Notebooks/9.1 Learning relationships.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Learning relationships"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Network representations\n",
    "\n",
    "There are many different representations for a network.  Here are some of them, for the same graph. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "adjmatrix = [\n",
    "[ 0, 1, 1, 1, 0, 1, 0, 0, 0, 1],\n",
    "[ 1, 0, 0, 1, 1, 0, 1, 0, 0, 1],\n",
    "[ 1, 0, 0, 1, 0, 1, 0, 0, 0, 0],\n",
    "[ 1, 1, 1, 0, 1, 1, 1, 0, 0, 0],\n",
    "[ 0, 1, 0, 1, 0, 0, 1, 0, 0, 0],\n",
    "[ 1, 0, 1, 1, 0, 0, 1, 0, 0, 0],\n",
    "[ 0, 1, 0, 1, 1, 1, 0, 0, 0, 0],\n",
    "[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],\n",
    "[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1],\n",
    "[ 1, 1, 0, 0, 0, 0, 0, 0, 1, 0]]\n",
    "\n",
    "adjlist = {0: [1, 2, 3, 5, 9], 1: [0, 9, 3, 4, 6], 2: [0, 3, 5], 3: [0, 1, 2, 4, 5, 6],\n",
    "4: [1, 3, 6], 5: [0, 2, 3, 6], 6: [1, 3, 4, 5], 7: [8], 8: [9, 7], 9: [8, 1, 0]}\n",
    "\n",
    "edgelist = {(0,1),(0,2),(0,3),(0,5),(0,9),(1,3),(1,4),(1,6),(1,9),(2,3),(2,5),(3,4),\n",
    "(3,5),(3,6),(4,6),(5,6),(7,8),(8,9)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## NetworkX"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xLzDwgxuCOnbrht+3bcPRo0d5q08Ur169+iBoK36em5uLzp07w8DAAAYGBpg+\nfToMDAzQvn17kQ81qcoCDw9YnT4Ny7dv0VGE59IBeKmqIsrDg9N6CBEVBbH4KIgVUExMDMzMzKAi\n4XtFSTRq1AivHj6EXqtWmFi79gc3BP1Zrx5yysrg4+kpNzcEMcbw7NmzT0a3d+7cQUlJyQdTyaNG\njYK+vj5at26NWrVks4zCxMQEq7y9McrdHaerGcbpAMwEAsxdvpxOLiK8o8Va4qMgVkAnT57E6NGj\neet/l68vVri7Y2lREaYxBq2ysg9+f1ZpKTYDCAgPh9Xp01jl7Y2Zbm4yqU0oFOLhw4efjG5TU1NR\nr16996NbfX19TJgwAfr6+mjevLlcbK+q+G80yN0dS4qK4MJYpe+McwAECATYoKqKYVZW2BsYiOkz\nZij0awCi+GhELD5arKVgGGNo0aIFEhIS0KFDB5n3v8vXF+tFHLWNUlPDMo7DuLy8HBkZGZ9MKf/9\n99/Q0tJ6P7qtCF19fX00bdqUs/6l6erVq/h+4UJcvHQJdioqVZ7hu3r1ahw9ehRxcXHQ0NDgu3xS\nQ8XExGD9+vU4e/Ys36UoHApiBXPz5k3Y2toiLS1N5n0nJSXBasgQxIvxHnOQmhqi4uJEnkItKSlB\nWlraB1PJqampSE9PR4sWLT6YUq5YodyoUSOR+pBH33zzDdq3bw/V+vWRlpKC/NxcqGtpVXqGL2MM\n8+fPR3JyMk6dOvXZleyESFN8fDw8PDyQkJDAdykKh4JYwXh6euLp06fYsmWLzPt2srGBsZgre6u6\nIaiwsPD9CuX/hu7Dhw/Rtm3bD0a3BgYG6Ny5s9IGTklJCZo3b46UlJQqD02pIBQK4eTkhMLCQhw5\ncoTzxWSEVOXq1auYNWsWrl69yncpCoeCWMEMHjwYy5cvl+nRlgB3e12TUlLw4sWLT6aUs7Ozoaen\n98mUcseOHWV2lra8iIqKwoYNG3DhwgWRnistLYWVlRVatGgBf39/uXjvTWqO27dvw97eHrdv3+a7\nFIVD/2xWIG/evMH