PythonGraphs.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "\n",
    "\n",
    "Using the graph from figure 10.1 from the textbook (http://infolab.stanford.edu/~ullman/mmds/book.pdf) to demonstrate\n",
    "\n",
    "<img src=\"images/smallsocialgraph.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Example Small social newtork as a connection matrix\n",
    "sc1 = ([(0, 1, 1, 0, 0, 0, 0), \n",
    "        (1, 0, 1, 1, 0, 0, 0),\n",
    "        (1, 1, 0, 0, 0, 0, 0),\n",
    "        (0, 1, 0, 0, 1, 1, 1),\n",
    "        (0, 0, 0, 1, 0, 1, 0),\n",
    "        (0, 0, 0, 1, 1, 0, 1),\n",
    "        (0, 0, 0, 1, 0, 1, 0)])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "http://networkx.github.io/documentation/latest/install.html\n",
    "\n",
    "pip install networkx\n",
    "\n",
    "\n",
    "to install networkx into your python modules\n",
    "\n",
    "pip install networkx  --upgrade \n",
    "\n",
    "to upgrade you previously installed version\n",
    "\n",
    "You may have to restart your ipython engine to pick up the new module\n",
    "Test your installation by running the new box locally\n",
    "\n",
    "A full tutorial is available at:\n",
    "http://networkx.github.io/documentation/latest/tutorial/index.html\n",
    "\n",
    "There are other packages for graph manipulation for python:\n",
    "python-igraph, (http://igraph.org/python/#pydoc1)\n",
    "Graph-tool, (https://graph-tool.skewed.de)\n",
    "\n",
    "I picked networkx because it took little effort to install.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "G1 = nx.Graph()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['A', 'C', 'B', 'E', 'D', 'G', 'F']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G1.add_nodes_from(['A','B','C','D','E','F','G'])\n",
    "G1.nodes()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "G1.add_edges_from([('A','B'),('A','C')])\n",
    "G1.add_edges_from([('B','C'),('B','D')])\n",
    "G1.add_edges_from([('D','E'),('D','F'),('D','G')])\n",
    "G1.add_edges_from([('E','F')])\n",
    "G1.add_edges_from([('F','G')])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "#drawing the graph\n",
    "%matplotlib inline  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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UKq9ptVq1fv16LVy4UOPGjdPixYs1ZMiQVnlttH2MiAG4le3btys8PLzVSliS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\nDACAQf8P0MdGrwrcihEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112345690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': <matplotlib.text.Text at 0x1125ab050>,\n",
       " 'B': <matplotlib.text.Text at 0x1125ab790>,\n",
       " 'C': <matplotlib.text.Text at 0x1125ab110>,\n",
       " 'D': <matplotlib.text.Text at 0x1125b7050>,\n",
       " 'E': <matplotlib.text.Text at 0x1125abbd0>,\n",
       " 'F': <matplotlib.text.Text at 0x1125b78d0>,\n",
       " 'G': <matplotlib.text.Text at 0x1125b7490>}"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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pHX/yiXVt2DDYsAH+3/+zr10iAUo9YhFp6pprzMYRjbfnOnTIrDm+7TY4csS2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\nKYhFRERs9P8BSq6FxQlREh4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112488f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pos=nx.spring_layout(G1)\n",
    "nx.draw(G1,pos,node_color='y', edge_color='r', node_size=600, width=3.0)\n",
    "nx.draw_networkx_labels(G1,pos,color='W',font_size=20,font_family='sans-serif')\n",
    "#https://networkx.github.io/documentation/latest/reference/generated/networkx.drawing.nx_pylab.draw_networkx.html\n",
