code.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "##import libraries\n",
    "\n",
    "import numpy as np\n",
    "float_formatter = lambda x: \"%.3f\" % x\n",
    "np.set_printoptions(formatter={'float_kind':float_formatter})\n",
    "from sklearn.datasets.samples_generator import make_circles\n",
    "from sklearn.cluster import SpectralClustering, KMeans\n",
    "from sklearn.metrics import pairwise_distances\n",
    "from matplotlib import pyplot as plt\n",
    "import networkx as nx\n",
    "from sklearn.metrics.pairwise import cosine_similarity\n",
    "from scipy import sparse\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "from matplotlib.pyplot import figure\n",
    "import ges\n",
    "import ges.scores\n",
    "import sempler\n",
    "import scipy as sp\n",
    "from matplotlib.pyplot import figure\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import adjecency matrix \n",
    "\n",
    "A = np.array([[0,\t1,\t0,\t1,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0,\t0],\n",
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    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = A * np.random.uniform(1, 2, A.shape) # sample weights\n",
    "data = sempler.LGANM(W,(0,1), (0,1)).sample(n=5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the score class\n",
    "score_class = ges.scores.GaussObsL0Pen(data)\n",
    "\n",
    "# Run GES with the Gaussian BIC score\n",
    "estimate, score = ges.fit_bic(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 0 ... 0 0 0]\n",
      " [1 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]\n",
      " ...\n",
      " [0 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]] 442056.3094620026\n"
     ]
    }
   ],
   "source": [
    "print(estimate, score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G = nx.from_numpy_array(A)\n",
    "G.edges(data=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_graph_with_labels(adjacency_matrix):\n",
    "    rows, cols = np.where(adjacency_matrix == 1)\n",
    "    edges = zip(rows.tolist(), cols.tolist())\n",
    "    gr = nx.DiGraph()\n",
    "    gr.add_edges_from(edges)\n",
    "    pos = nx.random_layout(gr)\n",
    "    nx.draw(gr, pos=pos, width=1, node_size=1000, cmap=plt.cm.Blues, edge_color=\"#cccccc\", with_labels=True)\n",
    "    figure(figsize=(10, 8), dpi=300)\n",
    "    plt.draw()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Local\\chakrabo\\Anaconda\\lib\\site-packages\\networkx\\drawing\\nx_pylab.py:579: MatplotlibDeprecationWarning: \n",
      "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n",
      "  if not cb.iterable(width):\n",
      "C:\\Local\\chakrabo\\Anaconda\\lib\\site-packages\\networkx\\drawing\\nx_pylab.py:676: MatplotlibDeprecationWarning: \n",
      "The iterable function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use np.iterable instead.\n",
      "  if cb.iterable(node_size):  # many node sizes\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 3000x2400 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#draw graph and dejecency matrix for the input graph\n",
    "\n",
    "show_graph_with_labels(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "degree matrix:\n",
      "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      "laplacian matrix:\n",
      "[[ 0 -1  0 ...  0  0  0]\n",
      " [ 0  0  0 ...  0  0  0]\n",
      " [ 0  0  0 ...  0  0  0]\n",
      " ...\n",
      " [ 0  0  0 ...  0  0  0]\n",
      " [ 0  0  0 ...  0  0  0]\n",
      " [ 0  0  0 ...  0  0  0]]\n"
     ]
    }
   ],
   "source": [
