Simplified Cliques, Triangles and Squares (Student).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import pandas\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Massively simplified from the tutorial example so I can see what's going on"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gwQI2btxIxYoVTccRESejEbGDJVitREKxawcDjAWqAxHAhmLerwJEWiwkWK2O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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff648aedf60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.Graph()\n",
    "G.add_nodes_from(range(6))\n",
    "G.add_edges_from([(1,2),(1,3),(1,4),(2,3),(2,5),(5,4)])\n",
    "nx.draw(G, with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "My attempt at implementing the `get_open_triangles()` function using list comprehensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def get_open_triangles(G, a):\n",
    "\n",
    "    return [\n",
    "        {a,b,c}\n",
    "        for b in set(G.neighbors(a))          # A knows B\n",
    "        for c in set(G.neighbors(b))          # B knows C\n",
    "        if c!=b                               # C isn't me\n",
    "        if c!=a                                \n",
    "        if c not in set(G.neighbors(a))       # C doesn't know A\n",
    "        \n",
    "    ] + [\n",
    "\n",
    "        {a,d,e}\n",
    "        for d in set(G.neighbors(a))\n",
    "        for e in set(G.neighbors(a))\n",
    "        if d>e  # avoid dupes!\n",
    "        if e not in set(G.neighbors(d))\n",
    "    ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def draw(nodes):\n",
    "    for i, triplet in enumerate(nodes):\n",
    "        fig = plt.figure(i)\n",
    "        nx.draw(G.subgraph(triplet), with_labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "There are 4 open triangles:\n",
      "[{1, 2, 5}, {2, 3, 5}, {1, 4, 5}, {2, 4, 5}]\n"
     ]
    },
    {
     "data": {
      "image/png": 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5cjqd8ng8crvdBBnoYmzKgJ9ZtXKlfjd/vnIaGzW8Dc/fLykjNFSDY2N1+L/+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\nAQCwif8HXWEzp0cvIAgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff648aabba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KGbgMBQ0YMmzYMFmWpQkTJpiOYsTnn3+uZ555RqNGjVL//v1NxwFsh0PcgEH/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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff648a95358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HSk1NlWEYmjZtmq655hqnJwJApyDKcIVz586ptLTUDnFwcLB9bGn8+PHq0YOD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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff6489a8cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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iiy/kuq4cx1HPnj1l27Ysy1JmZiZRBgDDCHGYCeZZ036/X9u3bw9E+eTJk7IsS5ZladKk\nSerRo0e3fA8AgK4jxGHo17svPe/zafZF7r50XFL5Nd59qa6uTo7jyHVdff/99yosLJRt25o8ebJ6\n9ep1zd8HAODyCHGY2rp1q14rKVFlVZWKPR5l+nyB+xHXJCbK6/crPy9Pzyxc2C03eti3b5+8Xq9c\n11VdXZ3y8/NlWZZycnKUmJh4za8PAOgcIQ5zR48e1bLyctXv3KmWpialpKUpY9QoPTJ7dtDOlP7h\nhx+0fPlyOY6jrVu3atq0abIsSzNmzFCfPn2C8t8EgFhFiHFJx44d04oVK+S6rj777DPdf//9sixL\nhYWFuvHGG02PBwARjxCjy06cOKFVq1bJdV2tXbtW48aNk23bKioqUv/+/U2PBwARiRDjqvh8Pq1Z\ns0au66qyslLDhw8PXIE9ePBg0+MBQMQgxLhmZ86c