04-fourth_assignment.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "fourth_assignment.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Jk7Uld3Nbyq_"
      },
      "source": [
        "#Fourth Assignment - Network"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "U1UA9HJ3MbWs"
      },
      "source": [
        "## Introduction"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KwP9xsi6b6nu"
      },
      "source": [
        "In this fourth assignment we are going to analyze a small network. The data was collected from Network Repository, in this [link](http://networkrepository.com/bn-mouse-visual-cortex-1.php). We are using python3.x in a Jupyter Notebook, in the end the *.py* code will be provided.\n",
        "\n",
        "Like any program in python we start by importing the necessary packages."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1tIrYPvJbpoS"
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.dates as mdates\n",
        "import networkx as nx\n",
        "from collections import Counter\n",
        "import seaborn; seaborn.set()\n",
        "\n",
        "%matplotlib inline "
      ],
      "execution_count": 188,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HzciVmrLfKXx"
      },
      "source": [
        "I was having some problem to open the data file. So I imported my network manually as a python list, as showed below"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sV92rWOZerFg"
      },
      "source": [
        "data  = [[1,14], [2,17], [2,18], [2,19],[2,20], [2,21], [2,28],[3,16],[3,17], [3,18], [5,1],\n",
        "         [5,13], [5,15], [5,16], [5,28],[6,15], [7,3],  [7,20],[7,21],[7,22], [8,22], [9,0],\n",
        "         [9,16], [9,19], [9,22], [9,23],[9,24], [9,25], [9,26],[9,28],[10,13],[10,22],[10,24],\n",
        "         [10,25],[10,26],[10,27],[11,0],[11,23],[11,27],[12,0],[12,1],[12,4], [12,14],[12,28]]"
      ],
      "execution_count": 189,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bz7eKE1f8hGQ"
      },
      "source": [
        "Visualizing our network using the NetworkX library"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 520
        },
        "id": "x-f0VnUAoMAp",
        "outputId": "7348f781-b157-48f3-f9a9-8844d858a948"
      },
      "source": [
        "G = nx.Graph()\n",
        "\n",
        "G.add_edges_from(data)\n",
        "\n",
        "fig, ax = plt.subplots(figsize=(16, 9))\n",
        "\n",
        "nx.draw(G, with_labels=True)\n",
        "plt.show()"
      ],
      "execution_count": 231,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1152x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wyb2BTzkKlqz"
      },
      "source": [
        "Retrieving some information"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7Mo20Kn0Knmh",
        "outputId": "01d4e133-2bd9-4c85-b1a8-15fbc9ad77fa"
      },
      "source": [
        "G.number_of_nodes()"
      ],
      "execution_count": 191,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "29"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 191
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4DZRxpIYKsiP",
        "outputId": "d64cb178-daed-425b-8ab5-db464b44ea97"
      },
      "source": [
        "G.number_of_edges()"
      ],
      "execution_count": 192,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "44"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 192
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sr-Zi267CcLU"
      },
      "source": [
        "##Clustering"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DZy3dSa5GeYf"
      },
      "source": [
        "We are interested in find our local and global cluster coeficients. The local coeficient is given by [[1]](https://en.wikipedia.org/wiki/Clustering_coefficient)\n",
        "\n",
        "\\begin{aligned}\n",
        "    C_i = \\frac{2N_c}{N_n(N_n - 1)}\n",
        "\\end{aligned}\n",
        "\n",
        "where $i$ is the index of the node, $N_c$ is the number of all connections (edges) and $N_n$ is number of possible connections between neighbors (nodes). It represents how close its neighbours are to being a network. We can also define our global cluster coeficient. Which is given by the average of our local cluster coeficients\n",
        "\n",
        "\\begin{aligned}\n",
        "    \\bar{C} = \\frac{1}{n} \\sum_{i=1}^{n}C_i\n",
        "\\end{aligned}\n",
        "\n",
        "where $n$ is the total number of nodes and $C_i$ is the local cluster coeficient, as given above."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y6TIdfvYI33z"
      },
      "source": [
        "Coding functions for both equations"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0tVkxNPHnhpy"
      },
      "source": [
