SuccessorRepresentation_ModelOutline.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from numpy.linalg import inv\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "#create an identity matrix, I\n",
    "I = np.identity(21)\n",
    "print(I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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     ]
    }
   ],
   "source": [
    "#create the adjacency matrix, A, where 1s will populate every connected node in 21-node temporal community structure\n",
    "A = np.zeros((21, 21))\n",
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "#TesserScan community memberships by node, last two numbers = boundary nodes\n",
    "#subtracting each community membership by 1 since Python array index starts at 0\n",
    "comm1_prim = np.array([1, 2, 19, 20, 21]); \n",
    "comm1_prim_py = comm1_prim - 1; \n",
    "comm1_bound = np.array([3, 18]);\n",
    "comm1_bound_py = comm1_bound - 1;\n",
    "connected_bound1 = np.array([3, 4]);\n",
    "connected_bound1_py = connected_bound1 - 1;\n",
    "\n",
    "comm2_prim = np.array([5, 6, 7, 8, 9]);\n",
    "comm2_prim_py = comm2_prim - 1;\n",
    "comm2_bound = np.array([4, 10]);\n",
    "comm2_bound_py = comm2_bound - 1; \n",
    "connected_bound2 = np.array([10, 11]);\n",
    "connected_bound2_py = connected_bound2 - 1; \n",
    "\n",
    "comm3_prim = np.array([12, 13, 14, 15, 16]);\n",
    "comm3_prim_py = comm3_prim - 1; \n",
    "comm3_bound = np.array([11, 17]);\n",
    "comm3_bound_py = comm3_bound - 1; \n",
    "connected_bound3 = np.array([17, 18]);\n",
    "connected_bound3_py = connected_bound3 - 1; "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "# connecting primary and boundary nodes of community\n",
    "#community1 \n",
    "for r in range(comm1_prim_py.size):\n",
    "    ro = comm1_prim_py[r]\n",
    "    for c in range(comm1_prim_py.size):\n",
    "        co = comm1_prim_py[c]\n",
    "        A[ro, co] = 1\n",
    "        \n",
    "for r in range(comm1_bound_py.size):\n",
    "    ro = comm1_bound_py[r]\n",
    "    for c in range(comm1_prim_py.size):\n",
    "        co = comm1_prim_py[c]\n",
    "        A[ro, co] = 1\n",
    "        \n",
    "for r in range(comm1_prim_py.size):\n",
    "    ro = comm1_prim_py[r]\n",
    "    for c in range(comm1_bound_py.size):\n",
    "        co = comm1_bound_py[c]\n",
    "        A[ro, co] = 1\n",
    "        \n",
    "for r in range(connected_bound1_py.size):\n",
    "    ro = connected_bound1_py[r]\n",
    "    for c in range(connected_bound1_py.size):\n",
    "        co = connected_bound1_py[c]\n",
    "        A[ro, co] = 1  \n",
    "        \n",
    "        \n",
    "#community2 \n",
    "for r in range(comm2_prim_py.size):\n",
    "    ro = comm2_prim_py[r]\n",
    "    for c in range(comm2_prim_py.size):\n",
    "        co = comm2_prim_py[c]\n",
    "        A[ro, co] = 1\n",
    "        \n",
    "for r in range(comm2_bound_py.size):\n",
    "    ro = comm2_bound_py[r]\n",
    "    for c in range(comm2_prim_py.size):\n",
    "        co = comm2_prim_py[c]\n",
    "        A[ro, co] = 1\n",
    "        \n",
    "for r in range(comm2_prim_py.size):\n",
    "    ro = comm2_prim_py[r]\n",
    "    for c in range(comm2_bound_py.size):\n",
    "        co = comm2_bound_py[c]\n",
    "        A[ro, co] = 1\n",
    "        \n",
    "for r in range(connected_bound2_py.size):\n",
    "    ro = connected_bound2_py[r]\n",
    "    for c in range(connected_bound2_py.size):\n",
    "        co = connected_bound2_py[c]\n",
    "        A[ro, co] = 1        \n",
    "        \n",
    "        \n",
    "#community3 \n",
    "for r in range(comm3_prim_py.size):\n",
    "    ro = comm3_prim_py[r]\n",
    "    for c in range(comm3_prim_py.size):\n",
    "        co = comm3_prim_py[c]\n",
    "        A[ro, co] = 1\n",
    "        \n",
    "for r in range(comm3_bound_py.size):\n",
    "    ro = comm3_bound_py[r]\n",
    "    for c in range(comm3_prim_py.size):\n",
    "        co = comm3_prim_py[c]\n",
    "        A[ro, co] = 1\n",
    "        \n",
    "for r in range(comm3_prim_py.size):\n",
    "    ro = comm3_prim_py[r]\n",
    "    for c in range(comm3_bound_py.size):\n",
    "        co = comm3_bound_py[c]\n",
    "        A[ro, co] = 1\n",
    "        \n",
    "for r in range(connected_bound3_py.size):\n",
    "    ro = connected_bound3_py[r]\n",