169cxZMgQmfcdFBAAa0CsEAb+vSFodHExunXtCqPu3d8HrZubGwwMDNC2bVvU\nrl2bw4oVV1hYGOzt7UV+rl69ejhy5Ai+/vprLFu2DF5eXlKojpDK0WIt8VEQK5CzZ89iwIABvEzJ\ncnFDkBkAdVtb7Nq3j5uilFBRURGOHz+O3377TaznGzRogBMnTmDQoEFo2rQpli5dynGFhFRORUUF\nRUVFfJdoW5ZVAAAgAElEQVShkCiIFYisb1v6r4I3bzi5Iajg9WsuylFa0dHRMDY2hq6urthtNG7c\nGGfOnMHAgQPRtGlTfPPNNxxWSEjlaEQsPrr0QUEwxnjdP9xQQ4NuCJIBcaelP9ayZUucPn0aP/74\nI8LDwzmojJAvowM9xEdBrCBu376NevXqQU9Pj5f+9YyM6IYgKSsoKMDp06dhY2PDSXt6enqIiorC\nzJkzcf78eU7aJORz6tevj+LiYtD6X9FRECuIimlpvlbCTpk2DccAiHv1fA6AY4xhyrRp3BWlZKKi\nojBgwAA0btyYszZ79+6NsLAw2Nra4saNG5y1S8jH6tSpg1q1aqG8vJzvUhQOBbGC4PtYSx0dHYwc\nPhx7xXyebgiqGlfT0h8bOnQoduzYAQsLC/zzzz+ct09IBVqwJR7aR6wA8vPz0aJFCzx79uyL99pK\n082bN2FpaYmi589xpbxcZidr1RSvX79GmzZt8PDhQ6kdU7l79254enoiISEBLVq0kEofpGbT1tbG\nX3/9BR0dHb5LUSg0IlYAsbGx6NevHy8hzBiDn58fRowYAW9vb3hu2YJRampIr+bz6QBGqqpilbc3\nhfAXREREYOjQoVI9K3rGjBmYMWMGRo0ahdxccV8yEPJ5tGBLPLR9SQHwNS1dWFiI2bNn49q1a4iP\nj0eXLl3e/96g/96+VMmzFTcEra1TB1rNmmEqbaH5orCwMDg7O0u9n+XLl+PFixewtLRETEwM1NTU\npN4nqTloC5N4aEQs5xhjvOwf/vvvv9G3b18wxnDlypUPQnimmxui4uJw3doa7VVU4Fi7NnwBBAPw\nBfCNqio6qKjghrU1ohMS0L1XL8yaNYtWU37Gq1evcPHiRYwdO1bqfQkEAnh7e6Njx46YOHEiyj66\nwpIQSVAQi4eCWM7dvXsXjDHo6+vLrM+wsDAMHDgQCxYsQGBgYKVT4sbGxth35AjSHj7ExRYtcGbU\nKERbWuKmszO6rlqFtIcPse/IEfTp0weBgYG4ceMGfHx8ZPY1KJKjR49i1KhRaNiwoUz6q1WrFvz8\n/FC7dm24uLhAKBTKpF+i/GixlnhoalrOVUxLy2LbUklJCdzd3REdHY3Tp0+jV69eVT6jra2Nt8XF\n2L53L5o3b17pZxo0aICIiAj069cPBgYGGDlyJNelK7SwsDC4cXhXc3XUrVsXBw8exMiRI7Fo0SJs\n2rSJLokgEqMRsXhoRCznZDUt/eDBA5iZmSErKwvXrl2rVggD/67oLiwsRLNmzb74uTZt2uDgwYNw\ndnbm5S5lefX8+XNcu3YNY8aMkXnfqqqqiIqKwh9//IG1a9fKvH+ifGixlngoiOVYYWEh/vzzTwwf\nPlyq/URHR6NPnz6wtbXF0aNHoampWe1nMzMz0a5du2qNpgYNGoRff/0VVlZWePPmjSQlK43Dhw/D\nwsKCt7uVNTU1cerUKezZswc7d+7kpQaiPGhELB6ampZjf/zxB4yNjaGuLul1C5UrLy/HihUrEBQU\nhCNHjmDgwIEit5GRkYH27dtX+/MzZsxAcnIyJk+ejKioqBp/9WFYWBiWLFnCaw3NmzfHmTNnYGZm\nhiZNmmDixIm81kMUFwWxeGhELMekOS397NkzjBw5EleuXMG1a9fECmEAuHfvnkhBDAAbN25ESUkJ\nPDw8xOpTWWRlZeGvv/6Si3fmHTp0wIkTJzB79mycPXuW73KIgqLFWuKhIJZT0rxtKS4uDr1798bA\ngQNx+vRpiU7BEXVEDPz/QqEjR45gXw2+m/jQoUMYN24c6tevz3cpAIAePXrg8OHDmDx5MpKSkvgu\nhyggGhGLh4JYTv3zzz8oKSmBIYe3FQmFQqxfvx52dnbYs2cPVq9eLfHUsDhBDABNmjRBZGQkFi1a\nhCtXrkhUg6IKCwuDnZ0d32V8wMzMDP7+/hg7dizu3r3LdzlEwdBiLfHQO2I5derUKU63LeXm5mLK\nlCl4+fIlkpKS0KpVK07aFTeIAaBr167Ys2cPJkyYgCtXrqBly5ac1KQIMjMzkZGRgWHDhvFdyies\nrKyQm5uLUaNGISEhgbM/K0T50YhYPDQillNcTktfvXoVvXr1QseOHREXF8fZN9Z3797hwYMHaNu2\nrdhtjB07FnPmzIG1tXWNerd08OBB2NjYoG7dunyXUqmpU6di/vz5GDVqFF69esV3OURBUBCLh4JY\nDhUVFeHixYv4+uuvJWqHMQZfX1+MGTMGGzZswKZNm1CvXj2OqgSePHmCxo0bS3xe8fLly9GhQwfM\nmDGjxhyDKY/T0h9bvHgxrKysMGbMGBQUFPBdDlEAtFhLPBTEciguLg49evQQaT/vxwoKCuDo6Igd\nO3bg4sWLUtmSIsm09H8JBAL4+/vjzp072LBhAweVybe0tDQ8ffoUZmZmfJdSJU9PTxgaGmLChAko\nLS3luxwi52hELB4KYjkk6bR0amoq+vTpA1VVVVy+fBmdOnXisLr/l5GRgQ4dOnDSlpqaGsLDw+Hj\n44MTJ05w0qa8CgsLw6RJkxRiD7VAIMCOHTugpqaGKVOm4N27d3yXROQYLdYSDwWxHJJk//D+/fsx\nePBgLFmyBP7+/lI9sYmrEXGFVq1a4fDhw3BxccGdO3c4a1feKMK09H/VqVMHoaGheP78OebNm1dj\nXh8Q0dGIWDwUxHImIyMDeXl56NGjh0jPFRcXY9asWVi1ahXOnj0LFxcXKVX4/7gOYgDo378/1q9f\nDysrK+Tk5HDatjy4ffs28vLy0L9/f75LEYmKigoiIiJw+fJlrFy5ku9yiJyiIBYPBbGcOXnyJEaN\nGiXStqWMjAwMGDAAr169wtWrV9G9e3cpVvj/xDlVqzpcXFwwduxY2NnZoby8nPP2+RQWFgZbW1vU\nqqV4f/UaNWqEU6dOITQ0FL///jvf5RA5RIu1xKN43w2UnKjT0pGRkejXrx+mTp2KgwcPolGjRlKs\n7kPSGBFX8PLyQq1ateDu7i6V9vnAGFO4aemP6ejo4MyZM/Dy8kJoaCjf5RA5QyNi8dCBHnKkuLgY\ncXFxCAwMrPKz5eXl+OGHHxAaGoqIiAiZT3Xm5+ejoKCgyusPxVWnTh0cOHAAffv2haGhIaZPny6V\nfmTp5s2bePfuHYyNjfkuRSJt27bFyZMnMXz4cGhpaUnlGFaimGixlngoiOVIfHw8unXrhsaNG3/x\nc0+ePIG9vT3U1NRw/fp1NG3aVEYV/j9Rrj8Ul5aWFiIjI2FmZoYuXbpgwIABUutLFg4cOAA7Ozup\n/jeTlW7duuHYsWMYP348L/8QJPKJRsTioalpOVKdaelz587B2NgYI0eORHR0NC8hDEh3Wvq/unTp\ngsDAQEyaNAkPHz6Uen/SwhjDwYMHFXpa+mOmpqYIDAyEtbU1/vrrL77LIXKAglg8NCLmSXZ2NoIC\nApCWnIyCN2/QUEMDkWfOICg4uNLPC4VCrF27Ftu2bcO+ffskPnVLUrIKYgAwNzfHokWLMG7cOCQk\nJKBBgwYy6ZdLiYmJqF+/PoyMjPguhVPm5ub47bffMHr0aMTHx0t03ClRfLRYSzwUxDKWlJQEH09P\nnDh5EjYATIqLoQ4g/38/7MaNg4W5ORZ4eMDExAQA8OrVKzg7OyM/Px9Xr16Vi8sRMjIypHZQSGUW\nL16M5ORkuLi4ICwsTOGmdw8cOAB7e3uFq7s6HB0d8erVK4wcORIJCQkSXatJFBuNiMVDU9MytMvX\nF1ZDhsA4PBwZxcXwLy7GLACOAGYBCAWQUVyM3uHhsBoyBLt8fXH58mX06tULXbt2RWxsrFyEMMDt\nqVrVIRAIsGvXLjx48ABr1qyRWb9cEAqFOHTokFJNS39s/vz5sLOzg7m5OfLy8vguh/CEFmuJh0bE\nMrLL1xfr3d0R//YtOn7hc1oAvmMMY9++xfAFC/C6fn0EBQdj3Lhxsiq1WmQ5NV1BRUUFx44dQ9++\nfdG1a1dYW1vLtH9xXbx4EY0bN4a+vj7fpUjV6tWr8fLlS4wfPx7R0dFQUVHhuyQiYzQiFg+NiGUg\nKSkJK9zdcbqKEP6vjgDOlZVB9d07uRkFVxAKhbh//z4v7wNbtGiBo0ePYubMmUhJSZF5/+KomJZW\ndgKBAFu3boW2tjYcHR3pXOoaiIJYPBTEMuDj6YllRUXVDuEKHQEsKy6Gj6enNMoS2+PHjzm5/lBc\nJiYm2Lx5M8aNG4eXL1/yUkN1lZeX4/Dhw0o9Lf1ftWvXRlBQEPLy8jBr1iw6l7qGqVOnDoRCodKd\niCdtFMRSlp2djRMnT2KqmN+QpjKG49HRePHiBceViY+PaemPOTo6wtbWFhMnTkRZWRmvtXxJXFwc\nWrVqJdP36XyrX78+jh07hlu3buGHH37guxwiQwKBgEbFYqAglrKggABY4993v+JoDMBaIEBQQAB3\nRUlIHoIYANasWYOGDRtiwYIFfJfyWWFhYTViWvpjDRs2RHR0NI4dO4aNGzfyXQ6RgezsbHh7eaFe\neTmmTZiAmU5O8PbykqtBhLyiIJaytORk9JHwX4cmRUVIk6P3ofISxLVr10ZISAjOnz8PX19fvsv5\nRFlZGY4ePQpbW1u+S+FF06ZNcfr0afj4+CAoKIjvcoiUJCUlwcnGBp3btMGdFSvgWVoK6zNn0Gv/\nfqSuXAm91q3hZGODpKQkvkuVWxTEUlbw5g3UJWxDHUB+bi4X5XBCXoIY+PdGoMjISKxcuRLnz5/n\nu5wPnD17Fnp6emjdujXfpfCmdevWOHXqFJYuXYqoqCi+yyEcq2pL5p6iok+2ZJJPURBLWUMNDeRL\n2EY+AHUtcSe3uSdPQQwAHTt2xP79+2Fvb4/MzEy+y3mvpk5Lf0xfXx+RkZH45ptvEB8fz3c5hCP/\n3ZK5kLHPvn6r2JIZ//Yt1ru7UxhXgoJYyvSMjJAo4X7KCwDOxsdjw4YNSEtL46YwCchbEAPA119/\nje+//x5WVlbIz5f0nz6SKy4uRmRkJCZOnMh3KXKhT58+CAkJwcSJE3Hr1i2+yyESEndL5um3b7HC\n3R1Xr16VZnkKh4JYyqZMm4ZjAMSdWM4BcKp+fazx9ERGRgaGDh2KLl26YOnSpUhISJD5Xs2CggLk\n5+ejefPmMu23OubNm4e+fftiypQpEAqFvNZy+vRpGBkZoUWLFrzWIU9GjBiBrVu3YsyYMcjIyOC7\nHCIBSbZkLi0qkrstmXyjIJYyHR0dWJibI1DMM4YDBQJYWljA3t4evr6+yMrKQnBwMFRUVDB37lw0\nb94cLi4uOHbsGAoKCjiu/lOyuP5QXAKBANu2bcOLFy+wcuVKXmsJCwurMXuHRTFp0iT89NNPGDly\nJJ49e8Z3OUQMyrglk3eMSF1iYiJrpqbG/gEYE+HHPwBrpqbGkpKSPtt2ZmYm27JlC/v666+Zuro6\ns7CwYDt37mSPHz+WytcSHh7OLC0tpdI2V549e8Zat27NwsLCeOm/sLCQaWhosOfPn/PSvyJYvXo1\n6969O8vNzeW7FCKiDevXMxcVFZG+l338w0VVlXl7efH9pcgNGhHLgImJCVZ5e2OUmhrSq/lMOoBR\nampY5e0NY2Pjz36ubdu2mDdvHmJiYvDo0SM4OTnh/Pnz6NatG/r06YM1a9YgJSWFsxOO5PH98Md0\ndXURHh6OOXPm4MaNGzLv/8SJE+jTpw/dQvQFP/74I8zMzGBlZUXX5ikYZdySyTcKYhmZ6eaGZd7e\nGKSmhk0CwWffGecA+E0gQJ/atbHU2xsz3dyq3YeGhgbs7e0REhKC58+fY926dcjOzoaVlRU6dOiA\nhQsXIjY2VqKTqO7duyf3QQwAPXv2xPbt2zF+/Hg8f/5cpn3TtHTVBAIBNm/ejFatWsHOzo6ORFQg\nyrglk28UxDI0080NUXFxuG5tjfYqKvhGVRW+AIIB+AL4RlUVHVRUcH3cODRu2xYaEmxZqlu3LoYN\nGwYfHx9kZGQgIiIC2traWL58OXR1deHg4IADBw7gzZs3IrWrCCPiCpMmTcLUqVNhY2ODkpISmfSZ\nn5+PmJgYhbkZik+1atXC3r17UVZWBldXV94X2JHqUcYtmXwTMK7mLIlIXrx4gaCAAKSlpCA/Nxfq\nWlrQMzTElGnToK2tjcuXL8Pa2hq3b99GkyZNOO37yZMnOH78OCIjI3HhwgX07dsXVlZWsLKyQps2\nbb74bJcuXXDkyBF07dqV05qkRSgUYsKECWjcuDH8/Pykvshs//79CA0NxfHjx6XajzIpLCzEiBEj\nYGpqig0bNsjlQkDy/1atWIF7a9ciSIJZjG9UVdF11SosXrKEw8oUFwWxHJs/fz7y8/Oxd+9eqfVR\nUFCAmJgYREZG4vjx42jZsuX7UO7du/cH3xSFQiHU1NSQk5PD281L4igoKICpqSlcXV0xf/58qfZl\nZWWFSZMmwdnZWar9KJucnByYmZnB2dkZy5Yt47sc8hGhUIhz587Bz88PJ0+ehLCwEI+EQrHO0M8B\n0EFFBWkPH0JbW5vrUhUTr0vFyBfl5eWxVq1asZiYGJn0V15ezuLj49mSJUtY586dWYsWLdisWbNY\ndHQ0KyoqYo8ePWLNmjWTSS1cy8jIYLq6uuzMmTNS6yMnJ4c1atSIvXnzRmp9KLOsrCzWtm1b5ufn\nx3cp5H8ePnzIVq1axdq0acN69OjBtm7dynJycpijtTXbJBCItWJ6o0DAnGxs+P7S5AoFsZyLiopi\n7du3Z4WFhTLv++7du8zLy4sNHDiQNWrUiJmZmbGOHTuyFy9eyLwWLvzxxx9MR0eHpaWlSaX9PXv2\nMGtra6m0XVOkpaWx5s2bs6NHj/JdSo1VUlLCDh8+zEaPHs20tLSYm5sbu3bt2gefkeaWzJqIglgB\n2NnZsaVLl/JaQ3Z2Nps+fTpr1aoVa9SoERs0aBDz9vaWWqhJi6+vL9PX12evX7/mvO1Ro0axAwcO\ncN5uTXPt2jWmra3NYmNj+S6lRklNTWWLFy9mOjo6zMzMjAUFBX1xALBz+3bWXoQw/gdg7dXU2M7t\n22X4VSkGCmIF8OzZM6atrc2uX7/Oax0//fQTW7FiBSsqKmInTpxgM2fOZM2bN2ddunRhS5cuZRcv\nXmTl5eW81lgdbm5uzMLCgtNas7OzWaNGjVhBQQFnbdZksbGxTFtb+5ORGOFWfn4+27NnDzM1NWXN\nmjVjy5YtY3///Xe1n9+5fTtrpqbGNgoELOczAfwKYL8JBKwZhfBnURAriD179rBevXqxsrIy3mpw\ndHRkgYGBH/zau3fvWGJiIvvxxx+ZoaEh09bWZi4uLuzYsWNyG0qlpaVsyJAhbNmyZZy1uWPHDmZn\nZ8dZe4Sxo0ePsmbNmokUDKRqQqGQXblyhc2YMYNpamqysWPHsvDwcFZaWipWe0lJSczJxoZpqqgw\nF1VVth1g+wC2/X8naGmqqDAnGxuajv4CWjWtIBhj+PrrrzFmzBgsXryYlxpMTU3h5eWFgQMHfvYz\nmZmZiIqKQmRkJBITEzF48GBYWVnB0tJSri6KePnyJfr06YNffvkFjo6OErc3bNgwzJs3j/YPc8zP\nzw9r1qxBQkICWrZsyXc5Cu3Vq1cIDg6Gn58fioqKMH36dEydOpWzi0mq2pJJPo+CWIGkp6ejX79+\nSExM5OVQDV1dXdy4caPaf3Fzc3Nx6tQpREZG4tSpU+jcufP7rVFdu3blfb9oSkoKhg0bhujoaJiY\nmIjdztOnT2FgYICnT59CRcIrL8mn1q1bh+DgYFy4cAGNGzfmuxyFIhQKERsbCz8/P5w6dQqWlpaY\nPn06Bg8ejFq16DwneUFBrGC8vLxw9uxZnD59WqZBVlBQAG1tbRQWFor1F7i0tBQXLlxAZGQkIiIi\nUKdOnfehPHDgQNStW1cKVVctPDwcc+fORWJiotgjg99//x1JSUkICgriuDoC/DsbtGTJEly6dAkx\nMTFo0KAB3yXJvUePHiEgIAB79uyBhoYGZsyYAQcHB2jRaVZyiYJYwZSXl8PExATfffcdpkyZIrN+\nU1JSYGdnh9TUVInbYowhOTkZkZGRiIyMREZGBszNzWFlZYXRo0ejUaNGHFRcfb/++iuioqIQFxcn\n1oh24MCB8PDwgIWFhRSqI8C/f2ZcXFyQnZ2NiIgI3v7hJs9KS0tx/Phx+Pn54fLly7C3t8f06dPR\nq1cv3mefyJdRECuga9euYcyYMUhJSZHZDT8RERHYvXu3VI5ufPz48fv3ygkJCejXrx/GjRuHsWPH\nonXr1pz39zHGGOzs7KCiooLAwECRvmk9evQIPXv2xJMnT1CvXj0pVknKy8thY2MDdXV17Nu3j6ZW\n/+fu3bvw9/dHUFAQunTpAldXV0yYMEGhTr+r6ehPsgLq3bs3nJ2d8d1338msT2le9tCyZUvMmjUL\n0dHRePz4MWbNmoXExET06tULPXv2xIoVK3D9+nXOrnL8mEAgwN69e3H79m389ttvIj178OBBjB8/\nnkJYBurUqYOwsDA8evQICxculNqfB0VQWFiIgIAADBw4EEOHDkXt2rURHx+PuLg4ODs7UwgrGpmv\n0yacKCgoYO3atWPR0dEy6W/u3Lls06ZNMumrQllZGbtw4QJzd3dnnTp1Yi1btmRubm7s5MmTrLi4\nmPP+Hjx4wJo3b85OnDhR7WdMTEykemwm+VRubi7r3r07W716Nd+lyFTFtqOZM2cyTU1NZmlpKdG2\nIyI/KIgV2JkzZ1ibNm1Yfn6+1PsaM2YMi4yMlHo/nyMUCtmdO3fY+vXrmampKdPQ0GATJ05kQUFB\n7OXLl5z1k5CQwLS1tdmdO3eq/Oy9e/eYtrY2r3u7a6qnT5+y9u3bs+014ICIly9fMh8fH2ZoaMja\nt2/P1qxZw7Kysvgui3CI3hEruClTpqBJkybYtGmTVPvR19fH4cOH5eb6w+zsbJw4cQKRkZGIjY1F\nz54936/C7tixo0Rt79mzB+vWrcOVK1ferzLNzs7+d49kcjIK3rxBQw0NZL16Bd1mzaR6Oxb5vHv3\n7sHMzAybNm2Cra0t3+VwqmLbkb+/P06ePAkLCwu4urrStiMlRUGs4F6+fIlu3bohMjISffr0kUof\nQqEQDRo0wKtXr+Ty3VNRURHOnTuHyMhIREVFQUtLC+PGjYOVlRX69u0r1jeuhQsXIjU1FatWrcK2\nDRtw4uRJ2AAwKS6GOv692