Project2 论文是如何被引用的.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 论文是如何被引用的？\n",
    "\n",
    "每一篇论文后面通常都会有参考文献，这些参考文献是如何被引用的呢？是（在同一领域论文中）被随机选中的吗？还是说存在着某种隐含模式，比如说马太效应（“穷则越穷，富则越富”）？"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# 从网页链接导入数据（由于数据存储在谷歌服务器，需科学上网，无法科学上网的小伙伴请下载文件数据并从本地导入）\n",
    "\n",
    "import urllib2\n",
    "\n",
    "# Code for loading citation graph\n",
    "\n",
    "CITATION_URL = \"http://storage.googleapis.com/codeskulptor-alg/alg_phys-cite.txt\"\n",
    "\n",
    "def load_graph(graph_url):\n",
    "    \"\"\"\n",
    "    Function that loads a graph given the URL\n",
    "    for a text representation of the graph\n",
    "    \n",
    "    Returns a dictionary that models a graph\n",
    "    \"\"\"\n",
    "    graph_file = urllib2.urlopen(graph_url)\n",
    "    graph_text = graph_file.read()\n",
    "    graph_lines = graph_text.split('\\n')\n",
    "    graph_lines = graph_lines[ : -1]\n",
    "    \n",
    "    print \"Loaded graph with\", len(graph_lines), \"nodes\"\n",
    "    \n",
    "    answer_graph = {}\n",
    "    for line in graph_lines:\n",
    "        neighbors = line.split(' ')\n",
    "        node = int(neighbors[0])\n",
    "        answer_graph[node] = set([])\n",
    "        for neighbor in neighbors[1 : -1]:\n",
    "            answer_graph[node].add(int(neighbor))\n",
    "\n",
    "    return answer_graph\n",
    "\n",
    "#citation_graph = load_graph(CITATION_URL)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loaded graph with 27770 nodes\n"
     ]
    }
   ],
   "source": [
    "# 从文本文件中导入数据，并存储成以字典表示的有向图（ directed graph）\n",
    "def load_graph(graph_file_path):\n",
    "    \"\"\"\n",
    "    从文本文件中导入数据（以文本表示的图）\n",
    "    返回存以字典表示的有向图（ directed graph）\n",
    "    \"\"\"\n",
    "    answer_graph = {}\n",
    "    \n",
    "    with open(graph_file_path) as data:\n",
    "        for line in data.xreadlines():\n",
    "            neighbors = line.split(' ')\n",
    "            node = int(neighbors[0])\n",
    "            answer_graph[node] = set([])\n",
    "            for neighbor in neighbors[1 : -1]:\n",
    "                answer_graph[node].add(int(neighbor)) \n",
    "    print \"Loaded graph with\", len(answer_graph), \"nodes\"\n",
    "    return answer_graph\n",
    "\n",
    "citation_graph = load_graph('e:\\\\python programs\\\\citation graph data.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 计算citation graph的in-degree distribution，并把数据标准化\n",
    "\n",
    "# 先定义一个辅助函数来计算有向图的in-degree\n",
    "def compute_in_degrees(digraph):\n",
    "    \"\"\"\n",
    "    Takes a directed graph digraph (represented as a dictionary) \n",
    "    and computes the in-degrees for the nodes in the graph\n",
    "    returns a dictionary\n",
    "    \"\"\"\n",
    "    # initialize the in_degrees dictionary\n",
    "    in_degrees_dic = {}\n",
    "    for node in digraph:\n",
    "        in_degrees_dic[node] = 0\n",
    "    # compute the indegrees of all nodes\n",
    "    for node in digraph:\n",
    "        adjacent_nodes = digraph[node]\n",
    "        for adj_node in adjacent_nodes:\n",
    "            in_degrees_dic[adj_node] += 1\n",
    "    return in_degrees_dic\n",
    "\n",
    "# 再定义函数来计算有向图的in-degree distribution（normalized）\n",
    "def in_degree_distribution(digraph):\n",
    "    \"\"\"\n",
    "    Takes a directed graph digraph (represented as a dictionary) \n",
    "    and computes the normalized distribution of the in-degrees of the graph\n",
    "    returns a dictionary \n",
    "    \"\"\"\n",
    "    in_degrees_dic = compute_in_degrees(digraph)\n",
    "    distribution_dic = {}\n",
    "    num_nodes = float(len(digraph))\n",
    "    for node in in_degrees_dic:\n",
    "        in_degree = in_degrees_dic[node]\n",
    "        if distribution_dic.has_key(in_degree):\n",
