day-6-complex-network-analysis-of-corruption/01 - Analysis of Structural Properties.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "# Analysis of Structural Properties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:25:09.444162Z",
     "start_time": "2019-07-05T12:25:05.345150Z"
    },
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "import nxviz as nv\n",
    "from collections import Counter\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Node degree, network average degree, degree distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:26:08.604182Z",
     "start_time": "2019-07-05T12:26:05.291549Z"
    }
   },
   "outputs": [],
   "source": [
    "# input edgelist from file\n",
    "G = nx.read_edgelist(\"datafiles/social/facebook/fb.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:26:42.683404Z",
     "start_time": "2019-07-05T12:26:42.588440Z"
    },
    "scrolled": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:27:36.555254Z",
     "start_time": "2019-07-05T12:27:36.502304Z"
    }
   },
   "outputs": [],
   "source": [
    "degrees = [deg for node, deg in nx.degree(G)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:28:19.634460Z",
     "start_time": "2019-07-05T12:28:19.608919Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum degree 1\n",
      "maximum degree 1098\n",
      "average degree 25.640112347209364\n"
     ]
    }
   ],
   "source": [
    "# kmin - minimum degree\n",
    "kmin = np.min(degrees)\n",
    "print('minimum degree {}'.format(kmin))\n",
    "# kmax - maximum degree\n",
    "kmax = np.max(degrees)\n",
    "print('maximum degree {}'.format(kmax))\n",
    "# kavg - average degree of the network\n",
    "kavg = np.mean(degrees)\n",
    "print('average degree {}'.format(kavg))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Degree distribution**: helps us understand connectivity trends in networks and how edges are distributed among nodes (does everyone have similar number of connections, or do we have hubs, nodes with significantly higher number of connections?)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:28:54.117531Z",
     "start_time": "2019-07-05T12:28:54.111378Z"
    }
   },
   "outputs": [],
   "source": [
    "def degree_distr(net):\n",
    "    degrees = dict(net.degree()) \n",
    "    hist = list(Counter(degrees.values()).items()) \n",
    "    hist.sort(key=lambda x:x[0])\n",
    "    hist = np.array(hist)\n",
    "    return hist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:29:24.781451Z",
     "start_time": "2019-07-05T12:29:24.713938Z"
    }
   },
   "outputs": [],
   "source": [
    "x,y=np.transpose(degree_distr(G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:30:07.318346Z",
     "start_time": "2019-07-05T12:30:06.538209Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'P(k)')"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.loglog(x,y)\n",
    "plt.xlabel(r'k')\n",
    "plt.ylabel(r'P(k)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Paths on Networks: average path length, shortest path, longest path"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:33:37.952648Z",
     "start_time": "2019-07-05T12:33:37.946908Z"
    }
   },
   "outputs": [],
   "source": [
    "G=nx.Graph()\n",
    "# assign weight to edge\n",
    "G.add_edge('Mary','Steven', weight=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:33:39.443165Z",
     "start_time": "2019-07-05T12:33:39.436215Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# average path length in graph\n",
    "nx.average_shortest_path_length(G, weight=None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clustering coefficient, triangles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:36:27.688584Z",
     "start_time": "2019-07-05T12:36:23.682149Z"
    }
   },
   "outputs": [],
   "source": [
    "G = nx.read_edgelist(\"datafiles/social/facebook/fb.txt\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:38:34.758764Z",
     "start_time": "2019-07-05T12:38:34.755788Z"
    }
   },
   "outputs": [],
   "source": [
    "# triangles\n",
    "nx.triangles(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:39:23.004108Z",
     "start_time": "2019-07-05T12:39:22.993039Z"
    }
   },
   "outputs": [],
   "source": [
    "g=nx.complete_graph(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:39:37.315506Z",
     "start_time": "2019-07-05T12:39:37.307979Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.clustering(g, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:37:34.503708Z",
     "start_time": "2019-07-05T12:37:34.496647Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6666666666666666"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# clustering coefficient of a node\n",
    "nx.clustering(G, '10')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:40:21.179630Z",
     "start_time": "2019-07-05T12:40:21.176716Z"
    }
   },
   "outputs": [],
   "source": [
    "# clustering coefficient of all nodes (returns a dictionary)\n",
