Implement the Spectral Clustering algorithm. To compute the Laplacian matrix $\\mathbf{L}$, you can use the [`laplacian_matrix()`](https://networkx.github.io/documentation/stable/reference/generated/networkx.linalg.laplacianmatrix.laplacian_matrix.html#networkx.linalg.laplacianmatrix.laplacian_matrix) function of NetworkX. To decompose the Laplacian matrix, you can use the [`eigs()`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.eigs.html) function of SciPy. Finally, to perform k-means, you can use scikit-learn's [implementation](https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html) of the algorithm. The Spectral Clustering algorithm must return a dictionary keyed by node to the cluster to which the node belongs.\n",
        "- After implementing the algorithm, apply it to the `karate` dataset, trying to identify 2 clusters."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "fi-lT0MeRask",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        },
        "outputId": "817994be-b567-47c9-c058-51b9bb455739"
      },
      "source": [
        "from scipy.sparse.linalg import eigs\n",
        "from sklearn.cluster import KMeans\n",
        "\n",
        "def spectral_clustering(G, k):\n",
        "    \n",
        "    L = nx.laplacian_matrix(G).astype(np.float64)\n",
        "    eigvals, eigvec = eigs(L, k=k, which='SR')\n",
        "\n",
        "    #print(eigvec[:,0].real)\n",
        "    eigvec = eigvec[:,1:].real\n",
        "\n",
        "    kmeans = KMeans(n_clusters=k)\n",
        "    kmeans.fit(eigvec)\n",
        "\n",
        "    clustering = dict()\n",
        "    for i, node in enumerate(G.nodes()):\n",
        "      clustering[node] = kmeans.labels_[i]\n",
        "    \n",
        "    return clustering\n",
        "\n",
        "clustering = spectral_clustering(G, 2)\n",
        "print(clustering)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "{'1': 0, '2': 1, '3': 1, '4': 1, '5': 0, '6': 0, '7': 0, '8': 1, '9': 1, '10': 1, '11': 0, '12': 0, '13': 0, '14': 1, '17': 0, '18': 0, '20': 1, '22': 0, '24': 1, '26': 1, '25': 1, '28': 1, '29': 1, '30': 1, '27': 1, '31': 1, '32': 1, '33': 1, '15': 1, '16': 1, '19': 1, '21': 1, '23': 1, '34': 1}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "0Tl7nKkGRasp"
      },
      "source": [
        "We will next visualize the clustering result.\n",
        "\n",
        "<u>Task</u>:\n",
        "- Use the [`draw`](https://networkx.github.io/documentation/stable/reference/generated/networkx.drawing.nx_pylab.draw.html#networkx.drawing.nx_pylab.draw) function of NetworkX to visualize the `karate` network. Use the same color for all the nodes belonging to the same cluster."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "Z2LpwzTQRasq",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 336
        },
        "outputId": "8e5eb263-b278-4104-f02a-45c32646f8de"
      },
      "source": [
        "colors = [clustering[node] for node in G.nodes()]\n",
        "print(colors)\n",
        "\n",
        "nx.draw(G, node_color=colors)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n"
          ],
          "name": "stdout"
        },
        {
          "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": {
        "colab_type": "text",
        "id": "7dDdsn9jRasv"
      },
      "source": [
        "To assess the quality of a clustering algorithm, several metrics have been proposed. Modularity is one of the most popular and widely used metrics to evaluate the quality of a network's partition into communities. Considering a specific partition of the network into clusters, modularity measures the number of edges that lie within a cluster compared to the expected number of edges of a null graph (or configuration model), i.e., a random graph with the same degree distribution. In other words, the measure of modularity is built upon the idea that random graphs are not expected to present inherent community structure; thus, comparing the observed density of a subgraph with the expected density of the same subgraph in case where edges are placed randomly, leads to a community evaluation metric. Modularity is given by the following formula:\n",
        "$$ Q = \\sum^{n_c} \\Bigg[ \\frac{l_c}{m} - \\Big(\\frac{d_c}{2m}\\Big)^2\\Bigg] $$\n",
        "where, $m=|E|$ is the total number of edges in the graph, $n_c$ is the number of communities in the graph, $l_c$ is the number of edges within the community $c$ and $d_c$ is the sum of the degrees of the nodes that belong to community $c$. Modularity takes values in the range $[-1, 1]$, with higher values indicating better community structure.\n",
        "\n",
        "<u>Task</u>:\n",
        "- Implement a function that given a graph and and an assignment of nodes to clusters, computes the modularity of the clustering result. Given a set of nodes, you can use the [`subgraph()`](https://networkx.github.io/documentation/stable/reference/classes/generated/networkx.Graph.subgraph.html) function of NetworkX to extract the subgraph induced by these nodes."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "t-xKnrqTRasv",