    "    for c in range(connected_bound3_py.size):\n",
    "        co = connected_bound3_py[c]\n",
    "        A[ro, co] = 1      \n",
    "        \n",
    "#make sure that all the diagonals (i.e. items to iteslf) are 0\n",
    "np.fill_diagonal(A, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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     ]
    }
   ],
   "source": [
    "print(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "   0.03660657  0.03660657  0.03660657]\n",
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      "   0.48824014 -0.22604558 -0.22604558 -0.22604558 -0.18760868 -0.05307953\n",
      "   0.01098197  0.01098197  0.01098197]\n",
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      "   0.01098197  0.01098197  0.01098197]\n",
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      "  -0.22604558 -0.22604558 -0.22604558  0.48824014 -0.18760868 -0.05307953\n",
      "   0.01098197  0.01098197  0.01098197]\n",
      " [-0.05307953 -0.05307953 -0.09151643  0.03660657  0.03660657  0.03660657\n",
      "   0.03660657  0.03660657  0.03660657 -0.09151643 -0.41182392 -0.18760868\n",
      "  -0.18760868 -0.18760868 -0.18760868 -0.18760868  0.69323694  0.17113572\n",
      "  -0.05307953 -0.05307953 -0.05307953]\n",
      " [-0.18760868 -0.18760868 -0.41182392 -0.09151643  0.03660657  0.03660657\n",
      "   0.03660657  0.03660657  0.03660657  0.03660657 -0.09151643 -0.05307953\n",
      "  -0.05307953 -0.05307953 -0.05307953 -0.05307953  0.17113572  0.69323694\n",
      "  -0.18760868 -0.18760868 -0.18760868]\n",
      " [-0.22604558 -0.22604558 -0.18760868 -0.05307953  0.01098197  0.01098197\n",
      "   0.01098197  0.01098197  0.01098197  0.03660657  0.03660657  0.01098197\n",
      "   0.01098197  0.01098197  0.01098197  0.01098197 -0.05307953 -0.18760868\n",
      "   0.48824014 -0.22604558 -0.22604558]\n",
      " [-0.22604558 -0.22604558 -0.18760868 -0.05307953  0.01098197  0.01098197\n",
      "   0.01098197  0.01098197  0.01098197  0.03660657  0.03660657  0.01098197\n",
      "   0.01098197  0.01098197  0.01098197  0.01098197 -0.05307953 -0.18760868\n",
      "  -0.22604558  0.48824014 -0.22604558]\n",
      " [-0.22604558 -0.22604558 -0.18760868 -0.05307953  0.01098197  0.01098197\n",
      "   0.01098197  0.01098197  0.01098197  0.03660657  0.03660657  0.01098197\n",
      "   0.01098197  0.01098197  0.01098197  0.01098197 -0.05307953 -0.18760868\n",
      "  -0.22604558 -0.22604558  0.48824014]]\n",
      "[[ 0.43213243 -0.12342312 -0.10807098 -0.07352867  0.00323203  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.06464059  0.06464059  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.00323203 -0.07352867 -0.10807098\n",
      "  -0.12342312 -0.12342312 -0.12342312]\n",
      " [-0.12342312  0.43213243 -0.10807098 -0.07352867  0.00323203  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.06464059  0.06464059  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.00323203 -0.07352867 -0.10807098\n",
      "  -0.12342312 -0.12342312 -0.12342312]\n",
      " [-0.10807098 -0.10807098  0.9234009   0.44460605 -0.07352867 -0.07352867\n",
      "  -0.07352867 -0.07352867 -0.07352867 -0.24240221  0.06464059  0.06464059\n",
      "   0.06464059  0.06464059  0.06464059  0.06464059 -0.24240221 -0.6262057\n",
      "  -0.10807098 -0.10807098 -0.10807098]\n",
      " [-0.07352867 -0.07352867  0.44460605  0.9234009  -0.10807098 -0.10807098\n",
      "  -0.10807098 -0.10807098 -0.10807098 -0.6262057  -0.24240221  0.06464059\n",
      "   0.06464059  0.06464059  0.06464059  0.06464059  0.06464059 -0.24240221\n",
      "  -0.07352867 -0.07352867 -0.07352867]\n",
      " [ 0.00323203  0.00323203 -0.07352867 -0.10807098  0.43213243 -0.12342312\n",
      "  -0.12342312 -0.12342312 -0.12342312 -0.10807098 -0.07352867  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.00323203  0.06464059  0.06464059\n",
      "   0.00323203  0.00323203  0.00323203]\n",
      " [ 0.00323203  0.00323203 -0.07352867 -0.10807098 -0.12342312  0.43213243\n",
      "  -0.12342312 -0.12342312 -0.12342312 -0.10807098 -0.07352867  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.00323203  0.06464059  0.06464059\n",
      "   0.00323203  0.00323203  0.00323203]\n",
      " [ 0.00323203  0.00323203 -0.07352867 -0.10807098 -0.12342312 -0.12342312\n",