        "def local_clustering(G, nodes=None):\n",
        "    td_iter = _triangles_and_degree_iter(G, nodes)\n",
        "    clusterc = {v: 0 if t == 0 else t / (d * (d - 1)) for v, d, t, _ in td_iter}\n",
        "    if nodes in G:\n",
        "        return clusterc[nodes]\n",
        "    return clusterc"
      ],
      "execution_count": 193,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "avesuhjdEweJ"
      },
      "source": [
        "def global_clustering(localc):\n",
        "    c1 = 0\n",
        "    c2 = 0\n",
        "\n",
        "    for name, dict_ in localc.items():\n",
        "        c1 += dict_\n",
        "        c2 +=1\n",
        "\n",
        "    return c1/c2"
      ],
      "execution_count": 194,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xXfVHshLI_rp"
      },
      "source": [
        "Then, evaluating the local cluster coeficient of our network"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DLP--BWdCR1A",
        "outputId": "937acb7b-ad0f-44c7-b40f-f5dc9bae429e"
      },
      "source": [
        "lc = local_clustering(G)\n",
        "\n",
        "for name, dict_ in lc.items():\n",
        "    if dict_ != 0:\n",
        "        print(\"Node: \", name, \"\\n C_i\", dict_,\"\\n\")"
      ],
      "execution_count": 195,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Node:  1 \n",
            " C_i 0.3333333333333333 \n",
            "\n",
            "Node:  14 \n",
            " C_i 1.0 \n",
            "\n",
            "Node:  12 \n",
            " C_i 0.1 \n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gblGvQA2JeOo"
      },
      "source": [
        "and, the global cluster coeficient"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6L_NUI1cJjCX",
        "outputId": "172c066a-aeda-411f-e125-064b10aeee6a"
      },
      "source": [
        "gc = global_clustering(lc)\n",
        "\n",
        "print(\"Global Cluster Coeficient:\", gc)"
      ],
      "execution_count": 196,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Global Cluster Coeficient: 0.04942528735632184\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OA3Z7gzNKHag"
      },
      "source": [
        "We find that, of 29 nodes only three have $C_i \\neq 0$. The nodes are 1, 12 and 14. We also find that our global cluster coeficient is\n",
        "\n",
        "\\begin{aligned}\n",
        "    \\bar{C} = 0.049\n",
        "\\end{aligned}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9TEMsXBMebdB"
      },
      "source": [
        "##Average Shortest Distance"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WIa42TMSeoRc"
      },
      "source": [
        "We can define the Average Shortest Distance of our Network, which is given by [[2]](https://en.wikipedia.org/wiki/Average_path_length).\n",
        "\n",
        "\\begin{aligned}\n",
        "    l_g = \\frac{1}{n(n - 1)}\\sum_{i \\neq j} d(v_1,v_2)\n",
        "\\end{aligned}\n",
        "\n",
        "where $n$ is the number of edges and $d(v_1,v_2)$ is the distance between two nodes. We use $d(v_1,v_2) = 0$ if they have no connection. The average shortest distance distinguishes an easily negotiable network from one, which is complicated and inefficient, with a shorter average path length being more desirable.\n",
        "\n",
        "Defining a code function for our $l_g$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WIE1gbHlQBYO"
      },
      "source": [
        "def average_shortest_distance(G):\n",
        "    n = len(G)\n",
        "    s = sum(l for u in G for l in nx.single_source_shortest_path_length(G, u).values())\n",
        "    return s / (n *(n-1))"
      ],
      "execution_count": 197,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ede0AiLEgL2G"
      },
      "source": [
        "evaluating"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BF5hi_DCQ6Js",
        "outputId": "db7ffdc9-4e59-4a13-cbef-8b4b4a9f3b9e"
      },
      "source": [
        "print(average_shortest_distance(G))"
      ],
      "execution_count": 198,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "2.9408866995073892\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eD82KErjg2nR"
      },
      "source": [
        "We find that our Average Shortest Distance is\n",
        "\n",
        "\\begin{aligned}\n",
        "    l_g = 2.941\n",
        "\\end{aligned}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JVUl0fd7hqsx"
      },
      "source": [
        "## Centrality"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BbaKaXR_ka3t"
      },
      "source": [
        "Centrality is how much connections a node have [[3]](https://en.wikipedia.org/wiki/Centrality). We convert those numbers into a 0-1 scale. Here is how we can do this in coding"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-W3DlPokh1NL"