    "# compute degree matrix (D) and compute the laplacian matrix (L) from formula L = D-A\n",
    "\n",
    "#degree matrix\n",
    "D = np.diag(A)\n",
    "print('degree matrix:')\n",
    "print(D)\n",
    "\n",
    "# contructing the laplacian matrix\n",
    "L = D - A\n",
    "print('laplacian matrix:')\n",
    "print(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#normalized Ln with Lsys formula \n",
    "L_n = np.array([\n",
    "      [1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "      [0, 1, 0, 0, -0.707, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "      [0, -0.578, 1.002252, 0, 0, 0, 0, -0.408646, -0.408646, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 1.002252, -0.408646, -0.408646, -0.408646, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 0, 0.999698, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 0, 0, 0.999698, 0, 0, 0, -0.707, 0, -0.707, 0, 0, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 0, 0, 0, 0.999698, 0, 0, -0.707, -0.499849, 0, 0, 0, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 0, 0, 0, -0.499849, 0.999698, -0.499849, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 0, 0, 0, -0.499849, -0.499849, 0.999698, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -0.707, 0, 0, 0, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 0, 0, -0.499849, 0, 0, 0, 0, 0.999698, 0, -0.707, 0, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 0, -0.707, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "      [0, 0, 0, 0, -0.707, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],\n",
    "      [0, 0, 0, 0, 0, 0, 0, 0, 0, -0.707, 0, 0, 0, 0, 0, 0, 0, 0.999698]\n",
    "      ])\n",
    "print('normalized laplacian matrix:')\n",
    "print(L_n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eigenvalues:\n",
      "[-5.139 -4.839 -4.838 -3.846 -3.798 -3.764 -2.948 -2.841 -2.832 -2.828\n",
      " -2.828 -2.536 -2.450 -2.424 -2.359 -2.346 -2.214 -2.003 -1.905 -1.684\n",
      " -1.618 -1.618 -1.591 -1.549 -1.460 -1.425 -1.414 -1.414 -1.414 -1.414\n",
      " -1.414 -1.355 -1.116 -1.075 -1.000 -1.000 -1.000 -0.864 -0.793 -0.792\n",
      " -0.694 -0.676 -0.618 -0.618 -0.521 -0.507 -0.000 -0.000 -0.000 -0.000\n",
      " -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000\n",
      " -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000\n",
      " -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000\n",
      " -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000\n",
      " -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.000 0.000 0.000\n",
      " 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000\n",
      " 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000\n",
      " 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000\n",
      " 0.493 0.521 0.618 0.618 0.656 0.678 0.792 0.800 0.851 1.000 1.000 1.000\n",
      " 1.075 1.119 1.365 1.414 1.414 1.414 1.414 1.414 1.425 1.460 1.549 1.616\n",
      " 1.618 1.618 1.684 1.905 2.030 2.210 2.346 2.359 2.422 2.450 2.536 2.828\n",
      " 2.828 2.832 2.841 2.950 3.764 3.800 3.846 4.838 4.839 5.132]\n",
      "eigenvectors:\n",
      "[[0.108 0.000 0.000 ... 0.000 0.000 -0.109]\n",
      " [0.108 0.000 0.000 ... 0.000 0.000 -0.109]\n",
      " [0.108 0.000 0.000 ... 0.000 0.000 -0.109]\n",
      " ...\n",
      " [0.000 0.016 0.003 ... -0.003 -0.016 0.000]\n",
      " [0.000 0.007 0.001 ... -0.001 -0.007 0.000]\n",
      " [0.000 0.007 0.001 ... -0.001 -0.007 0.000]]\n"
     ]
    }
   ],
   "source": [
    "# compute the eigenvalues and eigenvector matrices rusing numpy function linalg.eig \n",