    "#Some parameters to play with"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's play with some algorithms in class:\n",
    "https://networkx.github.io/documentation/latest/reference/algorithms.html\n",
    "\n",
    "Social Graph analysis algorithms\n",
    "\n",
    "Betweenness:\n",
    "https://networkx.github.io/documentation/latest/reference/algorithms.centrality.html#betweenness\n",
    "\n",
    "EigenVector centrality\n",
    "https://networkx.github.io/documentation/latest/reference/algorithms.centrality.html#eigenvector\n",
    "\n",
    "\n",
    "Clustering per node\n",
    "https://networkx.github.io/documentation/latest/reference/generated/networkx.algorithms.cluster.clustering.html\n",
    "\n",
    "All Shortest Paths\n",
    "https://networkx.github.io/documentation/latest/reference/generated/networkx.algorithms.shortest_paths.generic.all_shortest_paths.html\n",
    "\n",
    "Laplacian matrix\n",
    "https://networkx.github.io/documentation/latest/reference/generated/networkx.linalg.laplacianmatrix.laplacian_matrix.html#networkx.linalg.laplacianmatrix.laplacian_matrix\n",
    "\n",
    "\n",
    "\n",
    "Each of the students pair up and work on demonstrating a networkx algorithm\n",
    "Create a new ipython page and submit it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{('A', 'B'): 0.23809523809523808,\n",
       " ('A', 'C'): 0.047619047619047616,\n",
       " ('B', 'D'): 0.5714285714285714,\n",
       " ('C', 'B'): 0.23809523809523808,\n",
       " ('D', 'F'): 0.19047619047619047,\n",
       " ('D', 'G'): 0.21428571428571427,\n",
       " ('E', 'D'): 0.21428571428571427,\n",
       " ('E', 'F'): 0.07142857142857142,\n",
       " ('G', 'F'): 0.07142857142857142}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.edge_betweenness_centrality(G1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0.0,\n",
       " 'B': 0.5333333333333333,\n",
       " 'C': 0.0,\n",
       " 'D': 0.6333333333333333,\n",
       " 'E': 0.0,\n",
       " 'F': 0.03333333333333333,\n",
       " 'G': 0.0}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.betweenness_centrality(G1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('A', 0.0), ('C', 0.0), ('B', 0.5333333333333333), ('E', 0.0), ('D', 0.6333333333333333), ('G', 0.0), ('F', 0.03333333333333333)]\n"
     ]
    }
   ],
   "source": [
    "def most_important(G):\n",
    " \"\"\" returns a copy of G with\n",
    "     the most important nodes\n",
    "     according to the pagerank \"\"\" \n",
    " ranking = nx.betweenness_centrality(G).items()\n",
    " print ranking\n",
    " r = [x[1] for x in ranking]\n",
    " m = sum(r)/len(r) # mean centrality\n",
    " t = m*3 # threshold, we keep only the nodes with 3 times the mean\n",
    " Gt = G.copy()\n",
    " for k, v in ranking:\n",
    "  if v < t:\n",
    "   Gt.remove_node(k)\n",
    " return Gt\n",
    "\n",
    "Gt = most_important(G1) # trimming"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UeDzO+Pg4xWKR+fl5Go1Gr6sk0hVth4CZBYBPAm8HjgLvM7ObVpV5B3C9c+61wP3Ap9vd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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11245dcd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pylab import show\n",
    "# create the layout\n",
    "pos = nx.spring_layout(G1)\n",
    "# draw the nodes and the edges (all)\n",
    "nx.draw_networkx_nodes(G1,pos,node_color='b',alpha=0.2,node_size=8)\n",
    "nx.draw_networkx_edges(G1,pos,alpha=0.1)\n",
    "\n",
    "# draw the most important nodes with a different style\n",
    "nx.draw_networkx_nodes(Gt,pos,node_color='r',alpha=0.4,node_size=254)\n",
    "# also the labels this time\n",
