betweenness_!closeness_diameter.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import csv\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from multiprocessing import Pool\n",
    "import time\n",
    "import itertools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('name_name.csv', dtype={\"reps\": np.int64, \"comm\" : str, \"auth\" : str})\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>reps</th>\n",
       "      <th>auth</th>\n",
       "      <th>comm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>26</td>\n",
       "      <td>Maria Shaldibina</td>\n",
       "      <td>Stev Witzel</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>17</td>\n",
       "      <td>Eduardo Valentin</td>\n",
       "      <td>Daniel</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>24</td>\n",
       "      <td>Eric W. Biederman</td>\n",
       "      <td>geiti94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>519</td>\n",
       "      <td>Paul Jakma</td>\n",
       "      <td>Paul Jakma</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>122</td>\n",
       "      <td>Laxman Dewangan</td>\n",
       "      <td>Stephen Warren</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   reps               auth            comm\n",
       "0    26   Maria Shaldibina     Stev Witzel\n",
       "1    17   Eduardo Valentin          Daniel\n",
       "2    24  Eric W. Biederman         geiti94\n",
       "3   519         Paul Jakma      Paul Jakma\n",
       "4   122    Laxman Dewangan  Stephen Warren"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Cleaning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "345"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().values.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>reps</th>\n",
       "      <th>auth</th>\n",
       "      <th>comm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2295</th>\n",
       "      <td>225</td>\n",
       "      <td>NaN</td>\n",
       "      <td>root</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5867</th>\n",
       "      <td>24</td>\n",
       "      <td>NaN</td>\n",
       "      <td>mark</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12673</th>\n",
       "      <td>18</td>\n",
       "      <td>NaN</td>\n",
       "      <td>舒志凌</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13649</th>\n",
       "      <td>55</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Jeff Garzik</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18747</th>\n",
       "      <td>21</td>\n",
       "      <td>John Axel Eriksson</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23358</th>\n",
       "      <td>21</td>\n",
       "      <td>Fish</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25165</th>\n",
       "      <td>22</td>\n",
       "      <td>NaN</td>\n",
       "      <td>黄志伟</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27935</th>\n",
       "      <td>477</td>\n",
       "      <td>NaN</td>\n",
       "      <td>git-darcs-import</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29367</th>\n",
       "      <td>18</td>\n",
       "      <td>Lars van de Kerkhof</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29690</th>\n",
       "      <td>27</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Ease</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30927</th>\n",
       "      <td>491</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Zorba Build Bot</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34674</th>\n",
       "      <td>21</td>\n",
       "      <td>Ralf Baechle</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38869</th>\n",
       "      <td>36</td>\n",
       "      <td>NaN</td>\n",
       "      <td>James Bottomley</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47195</th>\n",
       "      <td>42</td>\n",
       "      <td>Bharat Mediratta</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47788</th>\n",
       "      <td>17</td>\n",
       "      <td>David Cramer</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48084</th>\n",
       "      <td>94</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Zsolt Zsuffa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49892</th>\n",
       "      <td>19</td>\n",
       "      <td>Alessandro Roncone</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>51842</th>\n",
       "      <td>26</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Flavio</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>53226</th>\n",
       "      <td>507</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>54115</th>\n",
       "      <td>48</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Macx</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>61682</th>\n",
       "      <td>17</td>\n",
       "      <td>Tim Almdal</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64176</th>\n",
       "      <td>485</td>\n",
       "      <td>NaN</td>\n",
       "      <td>CloudCannon</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>65894</th>\n",
       "      <td>22</td>\n",
       "      <td>Toon Verstraelen</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76792</th>\n",
       "      <td>21</td>\n",
       "      <td>NaN</td>\n",
       "      <td>李宁</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77816</th>\n",
       "      <td>74</td>\n",
       "      <td>amazonwebservices</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90434</th>\n",
       "      <td>17</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Paul Aurich</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97820</th>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>HenriDellal</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>103976</th>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>IR4T4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>108113</th>\n",
       "      <td>1</td>\n",
       "      <td>Deji69</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>111735</th>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Luke Schierer</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1466001</th>\n",