    "\n",
    "e, v = np.linalg.eigh(L)\n",
    "# eigenvalues\n",
    "print('eigenvalues:')\n",
    "print(e)\n",
    "# eigenvectors\n",
    "print('eigenvectors:')\n",
    "print(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1296x432 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot eigenvalues for all nodes\n",
    "\n",
    "fig = plt.figure(figsize=[18, 6])\n",
    "ax1 = plt.subplot(131)\n",
    "plt.plot(e, 'tab:orange')\n",
    "ax1.title.set_text('eigenvalues')\n",
    "\n",
    "#plot the eigenvector with eigenvalue 0 for second last and third last pairs\n",
    "\n",
    "i = np.where(e < 0.01)[0]\n",
    "ax2 = plt.subplot(132)\n",
    "plt.plot(v[:, i[1]], 'tab:green')\n",
    "ax2.title.set_text('first eigenvector with eigenvalue of 0')\n",
    "\n",
    "ax3 = plt.subplot(133)\n",
    "plt.plot(v[:, i[2]], 'tab:red')\n",
    "ax3.title.set_text('second eigenvector with eigenvalue of 0')\n",
    "\n",
    "fig.tight_layout()\n",
    "plt.show()\n",
    "fig.savefig('eigenvalues_183params.jpg')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4, 4, 4, 1, 4, 4, 4, 4, 4, 0, 4, 0, 0, 0, 4, 0, 3, 2, 1, 2, 1, 1,\n",
       "       2, 2, 1, 2, 2, 4, 4, 1, 4, 0, 0, 4, 4, 4, 0, 4, 4, 1, 1, 4, 4, 4,\n",
       "       4, 4, 4, 2, 1, 4, 4, 1, 4, 4, 4, 4, 2, 1, 4, 4, 1, 1, 4, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 1, 1, 1])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U = np.array(v[:, i[1]])\n",
    "kmeans = KMeans(init='k-means++', n_clusters=5)\n",
    "U_ = U.reshape(-1, 1)\n",
    "kmeans.fit(U_)\n",
    "kmeans.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x227aa5d6780>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#X, clusters = make_circles(n_samples=1000, noise=.05, factor=.5, random_state=0)\n",
    "U, clusters = make_circles(noise=.05, factor=.5, random_state=0)\n",
    "plt.scatter(U[:,0], U[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x227aa5f50b8>"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "km = KMeans(init='k-means++', n_clusters=4)\n",
    "km_clustering = km.fit(U)\n",
    "plt.scatter(U[:,0], U[:,1], c=km_clustering.labels_, cmap='rainbow', alpha=0.7, edgecolors='b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x227aa689c88>"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sc = SpectralClustering(n_clusters=4, affinity='nearest_neighbors', random_state=0)\n",
    "sc_clustering = sc.fit(U)\n",
    "plt.scatter(U[:,0], U[:,1], c=sc_clustering.labels_, cmap='rainbow', alpha=0.7, edgecolors='b')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "######PageRank\n",
    "def pagerank(G, alpha=0.85, personalization=None, \n",
    "\t\t\tmax_iter=100, tol=1.0e-6, nstart=None, weight='weight', \n",
    "\t\t\tdangling=None): \n",
    "\t\"\"\"Return the PageRank of the nodes in the graph. \n",
    "\tParameters \n",
    "\t---------- \n",
    "\tG : graph \n",
    "\tA NetworkX graph. Undirected graphs will be converted to a directed \n",
    "\tgraph with two directed edges for each undirected edge. \n",
    "\talpha : float, optional \n",
    "\tDamping parameter for PageRank, default=0.85. \n",
    "\tmax_iter : integer, optional \n",
    "\tMaximum number of iterations in power method eigenvalue solver. \n",
    "\ttol : float, optional \n",
    "\tError tolerance used to check convergence in power method solver. \n",
    "\tnstart : dictionary, optional \n",
    "\tStarting value of PageRank iteration for each node. \n",
    "\tweight : key, optional \n",
    "\tEdge data key to use as weight. If None weights are set to 1. \n",