    "            distribution_dic[in_degree] += (1.0/num_nodes)\n",
    "        else:\n",
    "            distribution_dic[in_degree] = (1.0/num_nodes)\n",
    "    return distribution_dic\n",
    "\n",
    "citation_distribution = in_degree_distribution(citation_graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0xefe9240>"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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P8kymsgz22FDLMxKf9ZKSEubNm9dh+oGKRx/IMJw+kEnu41ScCd7OwRmnvBS4UlU/DPB8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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd460d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 算好了in-degree distribution，画个图可视化一下\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "xdata = citation_distribution.keys()\n",
    "ydata = citation_distribution.values()\n",
    "plt.loglog(xdata, ydata,'c')\n",
    "plt.title(\"Log-Log Plot of In-degree Distribution of the Citation Graph\")\n",
    "plt.xlabel(\"Citations\")\n",
    "plt.ylabel(\"Fraction of Papers\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "根据上面的citation graph的in-degree分布图，我们可以看到，论文被引用次数少的占比较大，随着论文被引用次数增长，论文所占的比例是越来越低的，有点类似长尾分布。但是看了这个图还是没什么感觉，我们找个随机引用模式下的图来对比看看。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 生成随机有向图\n",
    "\n",
    "import random\n",
    "\n",
    "def random_digragh(n, p):\n",
    "    \"\"\"\n",
    "    Functions that generate random directed graphs with n nodes\n",
    "    with edge (i,j) in probability p\n",
    "    \n",
    "    Returns a directd graph in dictionary representation\n",
    "    \"\"\"\n",
    "    nodes = range(n)\n",
    "    # initialize the result_graph\n",
    "    result_graph = {}\n",
    "    for node in nodes:\n",
    "        result_graph[node] = set([])\n",
    "    # generate edges\n",
    "    for node in nodes:\n",
    "        rest_nodes = set(nodes) - set([node])\n",
    "        for other_node in rest_nodes:\n",
    "            # generate a random number in [0,1)\n",
    "            ran = random.random()\n",
    "            if ran < p:\n",
    "                # add j to the adjacent nodes\n",
    "                result_graph[node].add(other_node)\n",
    "    return result_graph\n",
    "\n",
    "# test       \n",
    "# print random_digragh(2,1)\n",
    "# print random_digragh(4,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# generate some random directed graphs with len(citation_graph) nodes\n",
    "# NODES = len(citation_graph) that's too large...\n",
    "NODES = 100\n",
    "r_digraph0 = random_digragh(NODES, 0.25)\n",
    "r_digraph1 = random_digragh(NODES, 0.5)\n",
    "r_digraph2 = random_digragh(NODES, 0.75)\n",
    "\n",
    "# compute the in-degrees distributions of the above graph\n",
    "r_digraph0_distribution = in_degree_distribution(r_digraph0)\n",
    "r_digraph1_distribution = in_degree_distribution(r_digraph1)\n",
    "r_digraph2_distribution = in_degree_distribution(r_digraph2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ZTzi+U7/jo0bt1VdeKebPn2+jR08akOeqq64qebxSWbVSru5G65g3b16/tpG3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\nowAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf0dd4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the citation and the three random graphs's in-degrees distribution graph in log/log scale\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "# 整张图的标题\n",
    "fig = plt.figure('Log-log In-degrees Distributions of Citation Graph & 3 Random Graphs ')\n",
    "# 在整张图上加入一个子图，2，2，1的意思是在一个2行2列的子图中的第一张\n",
    "ax1 = fig.add_subplot(2, 2, 1)\n",
    "ax1.set_title('Citation Graph')\n",
    "plt.scatter(citation_distribution.keys(), citation_distribution.values())\n",
    "plt.xlabel(\"k\")\n",
    "plt.ylabel(\"p(k)\")\n",
    "\n",
    "# 第2张\n",