      "   0.43213243 -0.12342312 -0.12342312 -0.10807098 -0.07352867  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.00323203  0.06464059  0.06464059\n",
      "   0.00323203  0.00323203  0.00323203]\n",
      " [ 0.00323203  0.00323203 -0.07352867 -0.10807098 -0.12342312 -0.12342312\n",
      "  -0.12342312  0.43213243 -0.12342312 -0.10807098 -0.07352867  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.00323203  0.06464059  0.06464059\n",
      "   0.00323203  0.00323203  0.00323203]\n",
      " [ 0.00323203  0.00323203 -0.07352867 -0.10807098 -0.12342312 -0.12342312\n",
      "  -0.12342312 -0.12342312  0.43213243 -0.10807098 -0.07352867  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.00323203  0.06464059  0.06464059\n",
      "   0.00323203  0.00323203  0.00323203]\n",
      " [ 0.06464059  0.06464059 -0.24240221 -0.6262057  -0.10807098 -0.10807098\n",
      "  -0.10807098 -0.10807098 -0.10807098  0.9234009   0.44460605 -0.07352867\n",
      "  -0.07352867 -0.07352867 -0.07352867 -0.07352867 -0.24240221  0.06464059\n",
      "   0.06464059  0.06464059  0.06464059]\n",
      " [ 0.06464059  0.06464059  0.06464059 -0.24240221 -0.07352867 -0.07352867\n",
      "  -0.07352867 -0.07352867 -0.07352867  0.44460605  0.9234009  -0.10807098\n",
      "  -0.10807098 -0.10807098 -0.10807098 -0.10807098 -0.6262057  -0.24240221\n",
      "   0.06464059  0.06464059  0.06464059]\n",
      " [ 0.00323203  0.00323203  0.06464059  0.06464059  0.00323203  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203 -0.07352867 -0.10807098  0.43213243\n",
      "  -0.12342312 -0.12342312 -0.12342312 -0.12342312 -0.10807098 -0.07352867\n",
      "   0.00323203  0.00323203  0.00323203]\n",
      " [ 0.00323203  0.00323203  0.06464059  0.06464059  0.00323203  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203 -0.07352867 -0.10807098 -0.12342312\n",
      "   0.43213243 -0.12342312 -0.12342312 -0.12342312 -0.10807098 -0.07352867\n",
      "   0.00323203  0.00323203  0.00323203]\n",
      " [ 0.00323203  0.00323203  0.06464059  0.06464059  0.00323203  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203 -0.07352867 -0.10807098 -0.12342312\n",
      "  -0.12342312  0.43213243 -0.12342312 -0.12342312 -0.10807098 -0.07352867\n",
      "   0.00323203  0.00323203  0.00323203]\n",
      " [ 0.00323203  0.00323203  0.06464059  0.06464059  0.00323203  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203 -0.07352867 -0.10807098 -0.12342312\n",
      "  -0.12342312 -0.12342312  0.43213243 -0.12342312 -0.10807098 -0.07352867\n",
      "   0.00323203  0.00323203  0.00323203]\n",
      " [ 0.00323203  0.00323203  0.06464059  0.06464059  0.00323203  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203 -0.07352867 -0.10807098 -0.12342312\n",
      "  -0.12342312 -0.12342312 -0.12342312  0.43213243 -0.10807098 -0.07352867\n",
      "   0.00323203  0.00323203  0.00323203]\n",
      " [-0.07352867 -0.07352867 -0.24240221  0.06464059  0.06464059  0.06464059\n",
      "   0.06464059  0.06464059  0.06464059 -0.24240221 -0.6262057  -0.10807098\n",
      "  -0.10807098 -0.10807098 -0.10807098 -0.10807098  0.9234009   0.44460605\n",
      "  -0.07352867 -0.07352867 -0.07352867]\n",
      " [-0.10807098 -0.10807098 -0.6262057  -0.24240221  0.06464059  0.06464059\n",
      "   0.06464059  0.06464059  0.06464059  0.06464059 -0.24240221 -0.07352867\n",
      "  -0.07352867 -0.07352867 -0.07352867 -0.07352867  0.44460605  0.9234009\n",
      "  -0.10807098 -0.10807098 -0.10807098]\n",
      " [-0.12342312 -0.12342312 -0.10807098 -0.07352867  0.00323203  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.06464059  0.06464059  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.00323203 -0.07352867 -0.10807098\n",
      "   0.43213243 -0.12342312 -0.12342312]\n",
      " [-0.12342312 -0.12342312 -0.10807098 -0.07352867  0.00323203  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.06464059  0.06464059  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.00323203 -0.07352867 -0.10807098\n",
      "  -0.12342312  0.43213243 -0.12342312]\n",
      " [-0.12342312 -0.12342312 -0.10807098 -0.07352867  0.00323203  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.06464059  0.06464059  0.00323203\n",
      "   0.00323203  0.00323203  0.00323203  0.00323203 -0.07352867 -0.10807098\n",
      "  -0.12342312 -0.12342312  0.43213243]]\n"
     ]