        "colab": {}
      },
      "source": [
        "def modularity(G, clustering):\n",
        "  modularity = 0\n",
        "  m = G.number_of_edges()\n",
        "  clusters = set(clustering.values())\n",
        "\n",
        "  for cluster in clusters:\n",
        "    nodes = [node for node in G.nodes() if clustering[node]==cluster]\n",
        "    subG = G.subgraph(nodes)\n",
        "    lc = subG.number_of_edges()\n",
        "\n",
        "    dc = 0\n",
        "    for node in nodes:\n",
        "      dc += G.degree(node)\n",
        "\n",
        "    modularity += lc/m - (dc/(2*m))**2\n",
        "  \n",
        "  return modularity"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0ilVCMN28nxw",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "21e42860-4be8-4368-a0b9-bea34c3ea143"
      },
      "source": [
        "print(modularity(G, clustering))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.233974358974359\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "g2k8sldvRas0"
      },
      "source": [
        "Next, we will use modularity to compare the following two clustering results of the `karate` dataset: (i) the one obtained by the Spectral Clustering algorithm, and (ii) the one obtained if we randomly partition the nodes into 2 clusters.\n",
        "To assign each node to a cluster, use the `randint(a,b)` function which returns a random integer $n$ such that $a \\leq n \\leq b$.\n",
        "\n",
        "<u>Tasks</u>:\n",
        "- Assign the nodes of the `karate` network randomly to 2 clusters to generate a random partitioning of the network.\n",
        "- Compare the two clustering results. What is the performance of the Spectral Clustering algorithm compared to the algorithm that randomly clusters the nodes?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab_type": "code",
        "id": "3aR1g-Q6Ras0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "a2dfd4c5-f979-4db7-e039-38a4be484e3f"
      },
      "source": [
        "from random import randint\n",
        "\n",
        "random_clustering = dict()\n",
        "for node in G.nodes():\n",
        "  random_clustering[node] = randint(0,1)\n",
        "\n",
        "print(\"Modularity of random clustering:\", modularity(G, random_clustering))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Modularity of random clustering: -0.050295857988165577\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GdgmxLFl-9t9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "944d8c45-ccb0-4fed-88e4-6616b467f33f"
      },
      "source": [
        "from networkx.algorithms.community import greedy_modularity_communities\n",
        "\n",
        "c = list(greedy_modularity_communities(G))\n",
        "greedy_clustering = dict()\n",
        "for i,s in enumerate(c):\n",
        "  for node in s:\n",
        "    greedy_clustering[node] = i\n",
        "\n",
        "print(\"Modularity of greedy clustering:\", modularity(G, greedy_clustering))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Modularity of greedy clustering: 0.3806706114398422\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UQeONyOTlr6Y",
        "colab_type": "text"
      },
      "source": [
        "## 3. Graph Classification\n",
        "In the last part of the lab, we will focus on the problem of graph classification. Graph classification arises in the context of a number of classical domains such as chemical data, biological data, and the web. In order to perform graph classification, we will employ graph kernels, a powerful framework for graph comparison.\n",
        "\n",
        "Kernels can be intuitively understood as functions measuring the similarity of pairs of objects. More formally, for a function $k(x,x')$ to be a kernel, it has to be (1) symmetric: $k(x,x') = k(x',x)$, and (2) positive semi-definite. If a function satisfies the above two conditions on a set $\\mathcal{X}$, it is known that there exists a map $\\phi : \\mathcal{X} \\to \\mathcal{H}$ into a Hilbert space $\\mathcal{H}$, such that $k(x,x') = \\langle \\phi(x), \\phi(x') \\rangle$ for all $(x, x') \\in \\mathcal{X}^2$ where $\\langle\\cdot, \\cdot\\rangle$ is the inner product in $\\mathcal{H}$. Kernel functions thus compute the inner product between examples that are mapped in a higher-dimensional feature space. However, they do not necessarily explicitly compute the feature map $\\phi$ for each example. One advantage of kernel methods is that they can operate on very general types of data such as images and graphs. Kernels defined on graphs are known as *graph kernels*. Most graph kernels decompose graphs into their substructures and then to measure their similarity, they count the number of common substructures. Graph kernels typically focus on some structural aspect of graphs such as random walks, shortest paths, subtrees, cycles, and graphlets.\n",