    "\tReturns \n",
    "\t------- \n",
    "\tpagerank : dictionary \n",
    "\tDictionary of nodes with PageRank as value \n",
    "\t\"\"\"\n",
    "\tif len(G) == 0: \n",
    "\t\treturn {} \n",
    "\n",
    "\tif not G.is_directed(): \n",
    "\t\tD = G.to_directed() \n",
    "\telse: \n",
    "\t\tD = G \n",
    "\n",
    "\t# Create a copy in (right) stochastic form \n",
    "\tW = nx.stochastic_graph(D, weight=weight) \n",
    "\tN = W.number_of_nodes() \n",
    "\n",
    "\t# Choose fixed starting vector if not given \n",
    "\tif nstart is None: \n",
    "\t\tx = dict.fromkeys(W, 1.0 / N) \n",
    "\telse: \n",
    "\t\t# Normalized nstart vector \n",
    "\t\ts = float(sum(nstart.values())) \n",
    "\t\tx = dict((k, v / s) for k, v in nstart.items()) \n",
    "\n",
    "\tif personalization is None: \n",
    "\n",
    "\t\t# Assign uniform personalization vector if not given \n",
    "\t\tp = dict.fromkeys(W, 1.0 / N) \n",
    "\telse: \n",
    "\t\tmissing = set(G) - set(personalization) \n",
    "\t\tif missing: \n",
    "\t\t\traise NetworkXError('Personalization dictionary '\n",
    "\t\t\t\t\t\t\t\t'must have a value for every node. '\n",
    "\t\t\t\t\t\t\t\t'Missing nodes %s' % missing) \n",
    "\t\ts = float(sum(personalization.values())) \n",
    "\t\tp = dict((k, v / s) for k, v in personalization.items()) \n",
    "\n",
    "\tif dangling is None: \n",
    "\n",
    "\t\t# Use personalization vector if dangling vector not specified \n",
    "\t\tdangling_weights = p \n",
    "\telse: \n",
    "\t\tmissing = set(G) - set(dangling) \n",
    "\t\tif missing: \n",
    "\t\t\traise NetworkXError('Dangling node dictionary '\n",
    "\t\t\t\t\t\t\t\t'must have a value for every node. '\n",
    "\t\t\t\t\t\t\t\t'Missing nodes %s' % missing) \n",
    "\t\ts = float(sum(dangling.values())) \n",
    "\t\tdangling_weights = dict((k, v/s) for k, v in dangling.items()) \n",
    "\tdangling_nodes = [n for n in W if W.out_degree(n, weight=weight) == 0.0] \n",
    "\n",
    "\t# power iteration: make up to max_iter iterations \n",
    "\tfor _ in range(max_iter): \n",
    "\t\txlast = x \n",
    "\t\tx = dict.fromkeys(xlast.keys(), 0) \n",
    "\t\tdanglesum = alpha * sum(xlast[n] for n in dangling_nodes) \n",
    "\t\tfor n in x: \n",
    " \n",
    "\t\t\t# doing a left multiply x^T=xlast^T*W \n",
    "\t\t\tfor nbr in W[n]: \n",
    "\t\t\t\tx[nbr] += alpha * xlast[n] * W[n][nbr][weight] \n",
    "\t\t\tx[n] += danglesum * dangling_weights[n] + (1.0 - alpha) * p[n] \n",
    "\n",
    "\t\t# check convergence, l1 norm \n",
    "\t\terr = sum([abs(x[n] - xlast[n]) for n in x]) \n",
    "\t\tif err < N*tol: \n",
    "\t\t\treturn x \n",
    "\traise NetworkXError('pagerank: power iteration failed to converge '\n",
    "\t\t\t\t\t\t'in %d iterations.' % max_iter) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 0.0046552928522577055, 1: 0.0046552928522577055, 2: 0.004189763661601549, 3: 0.0086122983173178, 4: 0.00680739299801871, 5: 0.00803657766226247, 6: 0.004106554924992854, 7: 0.004350588471558396, 8: 0.0053336461622438235, 9: 0.00682687678549026, 10: 0.004482852178408051, 11: 0.004472258809524813, 12: 0.0057256035500236006, 13: 0.006758347799146865, 14: 0.0043491995304293036, 15: 0.004338606161546066, 16: 0.020099547829399572, 17: 0.004610748518830078, 18: 0.0064438375347147985, 19: 0.005885113362071326, 20: 0.004486521365615213, 21: 0.004137872326628067, 22: 0.008812271228195171, 23: 0.005918195090975153, 24: 0.0035724592372295035, 25: 0.004892212520421998, 26: 0.004892212520421998, 