    }
   ],
   "source": [
    "# Calculating SR with A (adjacency) matrix \n",
    "sr_A1 = inv(I - (.4 * A)) #using the inv function from the numpy.linalg.inv library\n",
    "print(sr_A1)\n",
    "\n",
    "sr_A2 = inv(I - (.8 * A)) #using the inv function from the numpy.linalg.inv library\n",
    "print(sr_A2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQQAAAECCAYAAAAYUakXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvOIA7rQAACxxJREFUeJzt3U+IXfUZxvHnaUwTjAqJmpDatLYSiy50LJcoWEpE1NRNdCHURclCGBcKCm6CG90U3KjdFCFiSBZqEdSahTSGQUgLJe0oqUbSGpHUxISMmkUEqU3i28WcvJ3EGe+/c+6558z3A+Hee+bMOe+PM3n4nXvf+Y0jQgAgSd+ruwAA44NAAJAIBACJQACQCAQAiUAAkGoNBNubbP/L9ke2t9ZZS1lsH7b9vu39tqfrrmcQtrfbnrF9YM62Vbb32D5UPK6ss8Z+LTCmJ21/Wlyr/bbvrrPGftleZ/tt2wdtf2D7kWL7wNeqtkCwvUTS7yX9StL1ku63fX1d9ZTstoiYiIhO3YUMaIekTRds2yppKiLWS5oqXjfJDn17TJL0bHGtJiLizRHXNKwzkh6LiOsk3SLpoeL/0MDXqs4ZwgZJH0XExxHxX0l/kLS5xnpQiIi9kk5esHmzpJ3F852S7hlpUUNaYEyNFhHHI+Ld4vmXkg5KukpDXKs6A+EqSUfmvD5abGu6kPSW7XdsT9ZdTInWRMRxafYHUdLqmuspy8O23ytuKRp1GzSX7asl3SRpn4a4VnUGgufZ1oY+6lsj4ueavRV6yPYv6y4IC3pO0jWSJiQdl/R0veUMxvYlkl6V9GhEnBrmWHUGwlFJ6+a8/qGkYzXVUpqIOFY8zkh6XbO3Rm1wwvZaSSoeZ2quZ2gRcSIizkbEN5KeVwOvle2lmg2DFyPitWLzwNeqzkD4u6T1tn9i+/uSfi1pV431DM32CtuXnnsu6U5JB777uxpjl6QtxfMtkt6osZZSnPtPU7hXDbtWti3pBUkHI+KZOV8a+Fq5zt92LD7m+Z2kJZK2R8RvayumBLZ/qtlZgSRdJOmlJo7J9suSNkq6QtIJSU9I+qOkVyT9SNInku6LiMa8SbfAmDZq9nYhJB2W9OC5e+8msP0LSX+W9L6kb4rNj2v2fYSBrlWtgQBgvNCpCCARCAASgQAgEQgAEoEAINUeCC1r75XUzjFJ7RwXYzpf7YEgqXUXRO0ck9TOcTGmOcYhEACMiZE2Jn3fy2K5Vpy37bS+1lIt+9a+197wVenn//C9i0s/5nwWGlPTtXFcw46pip/TYX32xVldefmS87YdPnJan588O98vFJ7nosqqmsdyrdDNvr2nfXfv3l/6+e/6wUTpx8TiVsXPaRU23HWk+04a8pahjUugAYvZwIHQ8iXQgEVpmBkCS6ABLTNMIPS0BJrtSdvTtqdP6+shTgegasMEQk9LoEXEtojoRESnbe9QA20zTCC0cgk0YDEbJhBatwQasNgN3IcQEWdsPyxpt/6/BNoHpVUGYOSGakwq/tJNz3/t5tobvuq5kaPXJqLdx5rRGAI0Ab/LACARCAASgQAgEQgAEoEAIBEIABKBACARCAASgQAgjXQJtX702oHYz7Jo/XQ1stwaelHVz19dmCEASAQCgEQgAEgEAoBEIABIBAKARCAASAQCgEQgAEgEAoA00j8Hf5lXRa9//blXVbUjN6HNtF+0Yy9e+2JKp+Jk1z8HzwwBQCIQACQCAUAiEAAkAgFAIhAAJAIBQCIQACQCAUAiEACksV11uVd1r7rcpBZnVp1GN8wQACQCAUAiEAAkAgFAIhAAJAIBQCIQACQCAUAiEACkxncqVqXXrr7FvnAr2oUZAoBEIABIQ90y2D4s6UtJZyWdiYhOGUUBqEcZ7yHcFhGfl3AcADXjlgFAGjYQQtJbtt+xPVlGQQDqM+wtw60Rccz2akl7bP8zIvbO3aEIiklJWq6LhzwdgCoNNUOIiGPF44yk1yVtmGefbRHRiYjOUi0b5nQAKjZwINheYfvSc88l3SnpQFmFARi9YW4Z1kh63fa547wUEX8qpSoAtRg4ECLiY0k3llhLI1W1cCltzqgDHzsCSAQCgEQgAEgEAoBEIABIBAKARCAASAQCgEQgAEgEAoDEqssjVEWbMy3OKBMzBACJQACQCAQAiUAAkAgEAIlAAJAIBACJQACQCAQAiU7FMdVrByILt6JMzBAAJAIBQCIQACQCAUAiEAAkAgFAIhAAJAIBQCIQACQCAUBaVK3LbWzzrWLh1n6O288xMf6YIQBIBAKARCAASAQCgEQgAEgEAoBEIABIBAKARCAASAQCgLSoWpf70caW3CranJvS4t2vNl7/XjBDAJC6BoLt7bZnbB+Ys22V7T22DxWPK6stE8Ao9DJD2CFp0wXbtkqaioj1kqaK1wAarmsgRMReSScv2LxZ0s7i+U5J95RcF4AaDPoewpqIOC5JxePq8koCUJfKP2WwPSlpUpKW6+KqTwdgCIPOEE7YXitJxePMQjtGxLaI6EREZ6mWDXg6AKMwaCDskrSleL5F0hvllAOgTr187PiypL9K+pnto7YfkPSUpDtsH5J0R/EaQMM5IkZ2ssu8Km727SM7HwZXxSKrbexqbEpH476Y0qk46W770akIIBEIABKBACARCAASgQAgEQgAEoEAIBEIABKBACARCAASi6xiKFUs3NrvcVEeZggAEoEAIBEIABKBACARCAASgQAgEQgAEoEAIBEIABKBACDRuoyRqaLNmRbncjFDAJAIBACJQACQCAQAiUAAkAgEAIlAAJAIBACJQACQ6FTEWOq1A5GFW8vFDAFAIhAAJAIBQCIQACQCAUAiEAAkAgFAIhAAJAIBQCIQACRal9FoVSzc2u9x24QZAoDUNRBsb7c9Y/vAnG1P2v7U9v7i393VlglgFHqZIeyQtGme7c9GxETx781yywJQh66BEBF7JZ0cQS0AajbMewgP236vuKVYWVpFAGozaCA8J+kaSROSjkt6eqEdbU/anrY9fVpfD3g6AKMwUCBExImIOBsR30h6XtKG79h3W0R0IqKzVMsGrRPACAwUCLbXznl5r6QDC+0LoDm6NibZflnSRklX2D4q6QlJG21PSApJhyU9WGGNAEakayBExP3zbH6hgloA1IzWZcyr1zbfJrX4VtHmXFXrdF1oXQaQCAQAiUAAkAgEAIlAAJAIBACJQACQCAQAiUAAkBwRIztZ58bl8bfd60o9ZhO6v9A8vXYgNmXh1g13HdH0P/7jbvsxQwCQCAQAiUAAkAgEAIlAAJAIBACJQACQCAQAiUAAkAgEAKnxi6y2bZFLjIe6F1mtq82ZGQKARCAASAQCgEQgAEgEAoBEIABIBAKARCAASAQCgEQgAEiNb10GmqKKNueyW5yZIQBIBAKARCAASAQCgEQgAEgEAoBEIABIBAKARCAASHQqAmOo1w7EXjsaP4wvetqPGQKA1DUQbK+z/bbtg7Y/sP1IsX2V7T22DxWPK6svF0CVepkhnJH0WERcJ+kWSQ/Zvl7SVklTEbFe0lTxGkCDdQ2EiDgeEe8Wz7+UdFDSVZI2S9pZ7LZT0j1VFQlgNPp6D8H21ZJukrRP0pqIOC7Nhoak1WUXB2C0eg4E25dIelXSoxFxqo/vm7Q9bXv6sy/ODlIjgBHpKRBsL9VsGLwYEa8Vm0/YXlt8fa2kmfm+NyK2RUQnIjpXXr6kjJoBVKSXTxks6QVJByPimTlf2iVpS/F8i6Q3yi8PwCj10ph0q6TfSHrf9rluicclPSXpFdsPSPpE0n3VlAhgVLoGQkT8RZIX+PLt5ZYDoE6OiNGdzP5M0r8v2HyFpM9HVsRotHFMUjvHtVjG9OOIuLLbN440EOYtwJ6OiE6tRZSsjWOS2jkuxnQ+fpcBQCIQAKRxCIRtdRdQgTaOSWrnuBjTHLW/hwBgfIzDDAHAmCAQACQCAUAiEAAkAgFA+h+2RfomfRsHJQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the raw A (adjacency) matrix\n",