    "# nx.clustering(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:40:50.017086Z",
     "start_time": "2019-07-05T12:40:27.240654Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.22098240472748912\n"
     ]
    }
   ],
   "source": [
    "# clustering coefficient of the network\n",
    "cc = nx.clustering(G)\n",
    "avg_clust = sum(cc.values()) / len(cc)\n",
    "print(avg_clust)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Centrality measures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:45:13.852155Z",
     "start_time": "2019-07-05T12:45:13.847131Z"
    }
   },
   "outputs": [],
   "source": [
    "G=nx.Graph()\n",
    "# assign weight to edge\n",
    "G.add_edge('Mary','Steven', weight=5)\n",
    "G.add_edge('Mary','Adam', weight=1)\n",
    "G.add_edge('Luiz','Adam', weight=1)\n",
    "G.add_edge('Luiz','Mary', weight=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:45:14.891180Z",
     "start_time": "2019-07-05T12:45:14.795734Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/lgaalves/miniconda3/lib/python3.6/site-packages/networkx/drawing/nx_pylab.py:611: MatplotlibDeprecationWarning: isinstance(..., numbers.Number)\n",
      "  if cb.is_numlike(alpha):\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:45:18.964513Z",
     "start_time": "2019-07-05T12:45:18.957985Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DegreeView({'Mary': 3, 'Steven': 1, 'Adam': 2, 'Luiz': 2})"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.degree(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:45:22.540531Z",
     "start_time": "2019-07-05T12:45:22.535054Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Mary': 1.0,\n",
       " 'Steven': 0.3333333333333333,\n",
       " 'Adam': 0.6666666666666666,\n",
       " 'Luiz': 0.6666666666666666}"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# degree centrality\n",
    "nx.degree_centrality(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:45:27.131889Z",
     "start_time": "2019-07-05T12:45:27.124528Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Mary': 0.6666666666666666, 'Steven': 0.0, 'Adam': 0.0, 'Luiz': 0.0}"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# betweenness centrality of network\n",
    "nx.betweenness_centrality(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:46:36.200331Z",
     "start_time": "2019-07-05T12:46:36.192747Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Mary': 1.0, 'Steven': 0.6, 'Adam': 0.75, 'Luiz': 0.75}"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# closeness centrality of network\n",
    "nx.closeness_centrality(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:46:37.548559Z",
     "start_time": "2019-07-05T12:46:37.542475Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Mary': 0.6116286437343043,\n",
       " 'Steven': 0.2818457979386572,\n",
       " 'Adam': 0.5227204550943348,\n",
       " 'Luiz': 0.5227204550943348}"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eigenvector centrality of network\n",
    "nx.eigenvector_centrality(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Components"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-06-24T01:57:37.234090Z",
     "start_time": "2019-06-24T01:57:37.227548Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# checks whether the network is connected\n",
    "nx.is_connected(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:47:45.312878Z",
     "start_time": "2019-07-05T12:47:45.305090Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# find number of connected components\n",
    "nx.number_connected_components(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:47:55.325978Z",
     "start_time": "2019-07-05T12:47:55.320935Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Adam', 'Luiz', 'Mary', 'Steven'}"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get the nodes in the same component as *n*\n",
    "nx.node_connected_component(G, 'Mary')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Assortativity\n",
    "\n",
    "* Pearson correlation coefficient [-1; 1]\n",
    "* social networks are highly assortative (homophily): high degree nodes connect to other high degree nodes\n",
    "* technological are disassortative: high degree nodes connect to low degree nodes\n",
    "\n",
    "Assortativity computed based on:\n",
    "* degree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:48:15.729846Z",
     "start_time": "2019-07-05T12:48:15.725840Z"
    }
   },
   "outputs": [],
   "source": [
    "# Barabasi-Albert (scale-free) network \n",
    "ba = nx.barabasi_albert_graph(50, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-07-05T12:48:16.628311Z",
     "start_time": "2019-07-05T12:48:16.621117Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.1700403137475433"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.degree_assortativity_coefficient(ba)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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