       "      <td>6</td>\n",
       "      <td>Alexander Gavrilov</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1467211</th>\n",
       "      <td>6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>geng</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1479381</th>\n",
       "      <td>6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Tobias Rundstrom</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1479809</th>\n",
       "      <td>6</td>\n",
       "      <td>gumptionthomas</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1486616</th>\n",
       "      <td>6</td>\n",
       "      <td>root</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1487108</th>\n",
       "      <td>6</td>\n",
       "      <td>Matt Zweig</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1498227</th>\n",
       "      <td>7</td>\n",
       "      <td>Andy Staudacher</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1499273</th>\n",
       "      <td>7</td>\n",
       "      <td>Jeff Finch</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1508036</th>\n",
       "      <td>7</td>\n",
       "      <td>NaN</td>\n",
       "      <td>风往北吹_</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1514632</th>\n",
       "      <td>7</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Murthy Narkedimilli</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1515742</th>\n",
       "      <td>7</td>\n",
       "      <td>Andrew Whitworth</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1530103</th>\n",
       "      <td>8</td>\n",
       "      <td>NaN</td>\n",
       "      <td>唐资富</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1531532</th>\n",
       "      <td>8</td>\n",
       "      <td>babbaj</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1537327</th>\n",
       "      <td>8</td>\n",
       "      <td>Padillla</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1545907</th>\n",
       "      <td>9</td>\n",
       "      <td>Bishakh Ghosh</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1547038</th>\n",
       "      <td>9</td>\n",
       "      <td>Mike Christie</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1548045</th>\n",
       "      <td>9</td>\n",
       "      <td>Moore, Eric</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1553713</th>\n",
       "      <td>9</td>\n",
       "      <td>sierra</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1560096</th>\n",
       "      <td>10</td>\n",
       "      <td>andrew.vasquez@qlogic.com</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1589270</th>\n",
       "      <td>12</td>\n",
       "      <td>Andrew Dutcher</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1607642</th>\n",
       "      <td>15</td>\n",
       "      <td>Michael Bayne</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1610097</th>\n",
       "      <td>15</td>\n",
       "      <td>NaN</td>\n",
       "      <td>Tarmac</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1613815</th>\n",
       "      <td>15</td>\n",
       "      <td>NaN</td>\n",
       "      <td>ChanIan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1616698</th>\n",
       "      <td>16</td>\n",
       "      <td>J. David Ibanez</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1618849</th>\n",
       "      <td>16</td>\n",
       "      <td>Damien Lebrun</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1642867</th>\n",
       "      <td>62</td>\n",
       "      <td>NaN</td>\n",
       "      <td>GitHub</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1706765</th>\n",
       "      <td>79</td>\n",
       "      <td>NaN</td>\n",
       "      <td>GitHub</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1739879</th>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>GitHub</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1894007</th>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>GitHub</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2146176</th>\n",
       "      <td>9</td>\n",
       "      <td>NaN</td>\n",
       "      <td>GitHub</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>344 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         reps                       auth                 comm\n",
       "2295      225                        NaN                 root\n",
       "5867       24                        NaN                 mark\n",
       "12673      18                        NaN                  舒志凌\n",
       "13649      55                        NaN          Jeff Garzik\n",
       "18747      21         John Axel Eriksson                  NaN\n",
       "23358      21                       Fish                  NaN\n",
       "25165      22                        NaN                  黄志伟\n",
       "27935     477                        NaN     git-darcs-import\n",
       "29367      18        Lars van de Kerkhof                  NaN\n",
       "29690      27                        NaN                 Ease\n",
       "30927     491                        NaN      Zorba Build Bot\n",
       "34674      21               Ralf Baechle                  NaN\n",
       "38869      36                        NaN      James Bottomley\n",
       "47195      42           Bharat Mediratta                  NaN\n",
       "47788      17               David Cramer                  NaN\n",
       "48084      94                        NaN         Zsolt Zsuffa\n",
       "49892      19         Alessandro Roncone                  NaN\n",
       "51842      26                        NaN               Flavio\n",
       "53226     507                        NaN                  NaN\n",
       "54115      48                        NaN                 Macx\n",
       "61682      17                 Tim Almdal                  NaN\n",
       "64176     485                        NaN          CloudCannon\n",
       "65894      22           Toon Verstraelen                  NaN\n",