    "plt.matshow(A)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the Adjacency (A) SR with gamma = 0.4\n",
    "plt.matshow(sr_A1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the Adjacency (A) SR with gamma = 0.8\n",
    "plt.matshow(sr_A2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.         0.16666667 0.16666667 0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.16666667\n",
      "  0.16666667 0.16666667 0.16666667]\n",
      " [0.16666667 0.         0.16666667 0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.16666667\n",
      "  0.16666667 0.16666667 0.16666667]\n",
      " [0.16666667 0.16666667 0.         0.16666667 0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.16666667 0.16666667 0.16666667]\n",
      " [0.         0.         0.16666667 0.         0.16666667 0.16666667\n",
      "  0.16666667 0.16666667 0.16666667 0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.16666667 0.         0.16666667\n",
      "  0.16666667 0.16666667 0.16666667 0.16666667 0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.16666667 0.16666667 0.\n",
      "  0.16666667 0.16666667 0.16666667 0.16666667 0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.16666667 0.16666667 0.16666667\n",
      "  0.         0.16666667 0.16666667 0.16666667 0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.16666667 0.16666667 0.16666667\n",
      "  0.16666667 0.         0.16666667 0.16666667 0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.16666667 0.16666667 0.16666667\n",
      "  0.16666667 0.16666667 0.         0.16666667 0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.16666667 0.16666667\n",
      "  0.16666667 0.16666667 0.16666667 0.         0.16666667 0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.16666667 0.         0.16666667\n",
      "  0.16666667 0.16666667 0.16666667 0.16666667 0.         0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.16666667 0.\n",
      "  0.16666667 0.16666667 0.16666667 0.16666667 0.16666667 0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.16666667 0.16666667\n",
      "  0.         0.16666667 0.16666667 0.16666667 0.16666667 0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.16666667 0.16666667\n",
      "  0.16666667 0.         0.16666667 0.16666667 0.16666667 0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.16666667 0.16666667\n",
      "  0.16666667 0.16666667 0.         0.16666667 0.16666667 0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.16666667 0.16666667\n",
      "  0.16666667 0.16666667 0.16666667 0.         0.16666667 0.\n",
      "  0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.16666667\n",
      "  0.16666667 0.16666667 0.16666667 0.16666667 0.         0.16666667\n",
      "  0.         0.         0.        ]\n",
      " [0.16666667 0.16666667 0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.16666667 0.\n",
      "  0.16666667 0.16666667 0.16666667]\n",
      " [0.16666667 0.16666667 0.16666667 0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.16666667\n",
      "  0.         0.16666667 0.16666667]\n",
      " [0.16666667 0.16666667 0.16666667 0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.16666667\n",
      "  0.16666667 0.         0.16666667]\n",
      " [0.16666667 0.16666667 0.16666667 0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.16666667\n",
      "  0.16666667 0.16666667 0.        ]]\n"
     ]
    }
   ],
   "source": [
    "# T = transition probability matrix, where probability to move to every connected node in 21-node temporal community structure \n",
    "\n",
    "T = A/6\n",
    "print(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.04040894e+00 1.02908941e-01 9.72491735e-02 6.69289924e-03\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04 2.24593934e-04 2.24593934e-04 6.28863016e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.69289924e-03 9.72491735e-02 1.02908941e-01 1.02908941e-01\n",
      "  1.02908941e-01]\n",
      " [1.02908941e-01 1.04040894e+00 9.72491735e-02 6.69289924e-03\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04 2.24593934e-04 2.24593934e-04 6.28863016e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.69289924e-03 9.72491735e-02 1.02908941e-01 1.02908941e-01\n",
      "  1.02908941e-01]\n",
      " [9.72491735e-02 9.72491735e-02 1.03717479e+00 7.13759523e-02\n",
      "  6.69289924e-03 6.69289924e-03 6.69289924e-03 6.69289924e-03\n",