        "\n",
        "We will first create a very simple graph classification dataset. The dataset will contain two types of graphs: (1) cycle graphs, and (2) path graphs. A cycle graph $C_n$ is a graph on $n$ nodes containing a single cycle through all nodes, while a path graph $P_n$ is a tree with two nodes of degree 1, and all the remaining $n-2$ nodes of degree 2. Each graph is assigned a class label: label 0 if it is a cycle or label 1 if it is a path. The Figure below illustrates such a dataset consisting of three cycle graphs and three path graphs.\n",
        "\n",
        "<img src=\"http://www.db-net.aueb.gr/nikolentzos/dssp/graph_mining/figures/synthetic_graphs.png\" width=\"500\"/>\n",
        "    \n",
        "<u>Task</u>:\n",
        "- Use the [`cycle_graph()`](https://networkx.github.io/documentation/stable/reference/generated/networkx.generators.classic.cycle_graph.html#networkx.generators.classic.cycle_graph) and [`path_graph()`](https://networkx.github.io/documentation/stable/reference/generated/networkx.generators.classic.path_graph.html#networkx.generators.classic.path_graph) functions of NetworkX to generate 100 cycle graphs and 100 path graphs of size $n=3,\\ldots,102$, respectively. Store the 200 graphs in a list $Gs$ and their class labels in another list $y$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yY-pmrEElr6Z",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "a91cdaaf-05e0-4ffc-d1a8-07059e5d7db3"
      },
      "source": [
        "Gs = list()\n",
        "y = list()\n",
        "\n",
        "for i in range(3, 103):\n",
        "  Gs.append(nx.cycle_graph(i))\n",
        "  y.append(0)\n",
        "\n",
        "  Gs.append(nx.path_graph(i))\n",
        "  y.append(1)\n",
        "\n",
        "print(\"Size of the dataset:\", len(Gs))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Size of the dataset: 200\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OatljsrMlr6c",
        "colab_type": "text"
      },
      "source": [
        "We will next investigate if graph kernels can distinguish cycle graphs from path graphs. To this end, we will make use of the shortest path kernel, a kernel that compares shortest path lengths in two graps. Before computing the kernel, it is necessary to split the dataset into a training and a test set. We can use the [`train_test_split()`](https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html) function of scikit-learn as follows:\n",
        "    \n",
        "    from sklearn.model_selection import train_test_split\n",
        "\n",
        "    G_train, G_test, y_train, y_test = train_test_split(Gs, y, test_size=0.1)\n",
        "    \n",
        "<u>Task</u>:\n",
        "- Split the dataset into a training and a test set."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kHFpMYAxlr6d",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "G_train, G_test, y_train, y_test = train_test_split(Gs, y, test_size=0.1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xvmHv_dIlr6j",
        "colab_type": "text"
      },
      "source": [
        "The shortest path kernel compares the length of shortest paths of two graphs. More specifically, given two graphs $G=(V,E)$ and $G'=(V',E')$, the shortest path kernel is defined as:\n",
        "\n",
        "$$\n",
        "k(G,G') = \\sum_{(v_1,v_2) \\in V \\times V} \\sum_{(v'_1,v'_2) \\in V' \\times V'} k_{length}(sp_{v_1,v_2}, sp_{v'_1,v'_2})\n",
        "$$\n",
        "\n",
        "where $k_{length}$ is a kernel on shortest path lengths, and $sp_{v_i,v_j}$ is the length of the shortest path between vertices $v_i$ and $v_j$. We will use the following kernel for comparing shortest path lengths:\n",
        "\n",
        "$$\n",
        "k_{length}(sp_{v_1,v_2}, sp_{v'_1,v'_2}) = \\left\\{\n",
        "            \\begin{array}{lr}\n",
        "                1 & \\text{if }sp_{v_1,v_2} = sp_{v'_1,v'_2},\\\\\n",
        "                0 & \\text{otherwise}\n",
        "            \\end{array}\n",
        "            \\right.\n",
        "$$\n",
        "\n",
        "Therefore, $k_{length}(sp_{v_1,v_2}, sp_{v'_1,v'_2})$ is equal to 1 if $sp_{v_1,v_2}$ and $sp_{v'_1,v'_2}$ are equal to each other, and $0$ otherwise.\n",
        "\n",
        "Below you are given a function that takes as input two sets of graphs (of sizes $N_1$ and $N_2$), and computes the kernel matrix $K \\in \\mathbb{R}^{N_1\\times N_2}$ which stores the kernel values between the graphs of the first set and those of the second set."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Fb7ABITVlr6j",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def sp_kernel(Gs1, Gs2):\n",
        "    N1 = len(Gs1)\n",
        "    N2 = len(Gs2)\n",