27: 0.0049342184215117576, 28: 0.0049342184215117576, 29: 0.004962960129344194, 30: 0.004962960129344194, 31: 0.0036001490173681165, 32: 0.003668793403127154, 33: 0.0037292423669573163, 34: 0.009675508997615172, 35: 0.010125143105763117, 36: 0.008809335014952192, 37: 0.007535112848054314, 38: 0.003744598668045441, 39: 0.005797262070605111, 40: 0.005797262070605111, 41: 0.003768127080730292, 42: 0.003768127080730292, 43: 0.0048244321488228594, 44: 0.0048244321488228594, 45: 0.007780411986712251, 46: 0.006055699941240347, 47: 0.006739297419331476, 48: 0.01231103419093694, 49: 0.005750542149344909, 50: 0.005750542149344909, 51: 0.0038653014402028237, 52: 0.004812351489978323, 53: 0.004812351489978323, 54: 0.0038257736019118235, 55: 0.0036824107929137317, 56: 0.013226344098764395, 57: 0.003866493545636619, 58: 0.0038257736019118235, 59: 0.0038257736019118235, 60: 0.003866493545636619, 61: 0.0038257736019118235, 62: 0.003538050381251841, 63: 0.0037515647167921744, 64: 0.0037515647167921744, 65: 0.0037515647167921744, 66: 0.0037515647167921744, 67: 0.0037515647167921744, 68: 0.0037515647167921744, 69: 0.0037515647167921744, 70: 0.0037515647167921744, 71: 0.003866493545636619, 72: 0.003866493545636619, 73: 0.003866493545636619, 74: 0.003778306776128916, 75: 0.005938424723057485, 76: 0.005938424723057485, 77: 0.005938424723057485, 78: 0.006244605285754712, 79: 0.003774715406639079, 80: 0.005349456832486269, 81: 0.0064843729300686605, 82: 0.005694195315191038, 83: 0.004417506995916677, 84: 0.00512321270846865, 85: 0.0036189132904424336, 86: 0.0036189132904424336, 87: 0.013021780814097304, 88: 0.013021780814097304, 89: 0.013606418323313435, 90: 0.005203187697379376, 91: 0.009261018861830981, 92: 0.005945697386546576, 93: 0.005945697386546576, 94: 0.005945697386546576, 95: 0.004334260256586293, 96: 0.003787175179264633, 97: 0.005538519260512665, 98: 0.006497647883108146, 99: 0.005695643304841017, 100: 0.004417793166566722, 101: 0.004360885029634604, 102: 0.0036224664849132332, 103: 0.0036224664849132332, 104: 0.012900754541183335, 105: 0.013151941341154204, 106: 0.014607806185281525, 107: 0.005203187697379376, 108: 0.005933545141152776, 109: 0.004069783506750548, 110: 0.008806878003915414, 111: 0.0037747154066390793, 112: 0.0036189132904424336, 113: 0.0037747154066390793, 114: 0.0036902245446004513, 115: 0.0037747154066390793, 116: 0.0037747154066390793, 117: 0.004509600304554916, 118: 0.009189374929423826, 119: 0.009189374929423826, 120: 0.009189374929423826, 121: 0.009189374929423826, 122: 0.010912986422158995, 123: 0.004915226553737537, 124: 0.004915226553737537, 125: 0.004417603835129857, 126: 0.0038911895291587066, 127: 0.0038911895291587066, 128: 0.0038911895291587066, 129: 0.0038911895291587066, 130: 0.0038911895291587066, 131: 0.0038911895291587066, 132: 0.0038911895291587066, 133: 0.0038911895291587066, 134: 0.00400606781511957, 135: 0.00400606781511957, 136: 0.004665402420751562, 137: 0.004665402420751562, 138: 0.004665402420751562, 139: 0.0037747154066390793, 140: 0.003927152449457572, 141: 0.004503690533727249, 142: 0.004503690533727249, 143: 0.004503690533727249, 144: 0.004503690533727249, 145: 0.00400606781511957, 146: 0.00400606781511957, 147: 0.003787175179264633, 148: 0.0036224664849132332, 149: 0.003787175179264633, 150: 0.0037189662524328873, 151: 0.003787175179264633, 152: 0.003787175179264633, 153: 0.004514242551473467, 154: 0.009197809623806905, 155: 0.009197809623806905, 156: 0.009197809623806905, 157: 0.009197809623806905, 158: 0.010923556816312975, 159: 0.004945092842062891, 160: 0.004945092842062891, 161: 