Mouse_Brain_Network.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Mouse     Brain Network.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "_cEJ_VP6zw0C"
      ],
      "toc_visible": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "a0cIWJ0Q6uwN",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cd53f5b1-07f4-44d3-848f-df453a8b69bc"
      },
      "source": [
        "import networkx as nx\n",
        "import numpy as np\n",
        "from statsmodels.distributions.empirical_distribution import ECDF\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import poisson"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N9CQ5U69NH67"
      },
      "source": [
        "Networkx è una libreria che permette di lavorare con i grafi e di svolgere analisi di rete. [Documentazione](https://networkx.org/)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tMovcnBp7D1w"
      },
      "source": [
        "brain = nx.read_edgelist(\"/content/bn-mouse-kasthuri_graph_v4.edges\")"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F6cte6D-7ir1"
      },
      "source": [
        "## Numero di nodi e archi\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ATA9HKRG7mUO",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "79cd1180-bf6c-4687-9361-3ff0c54a6189"
      },
      "source": [
        "len(brain.nodes)"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1029"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tG-EhQX87qpd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f676ffab-7102-43fc-f772-2fb1bbd1b15c"
      },
      "source": [
        "len(brain.edges)"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1559"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PGl_ORDB8CT4"
      },
      "source": [
        "## Density"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WdOk515KKVcM"
      },
      "source": [
        "Calcoliamo la densità della rete"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2s6cge7F7zrg",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "090c0a92-f93e-4998-febb-1fea2f175303"
      },
      "source": [
        "density = nx.density(brain)\n",
        "density"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0029475937123042656"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EGDrUq6q8J6e"
      },
      "source": [
        "La rete non è sparsa quanto quella tipicamente di un social network (10<sup>-6</sup>) ma è comunque molto sparsa"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_cEJ_VP6zw0C"
      },
      "source": [
        "# 1 - Degree Distribution"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KggMOlpQz3pB"
      },
      "source": [
        " Media, mediana, deviazione standard, range interquartile, minimo e massimo sono dei buoni indici per riassumere la distribuzione."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mCUB1d0Zz4Nb"
      },
      "source": [
        "degrees = list(dict(brain.degree()).values())"
      ],
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uCqwqNBB1YSM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "af500186-0115-4ac3-cd80-81643611fd3d"
      },
      "source": [
        "print('Mean degree: \\t​​​​'+ str(np.mean(degrees)))\n",
        "print('Standard deviation: ​​​​' + str(np.std(degrees)))\n",
        "print('Median: ' + str(np.median(degrees)))\n",
        "print('iqr: ' + str(np.quantile(degrees, 0.75) - np.quantile(degrees, 0.25)))\n",
        "print('Min: ​​​​' + str(np.min(degrees)))\n",
        "print('Max: ​​​​' + str(np.max(degrees)))\n"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mean degree: \t​​​​3.0301263362487854\n",
            "Standard deviation: ​​​​6.286646968804228\n",
            "Median: 2.0\n",
            "iqr: 2.0\n",
            "Min: ​​​​1\n",
            "Max: ​​​​123\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f3wn9jOH3Dcb"
      },
      "source": [
        "Nelle reti scale free la media è molto più alta della mediana per via degli hub (sono outliers). Nel nostro caso invece i due valori sono vicini ma non coincidono, il che può essere un campanello d'allarme che si tratti di una rete broad-scale."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kAn1RCPg4CQo"
      },
      "source": [
        "Costruiamo il random graph (grafo di Erdos and Renyi) relativo al brain network in analisi e che avrà la distribuzione dei single scale (binomiale - Poisson).\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b2Q7aOBj27MF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1b5a1127-a99d-4330-912d-e9425cc7038a"
      },
      "source": [
        "random_graph_erdos = nx.fast_gnp_random_graph(len(brain.nodes), nx.density(brain))\n",
        "len(random_graph_erdos.nodes), len(random_graph_erdos.edges)"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1029, 1603)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3x-gZKE35jMJ"
      },
      "source": [
        "random_degrees = list(dict(random_graph_erdos.degree()).values())"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RTx8_Yis5goH",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 309
        },
        "outputId": "888d0b13-17fc-4205-bc12-ea1a275ab107"
      },
      "source": [
        "cdf = ECDF(degrees)\n",
        "x = np.unique(degrees)\n",
        "y = cdf(x)\n",
        "\n",
        "cdf_random = ECDF(random_degrees)\n",
        "x_random = np.unique(random_degrees)\n",
        "y_random = cdf_random(x_random)\n",
        " \n",
        "fig_cdf_fb = plt.figure(figsize=(8,4))\n",
        "axes = fig_cdf_fb.gca()\n",
        "axes.set_xscale('log')\n",
        "axes.set_yscale('log')\n",
        "axes.loglog(x,1-y,marker='o',ms=8, linestyle='--')\n",
        "axes.loglog(x_random,1-y_random,marker='+',ms=10, linestyle='--')\n",
        "axes.set_xlabel('Degree',size=20)\n",