PyCQIATdetirIUFFnh4SLQXmYjn1q1bGDFiBPbv348RI0bwXY7EsrKy\nEBAQAH9/f2hoaMDV1RUODg60f1rZ8TsgJ1wIDg5mhoaGUntXlJWVpTDXH757945dvnyZff/996xb\nt25MV1eXTZ8+nUVERIh0g1VZWRkz6NyZNa5Th236wjm6Of+71o3O0eXPhQsXmLa2Nrty5QrfpYil\ntLSUHTlyhI0ZM4ZpaWmxWbNmsatXrzKhUMh3aURGKIiVgFAoZKNHj2Zr1qyRSvtxcXHM1NRUKm1L\n271799imTZvY0KFDmbq6Ohs7dizz8/Njz549++JzO7dvZ+1UVelmGQURFRXFdHV1WWpqKt+lVNvd\nu3fZkiVLmK6uLhs0aBALDAzk5bpTwj8KYiWRmZnJmjRpIpUD8vfu3cucnJw4b1fWcnJy2P79+5mt\nrS3T0NBg/fr1Y2vXrmV//fXXB6MPumtVMQUGBrLWrVuzBw8e8F3KZxUUFLC9e/eygQMHMl1dXbZ0\n6VJ29+5dvssiPKN3xEpk8+bNCA8PR2xsLKcLOn7++WcIBAKsWrWKszb5Vlpairi4uPdHbtarV+/9\nYq9dmzejT2QkForxV2OTQIDr1tbYd+SIFKomVdm4cSN2796N+Ph4NG3alO9yAPx7YMzVq1fh7++P\ngwcPwtTUFK6urrCwsKATwggAWqylVN69e4f+/ftj5syZcHV15axdJycnjBgxAlOnTuWsTXnCGMOt\nW7cQGRmJw4cPIz0lBY8BiHMqbw6ADioqSHv4kG6c4YmHhwfOnTuHc+fOQV1dnbc6cnJyEBwcDH9/\nf+Tn52P69OmYNm0a3SJFPkHr4JVI7dq1sXv3bnz//fd4+vQpZ+1K81QteSAQCNCjRw/8/PPPmOLk\nBDsVFbFCGAAaA7AWCBAUEMBhhUQUa9euRffu3WFjY4OSkhKZ9i0UCnHu3Dk4ODigffv2uHz5MjZt\n2oT09HT88MMPFMKkUnX4LoBwq3v37nB1dcX8+fNx6NAhTtpU9iD+r7TkZPQtLpaoDZOiItxMSeGo\nIiIqgUAAX19f2NrawtnZGaGhoahdu/b7369sT7iekRGmuriIPYtRse1oz549UFdXh6urK7Zu3Urb\njki10NS0EioqKkL37t2xYcMGjBs3TqK2CgsL0bRpU7GvP1Q0DmPHwuL4cThK0EYwgPl16kCrdWs0\nbtwYWlpaaNy48Qc//9yvqaqq0k05HCkuLsaYMWPQuXNnbN++HVevXoWPp2ele8ITVVVxjDFYmJtX\ne094WVkZjh8/Dn9/f1y6dAm2trZwdXVF79696f9DIhIKYiV1/vx5ODs746+//pLoWsHbt2/D1taW\nk+sPFcFMJyf02r8fsyRowxfAFVtb/LhmDXJzc5GTk4OcnJz3P//SrzHGRAruil/T1NT8YNRH/pWX\nl4ehQ4eiha4ursbFYVlREaYyVumrh1wAAQIBvFRVscrbGzPd3Cpt8++//35/21GnTp3g6uqKiRMn\n0j3JRGw0Na2khgwZgtGjR8PDwwPbtm0Tu52aMi1dsbL17oMHyAckCuIkVVUYGhuLddRmUVHRJ+H8\n3+BOTU2tNMzfvHmDhg0bihXiampqSjuCa9SoESbb2WHj8uWIZwxf+n9EC8B3jGHs27cY5e4OAO/D\nuLCwEIcPH4a/vz/S0tIwZcoUnD9/Hl26dJH+F0GUHo2IlVhubi66du2KQ4cOYcCAAWK1sXnzZmRk\nZGDLli0cVycf7t69i9DQUISEhAAAxo0bB7/ff0dmaalCrZoWCoXIy8v77Ej7S6PwsrIykYK74uea\nmva749wAAAghSURBVJpyv/0mKSkJVkOGIP7t2y+G8MfSAQxSU8N6X19cunQJBw8eRP/+/eHq6gpL\nS0u5/7qJYqERsRLT0tLCli1bMGPGDNy4cQP169cXuY179+6hQ4cOUqiOP48ePUJYWBhCQkLw7Nkz\n2NvbIzQ09P27vWcZGQgMDxdrH3GgQADLMWNkvnWpVq1a0NTUhKampsgzGCUlJV8M7LS0tEpDPDc3\nF2pqapUGdlVh3rBhQ5mMwn08PbGsqEikEAaAjgAWv32LxW5uWODhgeTkZHz11VfSKJEQGhErO8YY\nxo8fj549e2LlypUiP29hYYFvv/0WVlZW3BcnQ69evcLhw4cREhKC27dvw8bGBpMnT8bgwYM/ebcq\n6SgqKi4OxsbGnNYvj4RCIfLz80UafVf8vLi4GFpaWiJPpWtpaaFevXrVqi87Oxud27RBRnGxQs1u\nkJqHgrgGyMrKQs+ePREXFwcDAwORntXX18ehQ4fQrVs3KVUnPQUFBYiMjERISAji4+Nhbm6OyZMn\nY