0.004447050042688014, 162: 0.0038917518194051654, 163: 0.0038917518194051654, 164: 0.0038917518194051654, 165: 0.0038917518194051654, 166: 0.0038917518194051654, 167: 0.0038917518194051654, 168: 0.0038917518194051654, 169: 0.0038917518194051654, 170: 0.00400677231484529, 171: 0.00400677231484529, 172: 0.004678951245824867, 173: 0.004678951245824867, 174: 0.004678951245824867, 175: 0.003787175179264633, 176: 0.003928482258014189, 177: 0.004504815114220167, 178: 0.004504815114220167, 179: 0.004504815114220167, 180: 0.004504815114220167, 181: 0.00400677231484529, 182: 0.00400677231484529}\n"
     ]
    }
   ],
   "source": [
    "pr=nx.pagerank(G, 0.4) \n",
    "\n",
    "print (pr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def katz_centrality(G, alpha=0.1, beta=1.0, \n",
    "\t\t\t\t\tmax_iter=1000, tol=1.0e-6, \n",
    "\t\t\t\t\tnstart=None, normalized=True, \n",
    "\t\t\t\t\tweight = 'weight'): \n",
    "\t\"\"\"Compute the Katz centrality for the nodes \n",
    "\t\tof the graph G. \n",
    "\n",
    "\n",
    "\tKatz centrality computes the centrality for a node \n",
    "\tbased on the centrality of its neighbors. It is a \n",
    "\tgeneralization of the eigenvector centrality. The \n",
    "\tKatz centrality for node `i` is \n",
    "\n",
    "\t.. math:: \n",
    "\n",
    "\t\tx_i = \\alpha \\sum_{j} A_{ij} x_j + \\beta, \n",
    "\n",
    "\twhere `A` is the adjacency matrix of the graph G \n",
    "\twith eigenvalues `\\lambda`. \n",
    "\n",
    "\tThe parameter `\\beta` controls the initial centrality and \n",
    "\n",
    "\t.. math:: \n",
    "\n",
    "\t\t\\alpha < \\frac{1}{\\lambda_{max}}. \n",
    "\n",
    "\n",
    "\tKatz centrality computes the relative influence of \n",
    "\ta node within a network by measuring the number of \n",
    "\tthe immediate neighbors (first degree nodes) and \n",
    "\talso all other nodes in the network that connect \n",
    "\tto the node under consideration through these \n",
    "\timmediate neighbors. \n",
    "\n",
    "\tExtra weight can be provided to immediate neighbors \n",
    "\tthrough the parameter :math:`\\beta`. Connections \n",
    "\tmade with distant neighbors are, however, penalized \n",
    "\tby an attenuation factor `\\alpha` which should be \n",
    "\tstrictly less than the inverse largest eigenvalue \n",
    "\tof the adjacency matrix in order for the Katz \n",
    "\tcentrality to be computed correctly. \n",
    "\n",
    "\n",
    "\tParameters \n",
    "\t---------- \n",
    "\tG : graph \n",
    "\tA NetworkX graph \n",
    "\n",
    "\talpha : float \n",
    "\tAttenuation factor \n",
    "\n",
    "\tbeta : scalar or dictionary, optional (default=1.0) \n",
    "\tWeight attributed to the immediate neighborhood. \n",
    "\tIf not a scalar, the dictionary must have an value \n",
    "\tfor every node. \n",
    "\n",
    "\tmax_iter : integer, optional (default=1000) \n",
    "\tMaximum number of iterations in power method. \n",
    "\n",
    "\ttol : float, optional (default=1.0e-6) \n",
    "\tError tolerance used to check convergence in \n",
    "\tpower method iteration. \n",
    "\n",
    "\tnstart : dictionary, optional \n",
    "\tStarting value of Katz iteration for each node. \n",
    "\n",
    "\tnormalized : bool, optional (default=True) \n",
    "\tIf True normalize the resulting values. \n",
    "\n",
    "\tweight : None or string, optional \n",
    "\tIf None, all edge weights are considered equal. \n",
    "\tOtherwise holds the name of the edge attribute \n",
    "\tused as weight. \n",
    "\n",
    "\tReturns \n",