        "axes.set_ylabel('ECCDF', size = 20)"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'ECCDF')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oH9GKOKx6T1K"
      },
      "source": [
        "La distribuzione dei gradi dei nodi del grafo random è quella stampata in arancione, mentre la distribuzione dei gradi dei nodi del brain network del topo è stampata in blu.\r\n",
        "\r\n",
        "La distribuzione del grafo random segue la distribuzione di Poisson, e non riesce a catturare i  piccoli hub del grafo, la cui presenza è evidenziata dalla distribuzione del grafo originario.\r\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KLyxiU3G6xSl"
      },
      "source": [
        "Ma pare pareto? Non mi pare. Gli hub anche se non sono catturati dalla poisson non distano troppo da essa, sono solo di un ordine di grandezza maggiore rispetto alla media calcolata prima. Per questo motivo non si tratta neanche di una rete scale-free ed è sensato dire che stiamo lavorando con una rete broad-scale"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NErp5KN9SlBg"
      },
      "source": [
        "Per chi si chiede come mai il plot della distribuzione sia stato fatto usando l'eccdf e la scala loglog, e non un semplice barplot, consiglio di consultare il libro *Network Science* di Barabasi sezione 4.12 argomento avanzato 3b."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nHNX_kip7kw2"
      },
      "source": [
        "Invece per chi è dubbioso che quella plottata prima sia una Poissoniana:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gXADqUu524MW",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "6416fdc5-89c2-46a8-bbf3-bce6c51f9cee"
      },
      "source": [
        "mu = np.mean(degrees)\n",
        "x = np.arange(poisson.ppf(0.01, mu),poisson.ppf(0.99, mu))\n",
        "prob = poisson.cdf(x, mu) \n",
        "\n",
        "mu_random = np.mean(random_degrees)\n",
        "x_random = np.arange(poisson.ppf(0.01, mu_random),poisson.ppf(0.99, mu_random))\n",
        "prob_random = poisson.cdf(x_random, mu_random) \n",
        " \n",
        "\n",
        "fig_cdf_fb = plt.figure(figsize=(8,4))\n",
        "axes = fig_cdf_fb.gca()\n",
        "axes.plot(x,prob,marker='o',ms=8, linestyle='--')\n",
        "axes.plot(x_random,prob_random,marker='+',ms=10, linestyle='--')\n",
        "axes.set_ylabel('CDF', size = 20)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'CDF')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bam25okQsY7X"
      },
      "source": [
        "# 2 - Connectivity"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C5_wDFeLswSP"
      },
      "source": [
        "E' un grafo connesso?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MldeTaeZsod9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "200fff77-a948-46d7-90fd-7e6c37b73f0b"
      },
      "source": [
        "nx.is_connected(brain)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "False"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WSOR0mzAs1FF"
      },
      "source": [
        "## C'è una giant component?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "srpwe1WtsYC6"
      },
      "source": [
        "components =  nx.connected_components(brain)\n",
        "component_list = list(components)"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eHYL2GrZupiH"
      },
      "source": [
        "Numero delle componenti connesse:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OtrF2sGEuGjw",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "644f985d-ad90-4a03-eab5-dc58b22e542b"
      },
      "source": [
        "len(component_list)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "20"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wlJIh7OIUPv0"
      },
      "source": [
        "Tracciamo l'ECDF della distribuzione delle size delle componenti connesse"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9iy8WqizuohW",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        },
        "outputId": "5e4bc21d-8eab-4a23-fd5c-b99349bcac62"
      },
      "source": [
        "sorted_components = sorted(component_list, key = lambda x : len(x), reverse=True)\n",
        "len_of_components = list ( map ( lambda x :  len(x) ,sorted_components ))\n",
        "ecdf = ECDF(len_of_components)\n",
        "plt.step(np.log(ecdf.x),ecdf.y, color = 'r', linewidth = 5)\n"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:4: RuntimeWarning: invalid value encountered in log\n",
            "  after removing the cwd from sys.path.\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f9f29f8e518>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        },
        {
          "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": {
        "id": "0TbIoVtGUZ2o"
      },
      "source": [
        "Il grafico evidenzia la presenza di una componente connessa che contiene più dell'80% dei nodi."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LbCFXlE0yJz6"
      },
      "source": [
        "#3 - Small World"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ikl8VaqUyR-C"
      },
      "source": [
        "Calcoliamo il diametro della giant component e non dell'intera rete perchè la distanza tra due nodi non connessi è infinito e quindi avremmo un errore sul calcolo del diametro"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3RjsLEj-yXM1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d6d06750-bc34-466b-bb72-39a6478c4651"
      },
      "source": [
        "giant_component = brain.subgraph(sorted_components[0])\n",
        "nx.diameter(giant_component)"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "12"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "39vaFu-Wzg2Y"
      },
      "source": [
        "Ci conferma che non è proprio small world."
      ]
    }
  ]
}