{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "# Node Centrality in SAN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### - Degree Centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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WHF9VxGa0q5GIFNjJkydZunQpISEhpKSk0K9fP/z8/PD09LS6bZ9hGISFhREQ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\nowAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1117cadd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "g = nx.Graph()\n",
    "g.add_edge(1,2)\n",
    "g.add_edge(1,3)\n",
    "g.add_edge(1,4)\n",
    "g.add_edge(2,3)\n",
    "g.add_edge(3,4)\n",
    "g.add_edge(4,5)\n",
    "g.add_edge(4,6)\n",
    "g.add_edge(5,6)\n",
    "g.add_edge(5,7)\n",
    "g.add_edge(5,8)\n",
    "g.add_edge(6,7)\n",
    "g.add_edge(6,8)\n",
    "g.add_edge(7,8)\n",
    "g.add_edge(7,9)\n",
    "nx.draw(g, node_size=500, with_labels=True, font_size=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "degree_centrality = nx.degree_centrality(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 0.375,\n",
       " 2: 0.25,\n",
       " 3: 0.375,\n",
       " 4: 0.5,\n",
       " 5: 0.5,\n",
       " 6: 0.5,\n",
       " 7: 0.5,\n",
       " 8: 0.375,\n",
       " 9: 0.125}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "degree_centrality "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(degree_centrality)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(1, 0.375), (2, 0.25), (3, 0.375), (4, 0.5), (5, 0.5), (6, 0.5), (7, 0.5), (8, 0.375), (9, 0.125)]\n"
     ]
    }
   ],
   "source": [
    "print degree_centrality.items()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import operator\n",
    "\n",
    "def sort_map(map):\n",
    "    sortedList = map.items()\n",
    "    sortedList.sort(key=operator.itemgetter(1), reverse=True)\n",
    "    return sortedList\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "sorted_degree_centrality = sort_map(degree_centrality)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(4, 0.5),\n",
       " (5, 0.5),\n",
       " (6, 0.5),\n",
       " (7, 0.5),\n",
       " (1, 0.375),\n",
       " (3, 0.375),\n",
       " (8, 0.375),\n",
       " (2, 0.25),\n",
       " (9, 0.125)]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_degree_centrality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### - Closeness  Centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "closeness_centrality = nx.closeness_centrality(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 0.47058823529411764,\n",
       " 2: 0.34782608695652173,\n",
       " 3: 0.47058823529411764,\n",
       " 4: 0.6153846153846154,\n",
       " 5: 0.6153846153846154,\n",
       " 6: 0.6153846153846154,\n",
       " 7: 0.5,\n",
       " 8: 0.47058823529411764,\n",
       " 9: 0.34782608695652173}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "closeness_centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sorted_closeness_centrality = sort_map(closeness_centrality)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(4, 0.6153846153846154),\n",
       " (5, 0.6153846153846154),\n",
       " (6, 0.6153846153846154),\n",
       " (7, 0.5),\n",
       " (1, 0.47058823529411764),\n",
       " (3, 0.47058823529411764),\n",
       " (8, 0.47058823529411764),\n",
       " (2, 0.34782608695652173),\n",
       " (9, 0.34782608695652173)]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_closeness_centrality "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### - Betweenness  Centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "bet_centrality = nx.betweenness_centrality(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 0.10714285714285714,\n",
       " 2: 0.0,\n",
       " 3: 0.10714285714285714,\n",
       " 4: 0.5357142857142857,\n",
       " 5: 0.21428571428571427,\n",
       " 6: 0.21428571428571427,\n",
       " 7: 0.25,\n",
       " 8: 0.0,\n",
       " 9: 0.0}"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bet_centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sorted_bet_centrality =sort_map(bet_centrality)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(4, 0.5357142857142857),\n",
       " (7, 0.25),\n",
       " (5, 0.21428571428571427),\n",
       " (6, 0.21428571428571427),\n",
       " (1, 0.10714285714285714),\n",
       " (3, 0.10714285714285714),\n",
       " (2, 0.0),\n",
       " (8, 0.0),\n",
       " (9, 0.0)]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_bet_centrality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### - Eigenvector Centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "eigenvector_centrality = nx.eigenvector_centrality(g)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 0.19575179821589203,\n",
       " 2: 0.11168619729756277,\n",
       " 3: 0.19575179821589203,\n",
       " 4: 0.3787497778502688,\n",
       " 5: 0.4680845766467968,\n",
       " 6: 0.4680845766467968,\n",
       " 7: 0.4099777873648636,\n",
       " 8: 0.3840189757284675,\n",
       " 9: 0.11695539517576153}"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenvector_centrality"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sorted_eigenvector_centrality= sort_map(eigenvector_centrality)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(5, 0.4680845766467968),\n",
       " (6, 0.4680845766467968),\n",
       " (7, 0.4099777873648636),\n",
       " (8, 0.3840189757284675),\n",
       " (4, 0.3787497778502688),\n",
       " (1, 0.19575179821589203),\n",
       " (3, 0.19575179821589203),\n",
       " (9, 0.11695539517576153),\n",
       " (2, 0.11168619729756277)]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sorted_eigenvector_centrality "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### - Build a table with four centralities \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rounded_degree_centrality = {k: round(v, 3) for k, v in degree_centrality.items()}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rounded_closeness_centrality = {k: round(v, 3) for k, v in closeness_centrality.items()}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rounded_bet_centrality = {k: round(v, 3) for k, v in bet_centrality.items()}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rounded_eigenvector_centrality = {k: round(v, 3) for k, v in eigenvector_centrality.items()}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "table = [[node, rounded_degree_centrality[node], \n",
    "          rounded_closeness_centrality[node], \n",
    "          rounded_bet_centrality[node], \n",
    "          rounded_eigenvector_centrality[node]] for node in g.nodes()]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 0.375, 0.471, 0.107, 0.196],\n",
       " [2, 0.25, 0.348, 0.0, 0.112],\n",
       " [3, 0.375, 0.471, 0.107, 0.196],\n",
       " [4, 0.5, 0.615, 0.536, 0.379],\n",
       " [5, 0.5, 0.615, 0.214, 0.468],\n",
       " [6, 0.5, 0.615, 0.214, 0.468],\n",
       " [7, 0.5, 0.5, 0.25, 0.41],\n",
       " [8, 0.375, 0.471, 0.0, 0.384],\n",
       " [9, 0.125, 0.348, 0.0, 0.117]]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table"
   ]
  }
 ],
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