    "\t------- \n",
    "\tnodes : dictionary \n",
    "\tDictionary of nodes with Katz centrality as \n",
    "\tthe value. \n",
    "\n",
    "\tRaises \n",
    "\t------ \n",
    "\tNetworkXError \n",
    "\tIf the parameter `beta` is not a scalar but \n",
    "\tlacks a value for at least one node \n",
    "\n",
    "\t\n",
    "\n",
    "\tNotes \n",
    "\t----- \n",
    "\t\n",
    "\tThis algorithm it uses the power method to find \n",
    "\tthe eigenvector corresponding to the largest \n",
    "\teigenvalue of the adjacency matrix of G. \n",
    "\tThe constant alpha should be strictly less than \n",
    "\tthe inverse of largest eigenvalue of the adjacency \n",
    "\tmatrix for the algorithm to converge. \n",
    "\tThe iteration will stop after max_iter iterations \n",
    "\tor an error tolerance ofnumber_of_nodes(G)*tol \n",
    "\thas been reached. \n",
    "\n",
    "\tWhen `\\alpha = 1/\\lambda_{max}` and `\\beta=0`, \n",
    "\tKatz centrality is the same as eigenvector centrality. \n",
    "\n",
    "\tFor directed graphs this finds \"left\" eigenvectors \n",
    "\twhich corresponds to the in-edges in the graph. \n",
    "\tFor out-edges Katz centrality first reverse the \n",
    "\tgraph with G.reverse(). \n",
    "\n",
    "\t\n",
    "\t\"\"\"\n",
    "\tfrom math import sqrt \n",
    "\n",
    "\tif len(G) == 0: \n",
    "\t\treturn {} \n",
    "\n",
    "\tnnodes = G.number_of_nodes() \n",
    "\n",
    "\tif nstart is None: \n",
    "\n",
    "\t\t# choose starting vector with entries of 0 \n",
    "\t\tx = dict([(n,0) for n in G]) \n",
    "\telse: \n",
    "\t\tx = nstart \n",
    "\n",
    "\ttry: \n",
    "\t\tb = dict.fromkeys(G,float(beta)) \n",
    "\texcept (TypeError,ValueError,AttributeError): \n",
    "\t\tb = beta \n",
    "\t\tif set(beta) != set(G): \n",
    "\t\t\traise nx.NetworkXError('beta dictionary '\n",
    "\t\t\t\t\t\t\t\t'must have a value for every node') \n",
    "\n",
    "\t# make up to max_iter iterations \n",
    "\tfor i in range(max_iter): \n",
    "\t\txlast = x \n",
    "\t\tx = dict.fromkeys(xlast, 0) \n",
    "\n",
    "\t\t# do the multiplication y^T = Alpha * x^T A - Beta \n",
    "\t\tfor n in x: \n",
    "\t\t\tfor nbr in G[n]: \n",
    "\t\t\t\tx[nbr] += xlast[n] * G[n][nbr].get(weight, 1) \n",
    "\t\tfor n in x: \n",
    "\t\t\tx[n] = alpha*x[n] + b[n] \n",
    "\n",
    "\t\t# check convergence \n",
    "\t\terr = sum([abs(x[n]-xlast[n]) for n in x]) \n",
    "\t\tif err < nnodes*tol: \n",
    "\t\t\tif normalized: \n",
    "\n",
    "\t\t\t\t# normalize vector \n",
    "\t\t\t\ttry: \n",
    "\t\t\t\t\ts = 1.0/sqrt(sum(v**2 for v in x.values())) \n",
    "\n",
    "\t\t\t\t# this should never be zero? \n",
    "\t\t\t\texcept ZeroDivisionError: \n",
    "\t\t\t\t\ts = 1.0\n",
    "\t\t\telse: \n",
    "\t\t\t\ts = 1\n",
    "\t\t\tfor n in x: \n",
    "\t\t\t\tx[n] *= s \n",
    "\t\t\treturn x \n",
    "\n",
    "\traise nx.NetworkXError('Power iteration failed to converge in '\n",
    "\t\t\t\t\t\t'%d iterations.' % max_iter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "ename": "PowerIterationFailedConvergence",