      "  6.69289924e-03 2.24593934e-03 2.24593934e-04 2.24593934e-04\n",
      "  2.24593934e-04 2.24593934e-04 2.24593934e-04 2.24593934e-04\n",
      "  2.24593934e-03 3.25661205e-02 9.72491735e-02 9.72491735e-02\n",
      "  9.72491735e-02]\n",
      " [6.69289924e-03 6.69289924e-03 7.13759523e-02 1.03717479e+00\n",
      "  9.72491735e-02 9.72491735e-02 9.72491735e-02 9.72491735e-02\n",
      "  9.72491735e-02 3.25661205e-02 2.24593934e-03 2.24593934e-04\n",
      "  2.24593934e-04 2.24593934e-04 2.24593934e-04 2.24593934e-04\n",
      "  2.24593934e-04 2.24593934e-03 6.69289924e-03 6.69289924e-03\n",
      "  6.69289924e-03]\n",
      " [6.28863016e-04 6.28863016e-04 6.69289924e-03 9.72491735e-02\n",
      "  1.04040894e+00 1.02908941e-01 1.02908941e-01 1.02908941e-01\n",
      "  1.02908941e-01 9.72491735e-02 6.69289924e-03 6.28863016e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  2.24593934e-04 2.24593934e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04]\n",
      " [6.28863016e-04 6.28863016e-04 6.69289924e-03 9.72491735e-02\n",
      "  1.02908941e-01 1.04040894e+00 1.02908941e-01 1.02908941e-01\n",
      "  1.02908941e-01 9.72491735e-02 6.69289924e-03 6.28863016e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  2.24593934e-04 2.24593934e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04]\n",
      " [6.28863016e-04 6.28863016e-04 6.69289924e-03 9.72491735e-02\n",
      "  1.02908941e-01 1.02908941e-01 1.04040894e+00 1.02908941e-01\n",
      "  1.02908941e-01 9.72491735e-02 6.69289924e-03 6.28863016e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  2.24593934e-04 2.24593934e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04]\n",
      " [6.28863016e-04 6.28863016e-04 6.69289924e-03 9.72491735e-02\n",
      "  1.02908941e-01 1.02908941e-01 1.02908941e-01 1.04040894e+00\n",
      "  1.02908941e-01 9.72491735e-02 6.69289924e-03 6.28863016e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  2.24593934e-04 2.24593934e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04]\n",
      " [6.28863016e-04 6.28863016e-04 6.69289924e-03 9.72491735e-02\n",
      "  1.02908941e-01 1.02908941e-01 1.02908941e-01 1.02908941e-01\n",
      "  1.04040894e+00 9.72491735e-02 6.69289924e-03 6.28863016e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  2.24593934e-04 2.24593934e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04]\n",
      " [2.24593934e-04 2.24593934e-04 2.24593934e-03 3.25661205e-02\n",
      "  9.72491735e-02 9.72491735e-02 9.72491735e-02 9.72491735e-02\n",
      "  9.72491735e-02 1.03717479e+00 7.13759523e-02 6.69289924e-03\n",
      "  6.69289924e-03 6.69289924e-03 6.69289924e-03 6.69289924e-03\n",
      "  2.24593934e-03 2.24593934e-04 2.24593934e-04 2.24593934e-04\n",
      "  2.24593934e-04]\n",
      " [2.24593934e-04 2.24593934e-04 2.24593934e-04 2.24593934e-03\n",
      "  6.69289924e-03 6.69289924e-03 6.69289924e-03 6.69289924e-03\n",
      "  6.69289924e-03 7.13759523e-02 1.03717479e+00 9.72491735e-02\n",
      "  9.72491735e-02 9.72491735e-02 9.72491735e-02 9.72491735e-02\n",
      "  3.25661205e-02 2.24593934e-03 2.24593934e-04 2.24593934e-04\n",
      "  2.24593934e-04]\n",
      " [6.28863016e-04 6.28863016e-04 2.24593934e-04 2.24593934e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04 6.69289924e-03 9.72491735e-02 1.04040894e+00\n",
      "  1.02908941e-01 1.02908941e-01 1.02908941e-01 1.02908941e-01\n",
      "  9.72491735e-02 6.69289924e-03 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04]\n",
      " [6.28863016e-04 6.28863016e-04 2.24593934e-04 2.24593934e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04 6.69289924e-03 9.72491735e-02 1.02908941e-01\n",
      "  1.04040894e+00 1.02908941e-01 1.02908941e-01 1.02908941e-01\n",
      "  9.72491735e-02 6.69289924e-03 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04]\n",
      " [6.28863016e-04 6.28863016e-04 2.24593934e-04 2.24593934e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04 6.69289924e-03 9.72491735e-02 1.02908941e-01\n",
      "  1.02908941e-01 1.04040894e+00 1.02908941e-01 1.02908941e-01\n",
      "  9.72491735e-02 6.69289924e-03 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04]\n",
      " [6.28863016e-04 6.28863016e-04 2.24593934e-04 2.24593934e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04 6.69289924e-03 9.72491735e-02 1.02908941e-01\n",