        "    \n",
        "    all_paths = dict()\n",
        "    sp_counts = dict()\n",
        "    \n",
        "    for i,G in enumerate(Gs1):\n",
        "        sp_lengths = dict(nx.shortest_path_length(G))\n",
        "        sp_counts[i] = dict()\n",
        "        nodes = G.nodes()\n",
        "        for v1 in nodes:\n",
        "            for v2 in nodes:\n",
        "                if v2 in sp_lengths[v1]:\n",
        "                    length = sp_lengths[v1][v2]\n",
        "                    if length in sp_counts[i]:\n",
        "                        sp_counts[i][length] += 1\n",
        "                    else:\n",
        "                        sp_counts[i][length] = 1\n",
        "\n",
        "                    if length not in all_paths:\n",
        "                        all_paths[length] = len(all_paths)\n",
        "                        \n",
        "    for i,G in enumerate(Gs2):\n",
        "        sp_lengths = dict(nx.shortest_path_length(G))\n",
        "        sp_counts[N1+i] = dict()\n",
        "        nodes = G.nodes()\n",
        "        for v1 in nodes:\n",
        "            for v2 in nodes:\n",
        "                if v2 in sp_lengths[v1]:\n",
        "                    length = sp_lengths[v1][v2]\n",
        "                    if length in sp_counts[N1+i]:\n",
        "                        sp_counts[N1+i][length] += 1\n",
        "                    else:\n",
        "                        sp_counts[N1+i][length] = 1\n",
        "\n",
        "                    if length not in all_paths:\n",
        "                        all_paths[length] = len(all_paths)\n",
        "\n",
        "    phi1 = np.zeros((N1, len(all_paths)))\n",
        "    for i in range(N1):\n",
        "        for length in sp_counts[i]:\n",
        "            phi1[i,all_paths[length]] = sp_counts[i][length]\n",
        "            \n",
        "    phi2 = np.zeros((N2, len(all_paths)))\n",
        "    for i in range(N2):\n",
        "        for length in sp_counts[N1+i]:\n",
        "            phi2[i,all_paths[length]] = sp_counts[N1+i][length]\n",
        "\n",
        "    K = np.dot(phi1,phi2.T)\n",
        "\n",
        "    return K"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zKaMhJ6mlr6n",
        "colab_type": "text"
      },
      "source": [
        "We are interested in generating two matrices. A symmetric matrix $\\mathbf{K}_{train}$ which contains the kernel values for all pairs of training graphs, and a second matrix $\\mathbf{K}_{test}$ which stores the kernel values between the graphs of the test set and those of the training set. We can obtain these two matrices very easily using the function defined above. After generating the two kernel matrices, we can use the SVM classifier to perform graph classification.\n",
        "\n",
        "<u>Tasks</u>:\n",
        "- Use the shortest path kernel to compute the $\\mathbf{K}_{train}$ and $\\mathbf{K}_{test}$ matrices.\n",
        "- Train an [SVM classifier](https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html) and use it to make predictions. Note that we have already pre-computed the kernel matrices (set parameter kernel equal to 'precomputed').  "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uHnEoGWllr6o",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "dd725d59-a1a8-48dd-f5f9-09411a061443"
      },
      "source": [
        "from sklearn.svm import SVC\n",
        "\n",
        "K_train = sp_kernel(G_train, G_train)\n",
        "print(\"Train matrix dim:\", K_train.shape)\n",
        "\n",
        "K_test = sp_kernel(G_test, G_train)\n",
        "print(\"Test matrix dim:\", K_test.shape)\n",
        "\n",
        "clf = SVC(kernel='precomputed')\n",
        "clf.fit(K_train, y_train)\n",
        "y_pred = clf.predict(K_test)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Train matrix dim: (180, 180)\n",
            "Test matrix dim: (20, 180)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aBsRQBTIlr6r",
        "colab_type": "text"
      },
      "source": [
        "Finally, we will evaluate the shortest path kernel. More specifically, we will compute its classification accuracy.\n",
        "\n",
        "<u>Tasks</u>:\n",
        "- Use the [`accuracy_score()`](https://scikit-learn.org/stable/modules/generated/sklearn.metrics.accuracy_score.html) function of scikit-learn to compute the classification accuracy of the shortest path kernel. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5572jQgulr6r",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "ededff57-faf0-4b6c-a963-951e9758aad0"
      },
      "source": [
        "from sklearn.metrics import accuracy_score\n",
        "\n",
        "print(\"Accuracy:\", accuracy_score(y_test, y_pred))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Accuracy: 1.0\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}