    "nx.draw_networkx_labels(Gt,pos,font_size=12,font_color='b')\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "G2 = nx.gnm_random_graph(15,25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rr7yCtLQ0i/hvay5sNFQNBrEFMFcQN6hVCyOnTYOjoyPu3r2Lu3fvIj8/v+Tf5f1cXFxc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\nTEREJCEGMRERkYT+D+P+jfhIsugbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1125507d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 0.20494505494505494), (1, 0.2884615384615385), (2, 0.03882783882783883), (3, 0.0293040293040293), (4, 0.0879120879120879), (5, 0.031135531135531136), (6, 0.0), (7, 0.009157509157509158), (8, 0.0), (9, 0.022893772893772892), (10, 0.26355311355311356), (11, 0.0), (12, 0.10054945054945054), (13, 0.024725274725274728), (14, 0.1952380952380953)]\n"
     ]
    }
   ],
   "source": [
    "Gt = most_important(G2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2UqkaFhcXR10sGjPe+N9MY61SqTQ6LjvpZwnlYXOHNW4PdY3h1KlTSKVSnsuX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\nfS4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1125ffe90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pos = nx.spring_layout(G2)\n",
    "# draw the nodes and the edges (all)\n",
    "nx.draw_networkx_nodes(G2,pos,node_color='b',alpha=0.2,node_size=8)\n",
    "nx.draw_networkx_edges(G2,pos,alpha=0.1)\n",
    "\n",
    "# draw the most important nodes with a different style\n",
    "nx.draw_networkx_nodes(Gt,pos,node_color='r',alpha=0.4,node_size=254)\n",
    "# also the labels this time\n",
    "nx.draw_networkx_labels(Gt,pos,font_size=12,font_color='b')\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "KeyError",
     "evalue": "15",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-18-a8a95a7f8c0f>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mG3\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconnected_caveman_graph\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mnx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdraw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mG3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 3\u001b[0;31m \u001b[0mnx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdraw_networkx_labels\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mG3\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mpos\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfont_size\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m12\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mfont_color\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'b'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/usr/local/lib/python2.7/site-packages/networkx/drawing/nx_pylab.pyc\u001b[0m in \u001b[0;36mdraw_networkx_labels\u001b[0;34m(G, pos, labels, font_size, font_color, font_family, font_weight, alpha, bbox, ax, **kwds)\u001b[0m\n\u001b[1;32m    719\u001b[0m     \u001b[0mtext_items\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m}\u001b[0m  \u001b[0;31m# there is no text collection so we'll fake one\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    720\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mlabels\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 721\u001b[0;31m         \u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpos\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    722\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcb\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_string_like\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlabel\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    723\u001b[0m             \u001b[0mlabel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlabel\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# this will cause \"1\" and 1 to be labeled the same\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyError\u001b[0m: 15"