/To0VXODuzy9cV6d3ecrmYYpwMYpaaGZV9Y5EP+X2lpKV6/fi3SQraKn9evX79awX0uJgYl+/Yh\nQIK9xN+oqqLrqlVYvGQJh189IR+iqeka4KuvvsKqVaswY8YMxMfHV3sbklAoxP3799GuXTspV8id\n0tJSnD59GqGhoYiOjsaAAQMwefJkhIaGinTKUkWYDnJ3x9KiIkz7zErbHPy70nZDFSttyYfq1asH\nHR0d6OjoiPQcYwwFBQVfDO779+8jJycHV+PjsUzCAz1oTziRBRoR1xBCoRCDBg2Co6MjZs+eXa1n\nHj9+jN69e+PZs2dSrk4yQqEQFy5cQGhoKI4cOQJ9fX04ODhg4sSJEk8pVuw9PR4dDWuBACZFRe/3\nnib9b++p5ZgxWODhUSOmoxUJV3vCoy0tERIVxVVZhHyCRsQ1RK1atbB7926YmZnBysqqWgtP5Hnr\nEmMMN27cQEhICA4cOICmTZvCwcEB169fR+vWrTnrx9jYGPuOHMGLFy8QFBCAmykpyM/NhbqWFroa\nGmL9tGn0/lBONdTQQL6EbeQDUNcS98BTQqqHgrgGMTAwwNy5czF79mxERERUuWo1IyND7lZMp6Wl\nvd9uVF5eDgcHB5w5c0bkd9+i0tbWpveECkbPyAiJR45glgRHliapqqKroSGHVRHyKeU/s5B8wMPD\nA+np6Th8+HCVn5WXEfHjx4+xceNGGBsbY/DgwcjNzUVQUBDS09Pxyy+/SD2EiWKaMm0ajuHfE7PE\nkQPgGGOYMm0ad0URUgkK4hqmfv362L17NxYsWIDc3C9/i+IziHNycrB7924MGzYMhoaGuH37Ntat\nW4dHjx5h8+bN6Nu3r9KeBkW4oaOjAwtzcwSK+eeErz3hpOahxVo11Jw5c1BaWordu3d/9jMDBgzA\nunXrMGjQIJnUVFhYiKioKISGhuL8+fMYOXIkHBwcYG5uDhUVFZnUQJQL7QknioCCuIbKy8tD165d\nsW/fPgwZMqTSzzRr1gzXrl2T6h2qZWVliImJQUhICI4fP45+/frBwcEB48ePl+iyCkIq0J5wIu8o\niGuwyMhIuLu749atW1BVVf3g96R5/aFQKMTFixcREhKCw4cPQ09PD5MnT8akSZOgq6vLaV+EAP+G\n8QraE07kFAVxDTdp0iR06tQJa9eu/eDC9KdZWUi6cQPuP/wg0YXpFRhjuHXr1vvtRpqampg8eTLs\n7e0V6sAQorhoTziRVxTENdyzZ8+gr6+PgT17IuHPPzm5MP2/0tPTERoaitDQULx9+xYODg6YPHky\nDGlLCOFJxZ7wtP/sCdczNMQU2hNOeEJBXMPt8vXFDwsXYnlpKb4BJLowvcLTp09x8OBBhISE4P79\n+7C1tYWDgwP69etHK50JIeQjFMQ1GJeLWF6/fo2jR48iJCQE165dw7hx4+Dg4IBhw4ahTh06N4YQ\nQj6HgriG4mJbR9euXXH8+HGEhIQgNjYWw4cPh4ODAywsLD5Z/EUIIaRyFMQ1lJONDYzDw7FQjP/7\nNwoE2PXVV3ienw9jY2M4ODjA2toampqaUqiUEEKUGwVxDcTFhelt69TBpRs3/q+9O0ZJMIzjOP53\nEExo6QqBY5ttzs1BZwg6QXP7C11BuoR0hdocpckDBFEHaIiakqRX+hnP57Mrbl9efXx+/3KnGGCf\nuOKyQXfzeZ3X9weztnFUVRfDYd0vFjv8VABtEuIGrZbLOu2xSFP1MZi+MpgO0JsQN+jt5aUOe77H\nYVW9/jAaAcDPhLhBBtMB9ocQN2hyclIPPdeMHg8OauJ2LIDenJpu0C5OTR+PRrVar10JCNCTJ+IG\nGUwH2B+eiBtlMB1gP3gibtR0Oq2brquz8bietnzN513TN10nwgA7IsQNu7y6quuuq9l4XLeDQW36\nM9JzfVxrOdsw+ADA7/lqGoPpAEFCzBeD6QB/T4gBIMhvxAAQJMQAECTEABAkxAAQJMQAECTEABAk\nxAAQJMQAECTEABAkxAAQJMQAECTEABAkxAAQJMQAECTEABAkxAAQJMQAECTEABAkxAAQJMQAECTE\nABAkxAAQJMQAECTEABAkxAAQJMQAECTEABAkxAAQJMQAECTEABAkxAAQJMQAECTEABAkxAAQJMQA\nECTEABAkxAAQJMQAECTEABAkxAAQJMQAECTEABAkxAAQJMQAECTEABAkxAAQJMQAECTEABAkxAAQ\nJMQAECTEABAkxAAQJMQAECTEABAkxAAQJMQAECTEABAkxAAQ9A5HVBbq/ha0wgAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112b90128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import networkx as nx\n",
