01_图基础及中心性指标.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 一.基础属性\n",
    "**基本定义**：节点、边   \n",
    "**基本类型**：有向图、无向图；加权图，非加权图；连通图，非连通图；连通分量，强连通分量，弱连通分量；二部图   \n",
    "**邻居，$k$阶邻居，度**  \n",
    "**子图、$k$阶子图、路径、图直径**  \n",
    "**表示方式**: 邻接矩阵，关联矩阵  \n",
    "**遍历方式**：深度优先，广度优先   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "#构建图\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "import networkx as nx\n",
    "G=nx.Graph()#无向图，有向图用DiGraph\n",
    "G.add_nodes_from([\"A\",\"B\",\"C\",\"D\",\"E\",\"F\",\"G\",\"H\"])\n",
    "G.add_edges_from([(\"A\",\"B\"),(\"A\",\"C\"),(\"B\",\"C\"),(\"C\",\"D\"),(\"E\",\"F\"),(\"F\",\"G\"),(\"G\",\"H\")])\n",
    "nx.draw_networkx(G)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DegreeView({'A': 2, 'B': 2, 'C': 3, 'D': 1, 'E': 1, 'F': 2, 'G': 2, 'H': 1})"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#度\n",
    "nx.degree(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'A', 'B', 'C', 'D'}, {'E', 'F', 'G', 'H'}]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#连通分量\n",
    "list(nx.connected_components(G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#图直径:所有两两节点直接最短路径的最大值\n",
    "subG=nx.subgraph(G,[\"A\",\"B\",\"C\",\"D\"])\n",
    "nx.diameter(subG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#路径长度\n",
    "nx.shortest_path_length(G,source=\"A\",target=\"D\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 二.中心性指标\n",
    "中心性指标主要用于衡量节点在图中的重要性/影响力，我们对节点重要性的解释有很多，不同的解释下判定中心性的指标也有所不同，通常有这些：点度中心性，中介中心性，接近中心性，特征向量中心性，PageRank，hits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0.2857142857142857,\n",
       " 'B': 0.2857142857142857,\n",
       " 'C': 0.42857142857142855,\n",
       " 'D': 0.14285714285714285,\n",
       " 'E': 0.14285714285714285,\n",
       " 'F': 0.2857142857142857,\n",
       " 'G': 0.2857142857142857,\n",
       " 'H': 0.14285714285714285}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#点度中心性\n",
    "#节点的邻居越多，它就越重要，定义为：度/(节点数-1)\n",
    "nx.degree_centrality(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0.0,\n",
       " 'B': 0.0,\n",
       " 'C': 0.09523809523809523,\n",
       " 'D': 0.0,\n",
       " 'E': 0.0,\n",
       " 'F': 0.09523809523809523,\n",
       " 'G': 0.09523809523809523,\n",
       " 'H': 0.0}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#中介中心性\n",
    "#如果该节点出现该其它两两节点路径上的次数越多，它就越重要\n",
    "nx.betweenness_centrality(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0.3214285714285714,\n",
       " 'B': 0.3214285714285714,\n",
       " 'C': 0.42857142857142855,\n",
       " 'D': 0.2571428571428571,\n",
       " 'E': 0.21428571428571427,\n",
       " 'F': 0.3214285714285714,\n",
       " 'G': 0.3214285714285714,\n",
       " 'H': 0.21428571428571427}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#接近中心性\n",
    "#如果该节点与其它节点之间的距离越近，它就越重要\n",
    "nx.closeness_centrality(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "#特征向量中心性\n",
    "#定义：取邻接矩阵特征分解后，最大特征值对应的特征向量\n",
    "#与某节点连接的节点的邻居越多，就越重要\n",
    "#新增加一个节点I来连接两块连通分量\n",
    "G=nx.Graph()\n",
    "G.add_nodes_from([\"A\",\"B\",\"C\",\"D\",\"E\",\"F\",\"G\",\"H\",\"I\"])\n",
    "G.add_edges_from([(\"A\",\"B\"),(\"A\",\"C\"),(\"B\",\"C\"),(\"C\",\"D\"),(\"E\",\"F\"),(\"F\",\"G\"),(\"G\",\"H\"),(\"I\",\"B\"),(\"I\",\"F\")])\n",
    "nx.draw_networkx(G)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0.44885390912200857,\n",
       " 'B': 0.5468450989996043,\n",
       " 'C': 0.5135021004101872,\n",
       " 'D': 0.21736961615213216,\n",
       " 'E': 0.09799461776528895,\n",
       " 'F': 0.2314938976977582,\n",
       " 'G': 0.11938887762076224,\n",
       " 'H': 0.0505393145300136,\n",
       " 'I': 0.3294789107351654}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.eigenvector_centrality(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': 0.10252135128679807,\n",
       " 'B': 0.14929077894067944,\n",
       " 'C': 0.153726203840718,\n",
       " 'D': 0.06022249294537078,\n",
       " 'E': 0.06475108608528522,\n",
       " 'F': 0.16971188372812845,\n",
       " 'G': 0.1235500933464885,\n",
       " 'H': 0.06917616539981883,\n",
       " 'I': 0.1070499444267125}"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#pagerank\n",
    "nx.pagerank(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "({'A': 0.17564701604305502,\n",
       "  'B': 0.21399245433642766,\n",
       "  'C': 0.2009454874842481,\n",
       "  'D': 0.08506205753671801,\n",
       "  'E': 0.03834543957793587,\n",
       "  'F': 0.09058495722206274,\n",
       "  'G': 0.04671661924357704,\n",
       "  'H': 0.019775570471702603,\n",
       "  'I': 0.1289303980842729},\n",
       " {'A': 0.1756470158158291,\n",
       "  'B': 0.21399245588711766,\n",
       "  'C': 0.2009454869245228,\n",
       "  'D': 0.085062057946483,\n",
       "  'E': 0.03834543855419052,\n",
       "  'F': 0.09058495938682286,\n",
       "  'G': 0.04671661787549817,\n",
       "  'H': 0.01977557118599924,\n",
       "  'I': 0.1289303964235366})"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#hits\n",
    "nx.hits(G)"
   ]
  },
  {
   "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}