     ]
    },
    {
     "data": {
      "image/png": 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GioqKZnt5gSzPcVaIOBitVguVSoWYyEgEK5WIjYhAbEQEgpVKxERGQqVSQafTWez4arUa\n69evx+zZs+Hh7IxNZuxrI4De3brZZEj5+vqiV9euDnt+jmTQoEE4ePAgXF1d0bNnT3z33XcWP6az\nszNatmyJS5cuWfxY1HwxiG3QmuxstA8MxAfJyUjNz8clvR6FGg0KNRqU6vV4Nj8fqyZPRjulEmuy\nsyU5pk6nw65duzB37lzce++9CAkJQWZmJtq1a4fUl19GpkJh8r4zvb2RkpYmSZ2WkJKWhuWeniZv\nb+vn50i8vb3x7rvv4r333sNTTz2FKVOm4PLlyxY9JqenyeIE2ZSMJUtEqIeHyAWEuMUrFxChnp4i\nY8mSJh/HYDCIgwcPivT0dDF8+HDh7e0toqKixAsvvCC2bt0qKioqat9bWVkpgnx8RF4jaqqvxiAf\nH6HVaqX8zySZ8vJyMXPmTOHp5OSQ5+fILl26JJKSkkRYWJj4/vvvLXacu+66S+zdu9di+ydiENuQ\nbJVKhHp4iBNNCIITf4Vxtkp1y/2fPHlSfPTRR+LRRx8VQUFBokOHDmLy5Mniiy++EBcuXJC1Njns\n3btX3HHHHWLcuHFiZVaWw51fc/HVV1+J4OBgMX36dKHRaCTf/7Bhw8TmzZsb9d633xaiTx8h3N2F\nmDjx6vd1OiEefliIsDAhnJyE2LlT8jLJjjGIbYQlRp1qtVps2LBBTJ8+XXTp0kX4+/uLsWPHiqys\nLPHHH380uUZrjdYtraKiQvzjH/8QQUFB4vPPP6/9vqOcX3N08eJF8dhjj4nbb79d/PDDD5Lue/z4\n8WL16tWNeu+6dUJs2CBESsqNQZyRIcSePUK0bcsgproYxDbis88+E7EKRZNDuOY1WKEQq1evFj/8\n8IN46aWXxH333ScUCoWIjY0Vb775psjNzRXV1dVm15mtUokgHx8Rq1CItYDQX1ODDhBfAmKwt7cI\n8vGxyZHiTz/9JO68804xZswYce7cuRt+bu/n19ytW7dOtGnTRqSmpory8nJJ9jl16lSxbNmyJm0z\nZ07dIL5WSAiDmOpiENuI6IgIsdbEEBZ/BYSvs7Po3bu3+Mc//iG+++47yX4RXU+r1QqVSiViIiOF\nl6uraO/lJdp7eQkPZ2cRFhAgVCqVzV0zraysFC+++KIIDAwUKpVKGAyGBt/b0Pl5ubqKmMhImzw/\nuqq4uFgkJCSIzp07S3Jtd+7cuWLevHlN2oZBTE3B+4htgGRtJF1ccPrCBavfZ1yzorSoqAjPPPMM\njh49arXjN0Zubi4mTJiATp064Z133kHr1q0bva2pLRpJfl988QWmT5+OCRMmYN68eWjRooVJ+1m6\ndCmOHz+OpUuXNnqbuXOB06eBDz648WehocCnnwL9+5tUDjkg3r5kA0pKSqB0dzerzZkrgFbu7la/\nzcLX17e2p3J0dDTOnDmDc+fOWbWGhuh0OsydOxdxcXH4v//7P+Tk5DQphIG652cLIfz440CbNoCv\nL9CxI/Daa3JXZLvGjh2L/Px8/Prrr4iKikJubq5J+/Hz8+PtS2RRDGKSzG233Ybo6Gjs2rVL7lKw\nb98+9OnTB/n5+Thw4ADGjx9vF48SvJUXXwQKCwG1Gvj6a2D5cuDbb+WuynYFBQVh7dq1mD17NoYP\nH465c+c2uREO7yMmS2MQ24CAgAAUa7XQm7EPPYyPmfP395eqLJMMGDAAO3fulO34Op0OL7/8MoYN\nG4ZZs2Zhw4YNaNOmjWz1SK1rV6BmhlUIwNUVUCrlrcnWOTk5Yfz48bUfyvr27YsDBw40ens3Nzec\nPXsWBQUFUKvVN31vdTVQWWn8Z1UVoNUavwYAnc74M8D4fa3W1DMihyP3RWoykmKxVlTnznKfhvjp\np59E9+7dZTn2gQMHREREhIiLixOnT5+WpQZrSEkRwtNTCBcXId55R+5q7IvBYBAfffSRUCqV4tVX\nXxU6na7e91VWVorPPvtMREdECC8XFxHo5CTCFArh5eoqoiMixGeffVbvgr1584z3CTs7X3298orx\nZ2Fhdb/v7CzEiROWPFuyFwxiG2Hu7UvR7u4iICBADBgwQGzcuFGSW5VModfrhbe3tyguLrbaMXU6\nnXjllVeEUqkUH3744U1XRDsKg0GIHTuECAgQ4uef5a7G/pw8eVIMHTpUREVFiUOHDtX5Wc0tbPd7\ne4ucem5hWwuIWIWCt7CRZBjENkKKhh5XrlwRKpVK9O7dW9xxxx1i5cqVdVpVWsvQoUNFTk6OVY51\n8OBB0atXLzFs2DBx8uRJqxzTlkyZIsSzz8pdhX0yGAxi5cqVolWrVuKNN94Qer2eTV1IFrxGbCPc\n3d2RkZWFUR4eKGrCdkUA4j09kZGVBU9PTyQmJiI3NxfvvvsuNmzYgLCwMMyfPx8XLlywVOk3GDhw\noMWvE1dVVeG1117D4MGDMW3aNGzZsgUhISEWPaYtqqoCzHheRbPm5OSESZMmITc3F9999x3u7NIF\ni2bPxu6KCkQ1YvsoALvLy7F47lzJHr5CzZTcnwSoLqk/kR85ckQ89dRTws/PT6SkpIjffvvN4ufw\n448/isjISIvt/9ChQyIqKkoMGTJEnGhGF9nOnxciO1sIjUaI6mohvvlGCF9fTk1Loby8XPi1aMEH\nf5AsGMQ2yBJtFs+ePSvmzJkjWrVqJeLj48WePXssVr9OpxPe3t7i4sWLku5Xr9eL119/XbRq1Upk\nZWU1i2vB1youFmLAACH8/IRo2VKIvn2F2LhR7qocgxQtZlW8XkwmYhDbKEu1WdRoNOLtt98WHTp0\nEPfee69Yu3atqKqqkrz++++/X2yUMCWOHj0q+vbtK2JjY8Xx48cl2y+RENLctRBjwVkgcmxscWkH\nLNFmsbq6GuvXr8eiRYtw4cIFpKamYsKECfCU6ILjggULcOnSJSxevNjsOtPT07Fw4UIsWLAAycnJ\nDtGYg2yHZC1mXV1xurjYJjqwkX3hYi07YIk2i7fddhvGjBmDvXv34l//+he+++47hIWF4aWXXpKk\nRaUUjT3+97//ITo6Gl9//TV++eUXTJkyhSFMkpOsxaybGztwkUkYxM2ck5MT+vXrh3Xr1mHPnj24\ncOECunTpgkmTJuHYsWMm7/euu+7CsWPHUFRUhIKCgkZ1JapRXV2NJUuWoF+/fnjsscewdetWhIeH\nm1wLEZEtYxBTrU6dOiEzMxO//vorQkNDMXDgQIwYMQI7d+5EU65gaLVa5OTkwAfAnR06IDYiArER\nEQhWKhETGQmVStVgv99ff/0V/fv3x8aNG/HTTz9h6tSpcHbmH1OyHEdqMUv2ib/h6AZKpRIvvfQS\njh8/jhEjRmDy5Mm46667sGbNGlRVVd102zXZ2WgfGIgPkpOx4soVqKurUajRoFCjQalej2fz87Fq\n8mS0Uyrr3HtpMBiwdOlS3HfffUhISMD27dvRsWNHS58qEXx9fdGra1dsMmMfGwH07taN14fJNDIv\nFiM7UF1dLTZs2CBiYmJE+/btxdKlS0VZWdkN7zP1HujffvtNxMTEiOjoaKvc50x0PbNvX/L25u1L\nZDKumqYm+emnn7BkyRJ8//33ePrppzFjxgy0bdsWa7KzMSspCbsrKtCukfsqAnCPqysuu7lh/oIF\nmD59Om677TZLlk9UL61Wi/aBgdhSVobeTdw2D0Ccjw+Kiovh5uZmifLIwXFqmprk7rvvxueff45f\nfvkFFRUV6N69Ox5//HFMnzQJ65sQwgDQDsAmvR4eTk5ISUlhCJNspGgxyxAmUzGIySTh4eHIyMjA\n77//Dr1ejw5XrjR5JAEY+/X2AJCTkyNxhURNk5CYiOcXLEC0hwfyGvH+PADRnp54fv58JCQmWro8\ncmCcmiazxURG4tn8fIw2cfu1ADIiI7Fr/34pyyIyyZrsbMxMTkZ3gwEpGg1GArX3GOthXJi1QqHA\nUWdnZGRlMYTJbAxiMgu7EpEj0ul0yMnJQebChdh35Aha/TXtfEGnQ0sPD8Q/8QSWLFnC6WiShDnN\nZIiudiXSm34X5rVdiRjEZAvc3NyQmJiIxMTEG1rMrl+/HuvWrWMIk2R4jZiILGLFCqBvX6BFCyAp\nqe7Ptm0D7rwTUCiA2FigqCkrpKzs+hazDz30ELZv346ysjK5SyMHwSAms7ArETUkOBiYOxd46qm6\n3y8pAcaMAV57Dbh4EYiKAhIS5KnRFC1btkT//v2xaZM5LUCIrmIQk1nYlYgaMmoUMHIkcP3nq5wc\noHt3YPRowM0NmDcPyM8Hfv1VljJNMm7cOHz++edyl0EOgkFMZktJS0OmQmHy9pne3khJS5OwIrJl\nR44AERFX/93TE7j9duP37cXIkSOxY8eORj/IhOhmGMRkttGjR+OwszP2mbBtHoAjTk4YPdrUm5/I\n3mg0wPWTHz4+wOXL8tRjCl9fXwwYMIDT0yQJBjGZjV2JqCkUCuD6dU5qNeDtLU89puL0NEmFQUyS\nYFciaqxu3YADB67++5UrwB9/GL9vjtJSID7eGPTh4YBKZd7+bmXkyJHYuXMnLl26ZNkDkcNjEJNk\nZqSmYtEHHyDOxwf3KxTIAXDtQxP1MHbRilUoEOfjg0WrVmFGaqo8xZLFVVcDlZXGf1ZVAVqt8ev4\neOP14HXrjN975RUgMhLo3Nm846WkGG+VKi4GPvkEeOYZ4Ngxac6lPj4+Phg0aBA2btxouYNQs8DO\nWiS5m3Ul8nZzw+MpKViwYAGnox3cK68YX05OV7/38svASy8B338PTJ1qvH/47ruBjz4C2jXliSHX\nKS8H/PyAo0eBmsdYP/mk8Raq11836zRu6tNPP0V2djavFZNZGMRkUdd3Jfr444+Rm5uLf/3rXzJX\nRo7kwAEgOtq4EKxGejqwcyewYYPljltWVobQ0FCcOHECLVu2tNyByKFxapos6vquRGPGjMHGjRuh\n1WrlLo0ciEZjXHl9LWusxPbx8cHgwYOxwZJpTw6PQUxW1bZtW/Ts2RPffvut3KXUaqgV408/AX/7\nGxAQAAQFGbs//fmnfHVSw+Rcic3V02QuBjFZXUJCgk394mqoFWNpKZCcDJw4YXwpFMDEifLUSDfX\nubNxQdgff1z9Xn6++SuxG+PBBx/E7t27UVpaavmDkUPiNWKyuj///BNdunTB2bNn4eHhIXc5tebO\nBU6fBj74oP6f798PDBxoHGmR7Rk/3rgw7L33gH37gBEjgB9/ND5cwtJGjx6NkSNHYsKECZY/GDkc\njojJ6lq3bo3evXvjm2++kbuUJtm50zojLDLNihXG1dOBgcBjjwHvvmudEAY4PU3mYRCTLGxtevpW\nDh4E5s8HFi+WuxJqiJ+f8d5kjQY4fty6T3R68MEHsWfPnto7BIiagkFMshg9ejS+/vprlJeXy13K\nLf3+OzB8OLB8OXDffZY7zs2e31vj1VcBZ2fjfbhkOxQKBe6//36uniaTMIhJFkqlEnfddRe2bNki\ndyk3deIEMGSIsRHF+PGWPVZDi8ZqFBQAX34JtG1r2TrINI46Pe3tbbwVzMfH+LWLCzBzptxVORYG\nMcnGVn5xNdSK8cwZIDYWmD4dmDTJ8nU09PzeGlOnAm+9Bbi6Wr4Warq4uDj8+OOPKCkpkbsUSV2+\nbLw1rKzMePuepycwbpzcVTkWBjHJJj4+Ht9++y0017ZDksGCBcZfLgsXAp9+avz6tdeA998HCguN\nD66vGQ1c3zTCWr74wjhlPWyYPMenW1MoFPjb3/6G9evXy12KxXz5pXExXL9+clfiWBjEJJuAgADc\nd9992Lx5s6x1vPwyYDAYR8E1r5deMr6qq6+OBmpGBtam0QCzZwPLlln/2NQ048aNwxdffCF3GRbz\n8cfAE0/IXYXjYRCTrGxletqWzZtn/OUXGip3JXQrw4cPx969ex1uehowrpfYtcv4MA2SFoOYZDVq\n1Chs3boVly3dFNiObdtmHA23aWN8nTxpvEa3aJHcldH1vLy8MHToUKxbt07uUiS3erXxwRrt28td\nieNhEJOs/Pz8EBMTw8fIoeFFY99/Dxw+bGzZmJ9vXDW9cqVx8RbZHked5Vm9GmDjMMtgEJPsHPUX\nV1M1tGjMz8+4QKbm5eICtGxp/DnZnuHDh+Pnn3/GhQsX5C5FMj/+aLyL4OGH5a7EMbHXNMlOrVaj\nXbt2KCoMgyPyAAAdHklEQVQqgq+vr9zlEJktISEB999/PyZZ4743K5gyxThb89FHclfimDgiJtn5\n+vpi4MCB2Lhxo9ylEEnC0WZ53n2XIWxJDGKyCY72i4uatwceeAC//PILiouL5S6F7ACDmGzCiBEj\nsGvXLj7TlRyCp6cnHnjgAYdcPU3SYxCTTfDx8UFsbCyb5pPDGDt2LGd5qFEYxGQzxo0bhzVr1shd\nBpEkHnjgAeTm5uL8+fNyl0I2jkFMNuPBBx90yKb51Dx5eHhg+PDhyMnJkbsUsnEMYrIZzaFpPjUv\n9fWebui508eOGb/v72+8dzw6Gti928oFkywYxGRTOD1NjmTo0KHIy8vDuXPnar/X0HOng4OBzz8H\nLl40vhIS2ECjuWAQk00ZPnw4fvrpJ972QQ7Bw8MDcXFxyMnJgVqtRkFBAXr2LMCAAeobnjvt4wOE\nhxu/rq4GnJ2N7UzJ8bnIXQDRtby8vGpv+5g8ebLc5RCZRavVonXr1pg/axZmzZwJpbs7AKBYq4W/\n39vocOf90OlC4ObmVruNnx9w5YoxhLdtk6tysiaOiMnmcHqaHMGa7Gy0DwxE/sqVWHHlCi7p9SjU\naFCo0aBUr8fd58/h1z170E6pxJrs7NrtSksBtdo4NT12rIwnQFbDICab88ADD9xwXY3InixLT8es\npCRsLivDVo0G8ag7/egKoAuAYVV6bC4rw6ynnsKy9PTan3t4AG++Cfz6