      "  1.02908941e-01 1.02908941e-01 1.04040894e+00 1.02908941e-01\n",
      "  9.72491735e-02 6.69289924e-03 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04]\n",
      " [6.28863016e-04 6.28863016e-04 2.24593934e-04 2.24593934e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04 6.69289924e-03 9.72491735e-02 1.02908941e-01\n",
      "  1.02908941e-01 1.02908941e-01 1.02908941e-01 1.04040894e+00\n",
      "  9.72491735e-02 6.69289924e-03 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04]\n",
      " [6.69289924e-03 6.69289924e-03 2.24593934e-03 2.24593934e-04\n",
      "  2.24593934e-04 2.24593934e-04 2.24593934e-04 2.24593934e-04\n",
      "  2.24593934e-04 2.24593934e-03 3.25661205e-02 9.72491735e-02\n",
      "  9.72491735e-02 9.72491735e-02 9.72491735e-02 9.72491735e-02\n",
      "  1.03717479e+00 7.13759523e-02 6.69289924e-03 6.69289924e-03\n",
      "  6.69289924e-03]\n",
      " [9.72491735e-02 9.72491735e-02 3.25661205e-02 2.24593934e-03\n",
      "  2.24593934e-04 2.24593934e-04 2.24593934e-04 2.24593934e-04\n",
      "  2.24593934e-04 2.24593934e-04 2.24593934e-03 6.69289924e-03\n",
      "  6.69289924e-03 6.69289924e-03 6.69289924e-03 6.69289924e-03\n",
      "  7.13759523e-02 1.03717479e+00 9.72491735e-02 9.72491735e-02\n",
      "  9.72491735e-02]\n",
      " [1.02908941e-01 1.02908941e-01 9.72491735e-02 6.69289924e-03\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04 2.24593934e-04 2.24593934e-04 6.28863016e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.69289924e-03 9.72491735e-02 1.04040894e+00 1.02908941e-01\n",
      "  1.02908941e-01]\n",
      " [1.02908941e-01 1.02908941e-01 9.72491735e-02 6.69289924e-03\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04 2.24593934e-04 2.24593934e-04 6.28863016e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.69289924e-03 9.72491735e-02 1.02908941e-01 1.04040894e+00\n",
      "  1.02908941e-01]\n",
      " [1.02908941e-01 1.02908941e-01 9.72491735e-02 6.69289924e-03\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.28863016e-04 2.24593934e-04 2.24593934e-04 6.28863016e-04\n",
      "  6.28863016e-04 6.28863016e-04 6.28863016e-04 6.28863016e-04\n",
      "  6.69289924e-03 9.72491735e-02 1.02908941e-01 1.02908941e-01\n",
      "  1.04040894e+00]]\n",
      "[[1.408606   0.52625305 0.47976637 0.0846296  0.03099112 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.02383932 0.02383932 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.03099112 0.0846296  0.47976637\n",
      "  0.52625305 0.52625305 0.52625305]\n",
      " [0.52625305 1.408606   0.47976637 0.0846296  0.03099112 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.02383932 0.02383932 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.03099112 0.0846296  0.47976637\n",
      "  0.52625305 0.52625305 0.52625305]\n",
      " [0.47976637 0.47976637 1.35139162 0.23660528 0.0846296  0.0846296\n",
      "  0.0846296  0.0846296  0.0846296  0.05959831 0.02383932 0.02383932\n",
      "  0.02383932 0.02383932 0.02383932 0.02383932 0.05959831 0.32779069\n",
      "  0.47976637 0.47976637 0.47976637]\n",
      " [0.0846296  0.0846296  0.23660528 1.35139162 0.47976637 0.47976637\n",
      "  0.47976637 0.47976637 0.47976637 0.32779069 0.05959831 0.02383932\n",
      "  0.02383932 0.02383932 0.02383932 0.02383932 0.02383932 0.05959831\n",
      "  0.0846296  0.0846296  0.0846296 ]\n",
      " [0.03099112 0.03099112 0.0846296  0.47976637 1.408606   0.52625305\n",
      "  0.52625305 0.52625305 0.52625305 0.47976637 0.0846296  0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.03099112 0.02383932 0.02383932\n",
      "  0.03099112 0.03099112 0.03099112]\n",
      " [0.03099112 0.03099112 0.0846296  0.47976637 0.52625305 1.408606\n",
      "  0.52625305 0.52625305 0.52625305 0.47976637 0.0846296  0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.03099112 0.02383932 0.02383932\n",
      "  0.03099112 0.03099112 0.03099112]\n",
      " [0.03099112 0.03099112 0.0846296  0.47976637 0.52625305 0.52625305\n",
      "  1.408606   0.52625305 0.52625305 0.47976637 0.0846296  0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.03099112 0.02383932 0.02383932\n",
      "  0.03099112 0.03099112 0.03099112]\n",
      " [0.03099112 0.03099112 0.0846296  0.47976637 0.52625305 0.52625305\n",
