2 Network Connectivity.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustering coefficient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.Graph()\n",
    "G.add_edges_from([('A', 'K'), \n",
    "                  ('A', 'B'),\n",
    "                  ('A', 'C'),\n",
    "                  ('B', 'C'),\n",
    "                  ('B', 'K'),\n",
    "                  ('C', 'E'),\n",
    "                  ('C', 'F'), \n",
    "                  ('D', 'E'), \n",
    "                  ('E', 'F'), \n",
    "                  ('E', 'H'), \n",
    "                  ('F', 'G'), \n",
    "                  ('I', 'J')])\n",
    "\n",
    "pos = nx.spring_layout(G)\n",
    "plt.figure(figsize=(8, 6))\n",
    "nx.draw_networkx_nodes(G, pos, node_color='lightblue')\n",
    "nx.draw_networkx_labels(G, pos)\n",
    "nx.draw_networkx_edges(G, pos, edge_color='grey')\n",
    "plt.axis('off');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Local clustering coefficient\n",
    "\n",
    "Local clustering coefficient describes how densely node's friends are connected. In particular, is a fraction of pairs of node's friends that are friends with each other"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3333333333333333"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.clustering(G, 'F')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In case of node F's friends, only C and E are friends with each other. For A, two thirds of its friends are also friends."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6666666666666666"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.clustering(G, 'A')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.clustering(G, 'J')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Global clustering coefficient\n",
    "\n",
    "What if we want to what is a clustering coefficient for the whole graph? In a first approach, we can average clustering for all nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.28787878787878785"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.average_clustering(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also check what fraction of \"open triads\" that are traingles in a network. Transitivity is used for that purpose.\n",
    "\n",
    "Transitivity = 3 * number of closed triads / number of open triads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4090909090909091"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.transitivity(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Transitivity has such property, that it weights the nodes with large degree higher"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Distance measures\n",
    "\n",
    "Distance between two nodes: the length of the shortest path between them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.Graph()\n",
    "G.add_edges_from([('A', 'K'), \n",
    "                  ('A', 'B'),\n",
    "                  ('B', 'C'),\n",
    "                  ('C', 'F'),\n",
    "                  ('F', 'G'),\n",
    "                  ('C', 'E'),\n",
    "                  ('C', 'F'), \n",
    "                  ('E', 'E'), \n",
    "                  ('E', 'D'), \n",
    "                  ('E', 'H'), \n",
    "                  ('E', 'I'), \n",
    "                  ('I', 'J')])\n",
    "\n",
    "pos = nx.spring_layout(G)\n",
    "plt.figure(figsize=(8, 6))\n",
    "nx.draw_networkx_nodes(G, pos, node_color='lightblue')\n",
    "nx.draw_networkx_labels(G, pos)\n",
    "nx.draw_networkx_edges(G, pos, edge_color='grey')\n",
    "plt.axis('off');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.shortest_path_length(G, 'A', 'H')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['A', 'B', 'C', 'E', 'H']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.shortest_path(G, 'A', 'H')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Breadth-first search\n",
    "\n",
    "An efficient way to find the distance to all the nodes, starting from a particular node is breadth-first search. We \"discover\" the nodes in layers.\n",
    "\n",
    "Networkx let's us visualize this process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = nx.bfs_tree(G, 'A')\n",
    "pos = nx.layout.spring_layout(T)\n",
    "plt.figure(figsize=(8, 6))\n",
    "nx.draw_networkx_nodes(T, pos, node_color='tomato')\n",
    "nx.draw_networkx_edges(T, pos, edge_color='grey', arrowstyle='->', arrowsize=15)\n",
    "nx.draw_networkx_labels(T, pos)\n",
    "plt.axis('off');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0,\n",
       " 'K': 1,\n",
       " 'B': 1,\n",
       " 'C': 2,\n",
       " 'F': 3,\n",
       " 'E': 3,\n",
       " 'G': 4,\n",
       " 'D': 4,\n",
       " 'H': 4,\n",
       " 'I': 4,\n",
       " 'J': 5}"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.shortest_path_length(G, 'A')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.8727272727272726"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.average_shortest_path_length(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Diameter - max shortest path length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.diameter(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Eccentricity of a node n is the largest distance between node n and all other nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 5,\n",
       " 'K': 6,\n",
       " 'B': 4,\n",
       " 'C': 3,\n",
       " 'F': 4,\n",
       " 'G': 5,\n",
       " 'E': 4,\n",
       " 'D': 5,\n",
       " 'H': 5,\n",
       " 'I': 5,\n",
       " 'J': 6}"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.eccentricity(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The radius of the graph is the min eccentricity of the network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.radius(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The periphery of a graph is a set of nodes that have eccentricity equal to the diameter of the graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['K', 'J']"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.periphery(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Opposite of a graph's periphery is the center of the graph - it's a set of nodes that are in the center of a graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['C']"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.center(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Karate club graph analysis\n",
    "\n",
    "Karate club graph describes friends within a university karate club. Two partitions of a graph are visible, indicating two groups of friends"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.karate_club_graph()\n",
    "G = nx.convert_node_labels_to_integers(G, first_label=1)\n",
    "\n",
    "pos = nx.spring_layout(G)\n",
    "plt.figure(figsize=(8, 6))\n",
    "nx.draw_networkx_nodes(G, pos, node_color='mediumpurple')\n",
    "nx.draw_networkx_labels(G, pos)\n",
    "nx.draw_networkx_edges(G, pos, edge_color='grey')\n",
    "plt.axis('off');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On average, distance between a pair of nodes is about 2.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.408199643493761"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.average_shortest_path_length(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Radius of a graph is three, what means that for one of the nodes the distance to all other nodes is three"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.radius(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The largest distance between a pair of nodes is five"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.diameter(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are some nodes that are central to the network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 4, 9, 14, 20, 32]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.center(G)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are also some nodes at the netowork's periphery - their eccentricity is equal to the diameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[15, 16, 17, 19, 21, 23, 24, 27, 30]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.periphery(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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