      },
      "source": [
        "def centrality(G):\n",
        "    if len(G) <= 1:\n",
        "        return {n: 1 for n in G}\n",
        "\n",
        "    s = 1.0 / (len(G) - 1.0)\n",
        "    centrality = {n: d * s for n, d in G.degree()}\n",
        "    return centrality"
      ],
      "execution_count": 199,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CNJO3F1pq_RH"
      },
      "source": [
        "evaluating for each node"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "J7DifsOkh6fl",
        "outputId": "5293ccc0-158a-4a82-814a-2d4b78e2475a"
      },
      "source": [
        "cnt = centrality(G)\n",
        "cnt"
      ],
      "execution_count": 201,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{0: 0.10714285714285714,\n",
              " 1: 0.10714285714285714,\n",
              " 2: 0.21428571428571427,\n",
              " 3: 0.14285714285714285,\n",
              " 4: 0.03571428571428571,\n",
              " 5: 0.17857142857142855,\n",
              " 6: 0.03571428571428571,\n",
              " 7: 0.14285714285714285,\n",
              " 8: 0.03571428571428571,\n",
              " 9: 0.3214285714285714,\n",
              " 10: 0.21428571428571427,\n",
              " 11: 0.10714285714285714,\n",
              " 12: 0.17857142857142855,\n",
              " 13: 0.07142857142857142,\n",
              " 14: 0.07142857142857142,\n",
              " 15: 0.07142857142857142,\n",
              " 16: 0.10714285714285714,\n",
              " 17: 0.07142857142857142,\n",
              " 18: 0.07142857142857142,\n",
              " 19: 0.07142857142857142,\n",
              " 20: 0.07142857142857142,\n",
              " 21: 0.07142857142857142,\n",
              " 22: 0.14285714285714285,\n",
              " 23: 0.07142857142857142,\n",
              " 24: 0.07142857142857142,\n",
              " 25: 0.07142857142857142,\n",
              " 26: 0.07142857142857142,\n",
              " 27: 0.07142857142857142,\n",
              " 28: 0.14285714285714285}"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 201
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_MuiHCReiHmU"
      },
      "source": [
        "##Assortativity\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ad6m-Hmmn9pH"
      },
      "source": [
        "The assortativity coefficient is the Pearson correlation coefficient of degree between pairs of linked nodes. Negative values indicate relationships between nodes of different degree, while positive values of $r$ reveals a correlation between nodes of similar degree. $r \\in [-1:1]$. When$r = −1$ the network is completely disassortative, when $r = 1$ the network is said to have perfect assortative mixing patterns and when $r = 0$ the network is non-assortative. The assortativity coefficient is given by [[4]](https://en.wikipedia.org/wiki/Assortativity)\n",
        "\n",
        "\\begin{aligned}\n",
        "    r = \\frac{\\sum_{i,j} ij(e_{ij} - q_i q_j)}{\\sigma^2_q}\n",
        "\\end{aligned}\n",
        "\n",
        "The term $q_{i}$ is the distribution of the remaining degree, $q_i$ is the degree distribution and $e_{ij}$ refers to the joint probability distribution. For this one I could not make a code, so I used the NetworkX function."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "E9VsS40eiUzV",
        "outputId": "443ccfea-452f-4b98-9358-84d939ed4776"
      },
      "source": [
        "r = nx.degree_assortativity_coefficient(G)\n",
        "\n",
        "print(r)"
      ],
      "execution_count": 229,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-0.4708960803161382\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xYrCldJop3vg"
      },
      "source": [
        "We obtain that\n",
        "\n",
        "\\begin{aligned}\n",
        "    r = -0.471\n",
        "\\end{aligned}\n",
        "\n",
        "which is a negative value, meaning that our network is likely to be disassortative."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rERcvvG2qVuR"
      },
      "source": [
        "##Last Comments"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qZusAixdj6qC"
      },
      "source": [
        "I really enjoyed this class. I learned a lot and I worked a lot. I would like to say thanks to Prof. Carlo Requião and to my classmates.\n",
        "\n",
        "If you want to download the *.py* or the *.ipynb* there is some link below.\n",
        "\n",
        "\n",
        "[Python Code](http://lief.if.ufrgs.br/~pedhmendes/cadeiras/econofisica/fourth_assignment.py)\n",
        "\n",
        "[Jupyter Notebook Code](http://lief.if.ufrgs.br/~pedhmendes/cadeiras/econofisica/fourth_assignment.ipynb)"
      ]
    }
  ]
}