    "ax2 = fig.add_subplot(2, 2, 2)\n",
    "ax2.set_title('Random Graph With p = 0.25')\n",
    "plt.scatter(r_digraph0_distribution.keys(), r_digraph0_distribution.values())\n",
    "#plt.xlim([0,max(r_digraph0_distribution.keys())])\n",
    "plt.xlabel(\"k\")\n",
    "plt.ylabel(\"p(k)\")\n",
    "\n",
    "# 第3张\n",
    "ax3 = fig.add_subplot(2, 2, 3)\n",
    "ax3.set_title('Random Graph With p = 0.5')\n",
    "plt.scatter(r_digraph1_distribution.keys(), r_digraph1_distribution.values())\n",
    "#plt.xlim([0,max(r_digraph1_distribution.keys())])\n",
    "plt.xlabel(\"k\")\n",
    "plt.ylabel(\"p(k)\")\n",
    "\n",
    "# 第4张\n",
    "ax4 = fig.add_subplot(2, 2, 4)\n",
    "ax4.set_title('Random Graph With p = 0.75')\n",
    "plt.scatter(r_digraph2_distribution.keys(), r_digraph2_distribution.values())\n",
    "#plt.xlim([0,max(r_digraph2_distribution.keys())])\n",
    "plt.xlabel(\"k\")\n",
    "plt.ylabel(\"p(k)\")\n",
    "\n",
    "# 调整subplot周围的距离\n",
    "# wspace,the amount of width reserved for blank space between subplots,expressed as a fraction of the average axis width\n",
    "# hspace,he amount of height reserved for white space between subplots,expressed as a fraction of the average axis height\n",
    "fig.subplots_adjust(wspace = 0.4, hspace = 0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对比我们的citation graph 跟 random graph的in-degree distribution,可以很明显得看到差别，citation graph的in-degree distribution散点图看起来是一条长尾，而random graph的in-degree distribution散点图看起来是个钟形图，很显然，论文引用的模式并不是随机的。我们再来看看另一种模式，这里需要设计一个算法来生成类似马太效应的graph，这里用了DPA算法，思路就是那些in-degree越大的节点被选中作为新节点的neighbor的概率越大，进而又使得它的in-degree更大。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "27770 12\n"
     ]
    }
   ],
   "source": [
    "# DPA Algorithm\n",
    "\n",
    "# choose values for n and m that yield a DPA graph \n",
    "# whose number of nodes and edges is roughly the same to those of the citation graph\n",
    "\n",
    "# helper function\n",
    "def compute_avg_outdegree(digraph):\n",
    "    \"\"\"\n",
    "    return average out-degree(integer) of the input graph\n",
    "    \"\"\"\n",
    "    nodes = 0\n",
    "    total_outdegree = 0\n",
    "    for node in digraph:\n",
    "        nodes += 1\n",
    "        total_outdegree += len(digraph[node])\n",
    "    return total_outdegree / nodes\n",
    "\n",
    "\n",
    "# let n be the number of nodes in the citation graph\n",
    "dpa_n = len(citation_graph)\n",
    "\n",
    "# let m be an integer close to the average out-degree of the citation graph\n",
    "dpa_m = compute_avg_outdegree(citation_graph)\n",
    "\n",
    "print dpa_n, dpa_m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Helper class for implementing efficient version\n",
    "of DPA algorithm\n",
    "\"\"\"\n",
    "class DPATrial:\n",
    "    \"\"\"\n",
    "    Simple class to encapsulate optimized trials for DPA algorithm\n",
    "    \n",
    "    Maintains a list of node numbers with multiple instances of each number.\n",
    "    The number of instances of each node number are\n",
    "    in the same proportion as the desired probabilities\n",
    "    \"\"\"\n",
    "    def __init__(self, num_nodes):\n",
    "        \"\"\"\n",
    "        Initialize a DPATrial object corresponding to a \n",
    "        complete graph with num_nodes nodes\n",
    "        \n",
    "        Note the initial list of node numbers has num_nodes copies of\n",
    "        each node number\n",
    "        \"\"\"\n",
    "        self._num_nodes = num_nodes\n",
    "        self._node_numbers = [node for node in range(num_nodes) for dummy_idx in range(num_nodes)]\n",
    "\n",
    "\n",
    "    def run_trial(self, num_nodes):\n",
    "        \"\"\"\n",
    "        Conduct num_node trials using by applying random.choice()\n",
    "        to the list of node numbers\n",
    "        \n",