K3DwoJWLJ6tjEJPNufa6\nGpG9WZOdjcVz5mB3RQWiGvH+KAC7y8uxeO7cOiPj6mrAYOBTtpoDBjHZJE5Pkz3SarWYmZyM9RUV\naNfAe6rhjEq4oxq3oQou0MINwXDGC+X3IuXpt1FZqUNZGZCaCtxxB3D77VY9BZIBg5hs0tChQ5Gf\nn4+zZ8/KXQrZkIEDjdO2Pj6Atzdw551yV1RXTk4OuhsM6H2T9yzAHHiiHAuRhk/xKDxRjtcwG4Fo\nicryVfD3d0KXLkBxMcAHkjUPfB4x2awnnngCffv2xfTp0+UuhWzEoEHAE08AEyfKXUn9YiIj8Wx+\nPkabuP1aABmRkdi1f7+UZZGN44iYbBYfjUj1sdWhg1qtxv6jRzHSjH2MBLDvyBGo1WqpyiI7wCAm\nmzVkyBAcOXIEp0+flrsUu/Xbb8ap3CeekLsS6bz4IhAYCMTEADt3yl3NVSUlJVC6u5vVnMEVQCs3\nN1y8eFGqssgOMIjJZrm7u+Ohhx7CF198UduVqKCggKOFJpg2DbjrLrmrkM5bbwEFBcDp08CkScCI\nEUBhodxVEZmHQUw2S6vVIjAwEG/Ono1gpRKxERGIjYhAsFKJmMhIqFQq6HQ6ucu0WdnZxi5NsbFy\nVyKdvn0BLy/A1dU4yu/XD9iyRe6qjAICAlCs1UJvxj70AC7odPC/vv8lOTQGMdmkmq5EeZmZeKe8\n/IauRM/m52PV5Mk3dCUio7Iy4OWXgfR0272mKgUnJ9s5P19fX/Tq2hWbzNjHRgC9u3aFr6+vVGWR\nHWAQk81pTFei0QC2ajT1diUi4KWXjFO3jvTQALUa+Pe/Aa3W2Ozi00+BH34Ahg2Tu7KrUtLSkKlQ\nmLz9ImdnFJaU4IMPPoBWq5WwMrJlDGKyKVJ1JWrODhwAtm4F/v53uSuRll4PzJljXKilVBqf67th\ng201vBg4cCB+0Wqxz4Rt8wAcVyiwcuVKfPHFFwgPD8drr72GkpISqcskG8P7iMlmaLVatA8MxJay\nsps2RKhPHoA4Hx8UFRfXeZJNc5SRYQwsb2/jtK1GYxxBdu0K5ObKXZ3j2rx5MyZPnowePXrg6K5d\n2H2T7lrXKwIQ7emJRatWISExEQBw6NAhpKenY8OGDXj00Ufx97//HR07drRY/SQfjojJZjSmK1FD\nogB0MxjYnxpAcjLwxx/GkXF+PjBlCvDgg8ZpXZKeWq1GUlISpk2bhk8//RTffPMNnl+wANEeHshr\nxPZ5MIbw8/Pn14YwAPTo0QMffvghDh8+DG9vb9xzzz14+OGHsXfvXoudC8mDQUw2I3PhQqRoNCZv\nn6LRIHPhQgkrsk8tWhinb2teCoXxe1yIK71///vf6NGjB9zd3XHw4EEMHDgQADAjNRWLPvgAcT4+\nuF+hQA6Aqmu208PYRSvW2xtxPj5YtGoVZqSm1nuMtm3b4vXXX0dhYSEGDBiARx99FP369UNOTg6q\nq6stfIZkDZyaJpugVqsRrFTikl5vckMEPQA/V1ecLi7mqlOyqMuXL+P555/H119/jVWrVmHIkCH1\nvk+n0yEnJweZCxdi35EjaPXXZZPiykq09PTEkpUrMXr06CZdTqmursa6deuwePFiXLhwAampqZgw\nYQI8+Zgmu8UgJptQUFCA2IgIFJoxIgaAMC8vbD90COHh4RJVRlTX9u3bkZSUhMGDByM9Pb3RH/rU\nanVtxywnJyf07NkTJSUlcHV1NakOIQR+/PFHLF68GHv27EFycjKmTZuGoKAgk/ZH8uHUNBFRI1y5\ncgXTp0/H448/jrfffhurVq1q0syLr68vwsPDER4ejrCwMHTs2BG//PKLyfU4OTmhX79+WLduHfbs\n2YOSkhJ06dIFTz/9NI4ePWryfsn6GMRkE9iViGzZ7t27ERERgUuXLuHQoUOIi4sze5+DBg3Cjh07\nzC8OQKdOnZCZmYnffvsN7du3x+DBgxEXF4ft27dDiklPtpi1LAYx2YTruxKtQAr64me0QAWSsKpR\n+9gIoHe3brw+TJKpqKhAamoqxo0bh8WLF2P16tXw8/OTZN8DBw7E9u3bJdlXjVatWmHu3Lk4fvw4\n4uPjkZKSgqioKHz22WfQ65v2MVer1UKlUiEmMpItZi1NENmIzz77TMQqFEIAYh0eEhswQqTgbTER\nq4Qw3hJ709dgb2+hUqnkPg1yEHv37hWdO3cWCQkJori4WPL9l5aWCoVCISorKyXfd43q6mqxadMm\nMXDgQBEaGioWL14s1Gr1LbfLVqlEkI+PuN/bW+QAQn/N3zMdINYCIlahEEE+PiKbf+fMxiAmm1FZ\nWSmCfHxE3jV/6efg1UYFcS4gfFxdxblz5+Q+DbJzFRUVIi0tTQQFBYnPP//coseKiooSP/zwg0WP\nUSM3N1c88sgjwt/fXzz33HOiqKio3vdlLFkiQj08RG4jPvzmAiLU01NkLFlilXNwVJyaJpvh7u6O\njKwsjPLwQFETtisCEO/hgbv690dUVBS+/vprS5VIDi4vLw9RUVH49ddfkZ+fj7Fjx1r0eJaYnm5I\nzRT1vn37IIRAREQEHn30Uezbd7UhJ1vMykTuTwJE17v2E/mtRsTXfyLfunWrCAsLExMnThSlpaUy\nnwnZC61WK+bOnSuUSqX45JNPhMFgsMpxv/rqKzFo0CCrHOt6paWl4q233hIhISFi8ODBYv369TfM\nSDX2lQuIIB8fodVqZTkXe8cgJptUc40qzPVNMRirbrhG9eVf14Tru0ZVVlYmnnnmGRESEiI2b94s\n0xmQvThw4ICIiIgQcXFx4vTp01Y9tlqtFl5eXqKiosKqx72WVqsVq1evFu3btxf3ODs3OYRr12go\nFFyjYSIGMdksrVYr4uMPiyD/dcLL1VW09/ISgc7OwtPFRcRERgqVSnXTT+Dbtm0TYWFhYsKECRwd\n0w10Op149dVXRatWrcSHH35otVHw9fr27St27Nghy7GvFd2zp1hrYgiLvz4cx0RGyn0adonXiMkm\nVVcDBoMbunTphr/FjULBqWJsPXAIXfv3xweffIJd+/cjMTHxpq0BBw8ejIMHD8LT0xM9evTAli1b\nrHgGZMuOHDmCe++9F7t378a+ffswYcIEODk5yVLLoEGDrHaduCFqtRr7jx3DSDP2MRLAviNHeJ+x\nCRjEZJMWLAA8PYGFC40PgG/TxheffRaOkJCQJj0w3dvbGytWrMDHH3+MadOmYcKECSgtLbVg5WTL\nqqursXDhQgwYMACTJ0/GN998g9DQUFlrkrKxh6lKSkqgdHc3uc87ALgCaOXmVtvGkxqPQUw26eWX\nAYPBODKueb30EuDv72/SX/RBgwbh4MGD8PLyQo8ePbB582YLVE227H//+x+io6Px7bffIjc3F5Mn\nT5ZtFHytfv36ITc3F3/++Se7VzVTDGKyK/7+/iaPaBUKBVasWIHVq1dj+vTpHB3bIVNaLVZXV+Of\n//wn+vXrh0cffRRbt25FWFiYZQttJK1Wi6+++goKIdAxJESW7lUVFRU4dOgQzpWXs8WsTBjEZFf8\n/PzMnvqqGR17e3ujR48e+OqrrySqjizBnFaLv//+OwYOHIicnBz85z//wbRp