     "evalue": "(PowerIterationFailedConvergence(...), 'power iteration failed to converge within 1000 iterations')",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mPowerIterationFailedConvergence\u001b[0m           Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-29-251fee2267ce>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m###Calculate Katz centrality\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      2\u001b[0m \u001b[0mphi\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m+\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m/\u001b[0m\u001b[1;36m2.0\u001b[0m \u001b[1;31m# largest eigenvalue of adj matrix\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mcentrality\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mkatz_centrality\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mG\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m/\u001b[0m\u001b[0mphi\u001b[0m\u001b[1;33m-\u001b[0m\u001b[1;36m0.01\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      4\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mn\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mc\u001b[0m \u001b[1;32min\u001b[0m \u001b[0msorted\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcentrality\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m     \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"%d %0.2f\"\u001b[0m\u001b[1;33m%\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mc\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<C:\\Local\\chakrabo\\Anaconda\\lib\\site-packages\\decorator.py:decorator-gen-266>\u001b[0m in \u001b[0;36mkatz_centrality\u001b[1;34m(G, alpha, beta, max_iter, tol, nstart, normalized, weight)\u001b[0m\n",
      "\u001b[1;32mC:\\Local\\chakrabo\\Anaconda\\lib\\site-packages\\networkx\\utils\\decorators.py\u001b[0m in \u001b[0;36m_not_implemented_for\u001b[1;34m(not_implement_for_func, *args, **kwargs)\u001b[0m\n\u001b[0;32m     80\u001b[0m             \u001b[1;32mraise\u001b[0m \u001b[0mnx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mNetworkXNotImplemented\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     81\u001b[0m         \u001b[1;32melse\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 82\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mnot_implement_for_func\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     83\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0m_not_implemented_for\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     84\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Local\\chakrabo\\Anaconda\\lib\\site-packages\\networkx\\algorithms\\centrality\\katz.py\u001b[0m in \u001b[0;36mkatz_centrality\u001b[1;34m(G, alpha, beta, max_iter, tol, nstart, normalized, weight)\u001b[0m\n\u001b[0;32m    193\u001b[0m                 \u001b[0mx\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mn\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m*=\u001b[0m \u001b[0ms\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    194\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mx\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 195\u001b[1;33m     \u001b[1;32mraise\u001b[0m \u001b[0mnx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mPowerIterationFailedConvergence\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmax_iter\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    196\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    197\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mPowerIterationFailedConvergence\u001b[0m: (PowerIterationFailedConvergence(...), 'power iteration failed to converge within 1000 iterations')"
     ]
    }
   ],
   "source": [
    "###Calculate Katz centrality\n",
    "phi = (1+math.sqrt(5))/2.0 # largest eigenvalue of adj matrix \n",
    "centrality = nx.katz_centrality(G,1/phi-0.01) \n",
    "for n,c in sorted(centrality.items()): \n",
    "    print(\"%d %0.2f\"%(n,c)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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