    "        Updates the list of node numbers so that the number of instances of\n",
    "        each node number is in the same ratio as the desired probabilities\n",
    "        \n",
    "        Returns:\n",
    "        Set of nodes\n",
    "        \"\"\"\n",
    "        \n",
    "        # compute the neighbors for the newly-created node\n",
    "        new_node_neighbors = set()\n",
    "        for dummy_idx in range(num_nodes):\n",
    "            new_node_neighbors.add(random.choice(self._node_numbers))\n",
    "        \n",
    "        # update the list of node numbers so that each node number \n",
    "        # appears in the correct ratio\n",
    "        self._node_numbers.append(self._num_nodes)\n",
    "        self._node_numbers.extend(list(new_node_neighbors))\n",
    "        \n",
    "        #update the number of nodes\n",
    "        self._num_nodes += 1\n",
    "        return new_node_neighbors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# helper function to generate complete graph\n",
    "def make_complete_graph(num_nodes):\n",
    "    \"\"\"\n",
    "    Takes the number of nodes num_nodes and\n",
    "    return complete directed graph in dictionary representation\n",
    "    \"\"\"\n",
    "    nodes_set = range(num_nodes)\n",
    "    graph_dic = {}\n",
    "    for node in nodes_set:\n",
    "        adjacent_nodes = set(nodes_set) - set([node])\n",
    "        graph_dic[node] = adjacent_nodes\n",
    "    return graph_dic\n",
    "\n",
    "\n",
    "# implement DPA algorithm\n",
    "def dpa_graph(n, m):\n",
    "    \"\"\"\n",
    "    given num_nodes n and interger m\n",
    "    generate a dpa graph\n",
    "    and return it\n",
    "    \"\"\"\n",
    "    # start from a complete graph of m nodes\n",
    "    num_nodes = m\n",
    "    graph = make_complete_graph(m)\n",
    "    # create a DPATrial object to encapsulate optimized trials for DPA algorithm\n",
    "    dpa_trial = DPATrial(num_nodes)\n",
    "    \n",
    "    for new_node in range(m, n):\n",
    "        new_node_neighbors = dpa_trial.run_trial(num_nodes)\n",
    "        # update graph\n",
    "        graph[new_node] = new_node_neighbors\n",
    "    \n",
    "    return graph  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# compute a DPA graph with the same number of nodes of the citation graph\n",
    "dpa_graph1 = dpa_graph(dpa_n, dpa_m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x133fc4e0>"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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qFbJLMYwcSyhCdQ0jTVx6KTB3LnM/ypRhHayGDYF77/X2KViQ09zOnJn8eYoU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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1053cc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compute a log/log plot of the points in the dpa graph's in-degree distribution\n",
    "# compute in-degree distribution of dpa_graph1\n",
    "dpa_graph1_distribution = in_degree_distribution(dpa_graph1)\n",
    "\n",
    "xdata1 = dpa_graph1_distribution.keys()\n",
    "ydata1 = dpa_graph1_distribution.values()\n",
    "plt.loglog(xdata1, ydata1, basex = 10, basey = 10, linestyle = \"dotted\")\n",
    "plt.title(\"Log-Log Plot of In-degree Distribution of DPA Graph\")\n",
    "plt.xlabel(\"In-degrees\")\n",
    "plt.ylabel(\"Fraction of nodes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "DPA graph的in-degree distribution plot看起来跟citation graph的in-degree distribution plot比较类似，都是随着论文被引用次数增长，论文数量占比下降。也就是说被引用次数很多的论文占的是少数，大部分论文都是被引用很少次的。这跟我们的认知是很相似的。\n",
    "\n",
    "**那么为什么是这样一种模式呢？**\n",
    "\n",
    "从DPA算法的设计中我们得到一些灵感，那些被引用次数越多的论文，其曝光次数越多，被越多的人看到，然后这些人又引用了这些论文，就像滚雪球一样，越滚越大。而那些默默无闻的论文，由于曝光次数太少，就渐渐沉了，更加不会被引用了。\n",
    "\n",
    "其实这个模式还是很显而易见的啦。"
   ]
  }
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