0+DsbBu/9tZkZ6N9\nYCA+SE7GO+XlUFdXo1CjQaFGg1K9Hs/m52PV5Mlop1RKeo+uXq/Hnj17MH/+fAwaNAhKpRJvvfUW\nglu1qm0xawq2mDWD3KvFiJpi9erVYvz48ZLtb/v27SI8PFw88cQT4uLFi5Ltl6RhaqvF6upqsXz5\nchEQECDS09NFVVWVjGdxI2t2r6qqqhJ5eXli0aJFYtiwYcLb21v06tVLPPfcc2LLli2irKxMCFG3\nxaxJty+xxazJGMRkVzZv3iyGDRsm6T4vX74spk2bJoKDg8XGjRsl3TeZztSwKiwsFIMGDRJ33323\n+O9//yv3adwgW6USoR4e4kQTQu7EX+fXmL7OBoNBHDlyRCxfvlzEx8cLPz8/ceedd4qpU6eKtWvX\nigsXLtS7XX0tZtnQwzoYxGRX9u7dK+6++26L7HvHjh2iQ4cO4vHHH+foWGamhlUbV1eh8PISb775\nptDr9XKfxg0sFXYFBQXi/fffF+PHjxetW7cW7du3F0lJSeKTTz5pUpMSS39IoPoxiC3g1CkhRowQ\nwt9fiDZthJg2TYjqarmrcgz//e9/RadOnSy2f41GI6ZPny7atm3L0bFMzA0rpUJhsyMzs6d//+pe\ndebMGfHpp5+KpKQkERYWJoKCgsQjjzwi3n//fVFQUGBWjXzog/UxiC1g9GghJkwQQqcT4tw5IXr0\nEGL5crmrcgznz58XAQEBFj/Ojh07RMeOHcVjjz0mSkpKLH48ukqqsLJF0RERZnevUrq7Cz8/PxEf\nHy+WL18ujhw5InlXsJpr87EKhViLG6/N36zFLDUdg9gCOncW4uuvr/77rFlCTJkiXz2ORK/Xi9tu\nu01UW2GKQaPRiBkzZoi2bduKDRs2WPx4ZCRFWNliq8VLly4JL1fXOqHW1JcOEJ4uLlb5cKjVaoVK\npRIxkZG1LWbbe3kJL1fXRrWYpcZzEkIIuVduO5qZM4HSUiArC7h4ERg2DHjtNWCkOf3jqJaPjw9O\nnjxptdskdu3ahaSkJNxzzz1YtmwZ75O0ILVajWClEpf0epO7POkB+Lm64nRx8S3/jBgMBlRVVdW+\n9Hp9nX+/1asp7//zzz/x0aJFOGXmfcFhXl7YfugQwsPDzdpPU6jV6trbBv39/XmLksTM6WhGDZg3\nD4iNBXx8jN2hnnySISylmu5a1vpl0L9/f+Tn52P27Nno0aMHMjMz8dBDD1nl2M1NbatFvemtJVwB\neFZVoXv37nBycrppOAoh4OrqChcXl9rX9f/emFdjtrly5Qrsddzj6+vL8LUgBrEFDB0KjBsH/Pwz\ncPkyMHEikJZm7JtM5qsJYmuOCLy8vLB06VKMGTMGEydOxOeff45ly5YhICCg0ftQq9UoKSkBAAQE\nBPAXG4xdr86cOYPCwkIUFBQgLy8PlZWVZu+3RYsW+Hj1aoSHh980JK3Z3EOtViP400+hh/HDginY\nvcoxMYglduECkJsLbNsGuLgAfn7GIJ47l0EsFVP7TUshJiYGBw8erDM6HjVqVIPv12q1yMnJQebC\nhdh/9CiU7u4AgGKtFr26dkVKWhrGjBlz06dI2btLly7VBm1BQUGdr4uKiuDv748OHTogPDwcbdu2\nhVoIs8PqYlUVevXqZVMfdnx9fdGra1dsys/HaBP3we5VjonXiC0gJMR4nTg11TgiTkoCvLyA1avl\nrswxjB07FmPHjsW4ceNkrWP37t2YOHEi+vbti+XLl98wOl6TnY2ZycnoIQRSLl/GCFz95KsHsAlA\npkKBw87OyMjKQkJiopXPQBo6nQ5FRUU3BG3NP/V6fW3QdujQoc7XYWFh8PDwqLO/mMhIPGtGWK0F\nkBEZiV3795t9blJTqVRYNXkytmo0Jm0f6+2NSStXItFO/6xQ/RjEFvDzz8BzzwGHDwOursDgwcDy\n5YBSKXdljiE5ORm9evXClClT5C4F5eXlmD17NtasWYMVK1YgPj4eALAsPR2L58zBuooKRN1iH3kA\n4j098fz8+ZiRmmrxmptKCIHz5883GLR//vkngoODa8P1+sBt1apVk55y5MhhpdVq0T4wEFvKytC7\nidvmAYjz8UFRcbFDz6A0RwxisjsvvvgivL298X//939yl1Jr9+7dSEpKQp8+fTBo0CDMnzkTuysq\n0K6R2xcBiPb0xKJVq2QZGV+5cuWGgL32n56eng0GbWhoKFxdTZ1IvpGjh9Wa7GzMSkqyqz8fZFm8\nRkx2x8/PD+fPn5e7jDqio6Nx4MABvPDCC/h7cjJ+EKLRv2QBoB2AdeXliEtORvzo0ZKHSHV1NU6d\nOlVv0BYUFKCsrAxhYWF1gnbQoEEIDw9HeHg4fHx8JK3nZtzd3ZGRlYVRJoRVvKcnMrKybDaEASAh\nMRHnzpxBtAkzJgxhx8QgJrvTokULnDhxAgUFBTa1+tjT0xP33nsvDq1ahd7l5U3ePgpAN4MBOTk5\nTZ5WFUKgtLS0wUVRJ0+ehFKprBO0w4YNq/26devWNvN4QMDxw2pGaiqC2rZFXHIyuhsMSNFoMBJ1\n1xBsBJDp7Y0jTk52vYaAbo1T02QXrl19vO/wYfgAaOHhYXOrjy250Eir1dZ+ALk+aAsLCyGEaHBR\nVPv27dGiRQuzzk0ONQveHDWsdDrd1T/XR46g1V9/fi/odOjdrRtS0tIw2gIzJGRbGMRk8+xl9bFU\nXaFaurgg/e23ce7cuTpBe/78eYSGhtYbtOHh4fD392/Soih70VzCit2rmi8GMdk0e1p9XFBQgNiI\nCBSauNq3RpCzM+6Oi0OPHj3qBG5ISAhcXJr31SSGFTkiBjHZLHtbXXrs2DEM69MHJ0y4PnwtOXoJ\nE5F8GMRkk2ztFpaqqiqcPXsWJ0+eRFFREU6ePHnDq7S0FM56PS7DvK5QjX1gARE5huY9z0U2Kycn\nB90NhiaHMND01cc1DSuuD9ZrA/fcuXNQKpUIDQ1FaGgo2rVrhw4dOmDAgAG13wsKCsKA3r3ZwpCI\nmoQjYrJJUq0+3rlvH9Rq9U1HsqdOnYK3t3dtoF77ateuHUJDQ9G2bdtGNa1w5K5QRGQZDGKyOVKt\nPvYG4OLlBWdn5xuC9dpXSEgIPD09Jand1qbUicj2cWqabI5Uz6QN9PDApj17EBERIV1xt+DoXaGI\nSHq200qHSGLOzs5Wbc1YY3hcHFyVStzt4oK8Rrw/D8aV3vbSFYqIpMUgJpsTEBCAYq0Wpo+H5XuA\n+pUrVxAXF4chDzyAf378MeJ8fHC/QoEcAFXX1bcWxmvCcT4+WLRqlU0+eYmILI9BTDan9gHqZuxD\njtXHlZWVGDVqFDp27IjMzEwkPvIIioqL8fR772FpZCRauroizMsLYV5e8HN1RUZkJCatXImi4mKO\nhImaMS7WIptkb6uPdTod4uPj4ePjg08++QS33XbbDe9hVygiqg+DmGySPa0+1uv1SEhIAACsWbNG\n0mfzEpHj49Q02aTa1cceHihqwnbWXn1cXV2NJ554ApWVlVCpVAxhImoyBjHZrITERDy/YAGiPTxs\ncvWxwWDA008/jfPnz2Pt2rVwd3e3+DGJyPEwiMmmzUhNxaIPPrjl6uPBCgX6OzlhUlqaVVYfCyEw\nbdo0/P7779i4cSM8PDwsfkwicky8Rkx2oTHPpNXr9Vi0aBHy8vIsOkUshMBzzz2HPXv24LvvvpPl\nXmUichwMYrI7Da0+FkJg6NChGDJkCGbNmmWx48+ePRtbtmzB999/Dz8/P4sdh4iaBwYxOZQ//vgD\nd999N/Ly8tC+fXvJ979gwQJkZ2djx44daNWqleT7J6Lmh9eIyaF07NgRzz77LKZOnQqpP2MuXrwY\nq1evxtatWxnCRCQZBjE5nFmzZqGgoAA5OTmS7fPtt99GZmYmtm3bhtatW0u2XyIiTk2TQ9q1axfG\njx+Po0ePmr2Y6v3338f8+fOxc+dOhIWFSVMgEdFfOCJu5rKzga5dAYUC6NQJ2LNH7oqk0b9/fwwd\nOhRz5841az+ffPIJ5s2bh61btzKEicgiOCJuxr77Dpg8Gfj8c6BvX+DsWeP327SRty6plJSUoFu3\nbvjqq6/Qp0+f2u+r1WqUlJQAMD7pqaGez19++SWmT5+Obdu2oWvXrlapmYiaH46Im7F584CXXjKG\nMGAMYEcJYcAYsgsXLkRycjKuXLkClUqFmMhIBCuViI2IQGxEBIKVSsRERkKlUkGn09Vuu2nTJkyd\nOhVff/01Q5iILIoj4mbKYAA8PIBXXwXefx/QaoGHHgIWLwYcqVOjEALdu3XD2cJCRLm6IuXyZYwA\n4PLXz/UANgHIVChw2NkZGVlZ8PP3x2OPPYbNmzejb82nFCIiC2EQN1NnzwLBwUCfPsBXXwEuLsDI\nkcCgQcD8+XJXJ51l6elYNHs21ldWIuoW780D8JC7OzQuLtj87bfo16+fNUokomaOU9PNVE1r5Bkz\ngMBAwN8fSE0FtmyRty4prcnOxuI5c7CnESEMAFEAftRqoaiqwqmTJy1dHhERAAZxs9WyJRASUvd7\nTk7y1GIJWq0WM5OTsb6iAu2asF07ABv+2vbaa8ZERJbCIG7GJk4Eli8HiouB0lLgn/8ERoyQuypp\n5OTkoLvBgN4mbBsFoJvBIGlDECKihvAacTNWVQXMnAl89plxqjohAVi4EPjrwUZ2LSYyEs/m52O0\niduvBZARGYld+/dLWRYR0Q0YxORw1Go1gpVKXNLra1dHN5UegJ+rK04XFzd4nzERkRQ4NU0Op6Sk\nBEp3d5NDGABcAbRyc6t93CIRkaUwiImIiGTEICaHExAQgGKtFnoz9qEHcEGng7+/v1RlERHVi0FM\nDsfX1xe9unbFJjP2sRFA727deH2YiCyOQUwOKSUtDZkKhcnbZ3p7IyUtTcKKiIjqx1XT5JC0Wi3a\nBwZiS1lZk+8lzgMQ5+ODouJiuDnCvVxEZNM4IiaH5O7ujoysLIzy8EBRE7YrAhDv6YmMrCyGMBFZ\nBYOYHFZCYiKeX7AA0R4eyGvE+/MARHt64vn585GQmGjp8oiIAHBqmpqBNdnZmJmcjO4GA1I0GoxE\n3ccgboTxmvARJydkZGUxhInIqhjE1CzodDrk5OQgc+FC7DtyBK3+mna+oNOhd7duSElLw+jRozkd\nTURWxyCmZketVtd2zPL39+ctSkQkKwYxERGRjLhYi4iISEYMYiIiIhkxiImIiGTEICYiIpIRg5iI\niEhGDGIiIiIZMYiJiIhkxCAmIiKSEYOYiIhIRgxiIiIiGTGIiYiIZMQgJiIikhGDmIiISEYMYiIi\nIhkxiImIiGTEICYiIpIRg5iIiEhGDGIiIiIZMYiJiIhkxCAmIiKSEYOYiIhIRgxiIiIiGTGIiYiI\nZMQgJiIikhGDmIiISEYMYiIiIhkxiImIiGTEICYiIpIRg5iIiEhGDGIiIiIZMYiJiIhkxCAmIiKS\nEYOYiIhIRgxiIiIiGTGIiYiIZMQgJiIikhGDmIiISEYMYiIiIhkxiImIiGTEICYiIpIRg5iIiEhG\nDGIiIiIZMYiJiIhkxCAmIiKSEYOYiIhIRgxiIiIiGTGIiYiIZMQgJiIikhGDmIiISEYMYiIiIhkx\niImIiGTEICYiIpIRg5iIiEhGDGIiIiIZMYiJiIhkxCAmIiKSEYOYiIhIRgxiIiIiGTGIiYiIZPT/\nNLRxJOLkF/4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112ad0b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G3 = nx.connected_caveman_graph(4,4)\n",
    "nx.draw(G3)\n",
    "nx.draw_networkx_labels(G3,pos,font_size=12,font_color='b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 0.23333333333333336), (1, 0.0), (2, 0.02936507936507937), (3, 0.2658730158730159), (4, 0.23333333333333336), (5, 0.0), (6, 0.02936507936507937), (7, 0.2658730158730159), (8, 0.2333333333333334), (9, 0.0), (10, 0.029365079365079365), (11, 0.26587301587301587), (12, 0.23333333333333336), (13, 0.0), (14, 0.029365079365079365), (15, 0.26587301587301587)]\n"
     ]
    },
    {
     "data": {
      "image/png": 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73Z5lkWjJMAgQnSGZTGJjYwOlUgmWZeHg4AC9Xm/exbpDp9NBv99HqVQaWlsJ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\nB5MLAHB1fGRPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112ae0b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Gt = most_important(G3)\n",
    "pos = nx.spring_layout(G3)\n",
    "# draw the nodes and the edges (all)\n",
    "nx.draw_networkx_nodes(G3,pos,node_color='b',alpha=0.2,node_size=8)\n",
    "nx.draw_networkx_edges(G3,pos,alpha=0.1)\n",
    "\n",
    "# draw the most important nodes with a different style\n",
    "nx.draw_networkx_nodes(Gt,pos,node_color='r',alpha=0.4,node_size=254)\n",
    "# also the labels this time\n",
    "nx.draw_networkx_labels(Gt,pos,font_size=12,font_color='b')\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}