       "76792      21                        NaN                   李宁\n",
       "77816      74          amazonwebservices                  NaN\n",
       "90434      17                        NaN          Paul Aurich\n",
       "97820       1                        NaN          HenriDellal\n",
       "103976      1                        NaN                IR4T4\n",
       "108113      1                     Deji69                  NaN\n",
       "111735      1                        NaN        Luke Schierer\n",
       "...       ...                        ...                  ...\n",
       "1466001     6         Alexander Gavrilov                  NaN\n",
       "1467211     6                        NaN                 geng\n",
       "1479381     6                        NaN     Tobias Rundstrom\n",
       "1479809     6             gumptionthomas                  NaN\n",
       "1486616     6                       root                  NaN\n",
       "1487108     6                 Matt Zweig                  NaN\n",
       "1498227     7            Andy Staudacher                  NaN\n",
       "1499273     7                 Jeff Finch                  NaN\n",
       "1508036     7                        NaN                风往北吹_\n",
       "1514632     7                        NaN  Murthy Narkedimilli\n",
       "1515742     7           Andrew Whitworth                  NaN\n",
       "1530103     8                        NaN                  唐资富\n",
       "1531532     8                     babbaj                  NaN\n",
       "1537327     8                   Padillla                  NaN\n",
       "1545907     9              Bishakh Ghosh                  NaN\n",
       "1547038     9              Mike Christie                  NaN\n",
       "1548045     9                Moore, Eric                  NaN\n",
       "1553713     9                     sierra                  NaN\n",
       "1560096    10  andrew.vasquez@qlogic.com                  NaN\n",
       "1589270    12             Andrew Dutcher                  NaN\n",
       "1607642    15              Michael Bayne                  NaN\n",
       "1610097    15                        NaN               Tarmac\n",
       "1613815    15                        NaN              ChanIan\n",
       "1616698    16            J. David Ibanez                  NaN\n",
       "1618849    16              Damien Lebrun                  NaN\n",
       "1642867    62                        NaN               GitHub\n",
       "1706765    79                        NaN               GitHub\n",
       "1739879     1                        NaN               GitHub\n",
       "1894007     2                        NaN               GitHub\n",
       "2146176     9                        NaN               GitHub\n",
       "\n",
       "[344 rows x 3 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nan_rows = df[df.isnull().any(1)]\n",
    "nan_rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df.dropna()\n",
    "df.isnull().values.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "graph = nx.from_pandas_edgelist(df, source = 'comm', target = 'auth', edge_attr = 'reps',create_using = nx.DiGraph())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "number_of_nodes = nx.number_of_nodes(graph)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(\"Betweenness\")\n",
    "b = nx.betweenn\n",
    "ess_centrality(graph, k=int(0.001*number_of_nodes))\n",
    "#b = betweenness_centrality_parallel(graph, 9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "len(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Diameter\n"
     ]
    }
   ],
   "source": [
    "print(\"Diameter\")\n",
    "largest = max(nx.connected_components(graph.to_undirected()), key=len)\n",
    "g = graph.to_undirected()\n",
    "removal = set(g.nodes) - largest\n",
    "g.remove_nodes_from(removal)\n",
    "dia = nx.diameter(g)\n",
    "\n",
    "print(\"Clustering\")\n",
    "avg_clust = nx.average_clustering(g, weight='weight')\n",
    "clustering = dict(nx.clustering(g))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "dia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Top X in each Centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 20\n",
    "from heapq import nlargest\n",
    "sb = nlargest(x, b, key=b.get)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Betweenness ['Jason Laster', 'Michal Frystacky', 'GitHub', 'Mark', 'Dale  Harvey', 'Roland Levillain', 'Anthony Seure', 'James Kyle', 'Pierre Krieger', 'zml', 'jdalton', 'Robert Wagner', 'Andrew Naylor', 'Olivier Louvignes', 'Nolan Lawson', 'Emilio Cobos Álvarez', 'Bryan Clark', 'Daniel Naylor', 'Teddy Zeenny', 'Sam Saccone']\n"
     ]
    }
   ],
   "source": [
    "print(\"Betweenness\", sb)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import defaultdict\n",
    "\n",
    "  \n",
    "#b\n",
    "counter_b = defaultdict(int)\n",
    "for k, v in b.items():\n",
    "    counter_b[v]+=1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Betweeness Centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.bar(counter_b.keys(), counter_b.values(), 0.05)\n",
    "lists = sorted(counter_b.items()) # sorted by key, return a list of tuples\n",
    "x, y = zip(*lists) # unpack a list of pairs into two tuples\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.xlim([0, 0.000002]);\n",
    "plt.ylim([0.00000000, 5.000000])\n",
    "plt.xlabel(\"Betweenness Centrality\", fontsize=18)\n",
    "plt.ylabel(r'$\\log_{10}(freuqncy)$', fontsize=18)\n",
    "plt.plot(x, np.log10(y))\n",
    "plt.savefig('dist_centrality_betweeness.png', bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Closeness Centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#plt.bar(counter_c.keys(), counter_c.values(), 0.05)\n",
    "lists = sorted(counter_c.items()) # sorted by key, return a list of tuples\n",
    "x, y = zip(*lists) # unpack a list of pairs into two tuples\n",
    "plt.figure(figsize=(20,10))\n",
    "plt.savefig('dist_centrality_closeness.png', bbox_inches='tight')\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}