      "  0.52625305 1.408606   0.52625305 0.47976637 0.0846296  0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.03099112 0.02383932 0.02383932\n",
      "  0.03099112 0.03099112 0.03099112]\n",
      " [0.03099112 0.03099112 0.0846296  0.47976637 0.52625305 0.52625305\n",
      "  0.52625305 0.52625305 1.408606   0.47976637 0.0846296  0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.03099112 0.02383932 0.02383932\n",
      "  0.03099112 0.03099112 0.03099112]\n",
      " [0.02383932 0.02383932 0.05959831 0.32779069 0.47976637 0.47976637\n",
      "  0.47976637 0.47976637 0.47976637 1.35139162 0.23660528 0.0846296\n",
      "  0.0846296  0.0846296  0.0846296  0.0846296  0.05959831 0.02383932\n",
      "  0.02383932 0.02383932 0.02383932]\n",
      " [0.02383932 0.02383932 0.02383932 0.05959831 0.0846296  0.0846296\n",
      "  0.0846296  0.0846296  0.0846296  0.23660528 1.35139162 0.47976637\n",
      "  0.47976637 0.47976637 0.47976637 0.47976637 0.32779069 0.05959831\n",
      "  0.02383932 0.02383932 0.02383932]\n",
      " [0.03099112 0.03099112 0.02383932 0.02383932 0.03099112 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.0846296  0.47976637 1.408606\n",
      "  0.52625305 0.52625305 0.52625305 0.52625305 0.47976637 0.0846296\n",
      "  0.03099112 0.03099112 0.03099112]\n",
      " [0.03099112 0.03099112 0.02383932 0.02383932 0.03099112 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.0846296  0.47976637 0.52625305\n",
      "  1.408606   0.52625305 0.52625305 0.52625305 0.47976637 0.0846296\n",
      "  0.03099112 0.03099112 0.03099112]\n",
      " [0.03099112 0.03099112 0.02383932 0.02383932 0.03099112 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.0846296  0.47976637 0.52625305\n",
      "  0.52625305 1.408606   0.52625305 0.52625305 0.47976637 0.0846296\n",
      "  0.03099112 0.03099112 0.03099112]\n",
      " [0.03099112 0.03099112 0.02383932 0.02383932 0.03099112 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.0846296  0.47976637 0.52625305\n",
      "  0.52625305 0.52625305 1.408606   0.52625305 0.47976637 0.0846296\n",
      "  0.03099112 0.03099112 0.03099112]\n",
      " [0.03099112 0.03099112 0.02383932 0.02383932 0.03099112 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.0846296  0.47976637 0.52625305\n",
      "  0.52625305 0.52625305 0.52625305 1.408606   0.47976637 0.0846296\n",
      "  0.03099112 0.03099112 0.03099112]\n",
      " [0.0846296  0.0846296  0.05959831 0.02383932 0.02383932 0.02383932\n",
      "  0.02383932 0.02383932 0.02383932 0.05959831 0.32779069 0.47976637\n",
      "  0.47976637 0.47976637 0.47976637 0.47976637 1.35139162 0.23660528\n",
      "  0.0846296  0.0846296  0.0846296 ]\n",
      " [0.47976637 0.47976637 0.32779069 0.05959831 0.02383932 0.02383932\n",
      "  0.02383932 0.02383932 0.02383932 0.02383932 0.05959831 0.0846296\n",
      "  0.0846296  0.0846296  0.0846296  0.0846296  0.23660528 1.35139162\n",
      "  0.47976637 0.47976637 0.47976637]\n",
      " [0.52625305 0.52625305 0.47976637 0.0846296  0.03099112 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.02383932 0.02383932 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.03099112 0.0846296  0.47976637\n",
      "  1.408606   0.52625305 0.52625305]\n",
      " [0.52625305 0.52625305 0.47976637 0.0846296  0.03099112 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.02383932 0.02383932 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.03099112 0.0846296  0.47976637\n",
      "  0.52625305 1.408606   0.52625305]\n",
      " [0.52625305 0.52625305 0.47976637 0.0846296  0.03099112 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.02383932 0.02383932 0.03099112\n",
      "  0.03099112 0.03099112 0.03099112 0.03099112 0.0846296  0.47976637\n",
      "  0.52625305 0.52625305 1.408606  ]]\n"
     ]
    }
   ],
   "source": [
    "# Calculating and plotting SR with T matrix\n",
    "sr_T1 = inv(I - (.4 * T));\n",
    "print(sr_T1)\n",
    "\n",
    "sr_T2 = inv(I - (.8 * T));\n",
    "print(sr_T2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the raw T (transition) matrix\n",
    "plt.matshow(T)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the Transition matrix (T) SR with gamma = 0.4\n",
    "plt.matshow(sr_T1)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the Transition matrix (T) SR with gamma = 0.8\n",
    "plt.matshow(sr_T2)\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}