    "\n",
    "edgelist = {(0,1),(0,2),(0,3),(0,5),(0,9),(1,3),(1,4),(1,6),\n",
    "(1,9),(2,3),(2,5),(3,4),(3,5),(3,6),(4,6),(5,6),(7,8),\n",
    "(8,9)}\n",
    "\n",
    "G = nx.Graph()\n",
    "for edge in edgelist:\n",
    "    G.add_edge(edge[0], edge[1])\n",
    "\n",
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Influence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree centrality:\n",
      "{0: 0.5555555555555556, 1: 0.5555555555555556, 2: 0.3333333333333333, 3: 0.6666666666666666, 4: 0.3333333333333333, 5: 0.4444444444444444, 6: 0.4444444444444444, 7: 0.1111111111111111, 8: 0.2222222222222222, 9: 0.3333333333333333}\n",
      "\n",
      "Betweenness centrality:\n",
      "{0: 0.23148148148148143, 1: 0.23148148148148143, 2: 0.0, 3: 0.10185185185185183, 4: 0.0, 5: 0.023148148148148143, 6: 0.023148148148148143, 7: 0.0, 8: 0.2222222222222222, 9: 0.38888888888888884}\n",
      "\n",
      "Closeness centrality:\n",
      "{0: 0.6428571428571429, 1: 0.6428571428571429, 2: 0.5, 3: 0.6, 4: 0.5, 5: 0.5294117647058824, 6: 0.5294117647058824, 7: 0.3103448275862069, 8: 0.42857142857142855, 9: 0.6}\n",
      "\n",
      "Eigenvector centrality:\n",
      "{0: 0.39769090281372055, 1: 0.39769090281372055, 2: 0.28583482369644964, 3: 0.4810206692001181, 4: 0.28583482369644964, 5: 0.3522091841983857, 6: 0.35220918419838565, 7: 0.011163556091491361, 8: 0.04807425308073236, 9: 0.19586101425312444}\n"
     ]
    }
   ],
   "source": [
    "print('Degree centrality:\\n{}\\n'.format(nx.degree_centrality(G)))\n",
    "print('Betweenness centrality:\\n{}\\n'.format(nx.betweenness_centrality(G)))\n",
    "print('Closeness centrality:\\n{}\\n'.format(nx.closeness_centrality(G)))\n",
    "print('Eigenvector centrality:\\n{}'.format(nx.eigenvector_centrality(G)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cliques:\n",
      "[[8, 9], [8, 7], [9, 0, 1], [3, 0, 1], [3, 0, 2, 5], [3, 4, 1, 6], [3, 6, 5]]\n",
      "Cores:\n",
      "[frozenset({0, 1, 2, 3, 4, 5, 6, 9})]\n"
     ]
    }
   ],
   "source": [
    "cliques = nx.find_cliques(G)\n",
    "kcores = nx.k_clique_communities(G, 3)\n",
    "print('Cliques:\\n{}'.format(list(cliques)))\n",
    "print('Cores:\\n{}'.format(list(kcores)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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