0fr16+U4jioqKjRgwIDAASLDhw83PR4AhDVC\njG7V3t6uTZs2yXVdua6r5OTkwAEiY8eO5QARALgAIUbQ+P1+1dTUBA4QOXv2bODt63vvvVdxcRx1\nDgCEGCHh9/u1a9euwAEix44dU1FRkWzb1v3336+ePXuaHhEAjCDEMGL37t2Bt6/37t2rmTNnyrZt\nPfjgg0q4yO0gASAaEWIYd/DgQXm9XjmOox07dmj69OmybVu5ublKTk42PR4ABBUhRlg5cuSIVqxY\nIcdx9MUXX2jy5MmyLEszZ85UWlpnp24DQGQjxAhbTU1NqqyslOu6+vTTTzVhwgTZtq3CwkL169fP\n9HgA0C0IMSLCyZMn9dFHH8lxHK1evVqjR4+WbdsqLi7WbbfdZno8ALhqhBgRp7W1VevWrZPjOFqx\nYoXS09MDB4gMHTrU9HgAcEUIMSLa2bNntXHjRrmuK6/XqxtvvDEQ5VGjRnGACICwR4gRNTo6OrRl\ny5bAASLx8fGBA0QyMzM5QARAWCLEiEp+v19fffVV4ACRlpYWFRcXy7IsZWVlqUePHqZHBABJhBgx\noq6uLnCAyMGDB1VYWCjbtjVlyhT16tXL9HgAYhghRsxpaGiQ1+uV67r65ptvlJeXJ9u2lZOTo6Sk\nJNPjAYgxhBgx7dChQ1q+fLkcx1FNTY0eeughWZal/Px89enTx/R4AGIAIQZ+8eOPP2rFihVyXVcb\nN25UVlaWLMtSYWGhbrrpJtPjAYhShBjoxIkTJ1RVVSXXdbVmzRrdfffdsm1bRUVFGjBggOnxAEQR\nQgxchs/n09q1a+U4jiorKzVs2LDAx6LS09NNjwcgwhFi4AqcOXNG69evl+u6Wr58ufr37x84QGT4\n8OEcIALgihFi4Cq1t7dr8+bNgY9FJSUlybZtWZalu+66iygD6BJCDHQDv9+vrVu3ynEcOY6jtra2\nwNvXEydO5FQvABdFiIFu5vf79fXXXwdO9WpsbFRRUZEsy1J2drZ69uxpekQAYYQQA0G2e/dueb1e\nOY6jPXv2aObMmbJtWw899JASEhJMjwfAMEIMhNDBgwcDp3p99dVXmj59uizLUm5urlJSUkyPB8AA\nQgwY0tjYqIqKCrmuq82bN2vy5MmyLEsFBQVKS0szPR6AECHEQBj46aefVFlZKdd1tW7dOt1zzz2y\nbVuFhYW65ZZbTI8HIIgIMRBmfv75Z3300UdyHEerV6/WyJEjZdu2iouLNXDgQNPjAehmhBgIY6dP\nn9a6devkOI5WrFihQYMGBQ4QycjIMD0egG5AiIEIcfbsWX322WdyXVder1dpaWmBKI8ePZoDRIAI\nRYiBCNTR0aEvv/xSruvKcRzFxcUFDhAZP348B4gAEYQQAxHO7/drx44dgQNEmpubVVxcLMuylJWV\npfj4eNMjArgEQgxEmW+//TawKR84cECFhYWybVtTpkxR7969TY8H4AKEGIhi//znPwOnen399dfK\ny8uTbdvKycnRddddZ3o8ACLEQMw4dOiQli9fLtd1VV1drQcffFCWZSk/P1+pqammxwNiFiEGYtCP\nP/6olStXynVdbdiwQZMmTZJlWSosLFTfvn1NjwfEFEIMxLiWlhZVVVXJcRytWbNGd911V+AAkQED\nBpgeD4h6hBhAgM/n09q1a+W6riorK5WRkRH4WNSQIUNMjwdEJUIMoFNtbW1av369XNfV8uXLdcst\ntwQOEBkxYgQHiADdhBADuKz29nb9/e9/D3xWOTExUbZty7Is3X333UQZuAaEGMAV8fv92rp1a+Cz\nyqdPnw68fT1x4kT16NHD9IhARCHEAK6a3+/X119/Ldd15bquDh8+rKKiIlmWpcmTJ6tnz56mRwTC\nHiEG0G327NkTOEBk9+7dys/Pl23beuihh5SYmGh6PCAsEWIAQfGvf/1LXq9Xrutq+/btysnJkWVZ\nysvLU0pKiunxgLBBiAEE3dGjR1VRUSHXdbVp0yZlZ2fLsiwVFBTohhtuMD0eYBQhBhBSP/30k1at\nWiXHcbRu3TqNHz9etm2rqKhIt9xyi+nxgJAjxACM+fnnn7VmzRo5jqOqqir96U9/CpzqNWjQINPj\nASFBiAGEhdOnT2vdunVyXVcVFRUaOHBg4GNRw4YNMz0eEDSEGEDYOXv2rD7//HM5jiOv16vrr78+\ncKrXmDFjOEAEUYUQAwhrHR0dqq6uluM4chxHkgJRvueeexQXF2d4QuDaEGIAEcPv92vHjh2BU71+\n+uknFRcXy7Is3X///YqPjzc9InDFCDGAiPXtt98GDhDZv3+/CgoKZNu2pk6dqt69e5seD+gSQgwg\nKuzfvz9w1OauXbuUm5sr27Y1ffp0XXfddabHAy6KEAOIOocOHQocIPLll19q6tSpsixL+fn5uv76\n602PB/wGIQYQ1Y4fP66VK1fKcRxt2LBB9913nyzLUlFRkfr27Wt6PIAQA4gdLS0tqqqqkuu6WrNm\nje68887AASJ//OMfTY+HGEWIAcQkn8+njz/+WK7rauXKlRo6dGjgAJHbb7/d9HiIIYQYQMxra2vT\nhg0b5LquvF6v+vXrF4jyyJEjOUAEQUWIAeA87e3t+uKLL+Q4jlzXVe/evQMHiIwbN44oo9sRYgC4\nCL/fr23btgUOEPH5fIFN+b777lOPHj1Mj4goQIgBoAv8fr+++eabQJQPHTqkoqIiWZalyZMnq1ev\nXqZHRIQixABwFfbu3Rs4QOS7775Tfn6+bNvWtGnTlJiYaHo8RBBCDADX6Pvvv5fX65Xrutq2bZty\ncnJkWZby8vLUp08f0+MhzBFiAOhGR48e1YoVK+Q4jjZt2qQHHnhAlmWpoKBAN954o+nxEIYIMQAE\nSXNzsyorK+W6rj755BNlZmbKtm0VFRXpD3/4g+nxECYIMQCEwKlTp/TRRx/JdV2tWrVKI0aMCJzq\nNXjwYNPjwSBCDAAhdvr0aX366adyHEcVFRW69dZbZdu2LMvS8OHDTY+HECPEAGDQ2bNntWnTpsAB\nIqmpqYEDRO68885uO0CksbFRy8rLVV9bq5PNzUpOTVXG6NF69LHHuPmFYYQYAMJER0eHqqurA59V\n9vv9gQNEJkyYoLi4uCt+zZqaGr1WUqJVq1fLkpTZ2qoUSS2SqhMT5fX7NSM3V88sXKjMzMzu/pbQ\nBYQYAMKQ3+9XbW1tIMrHjx9XcXGxLMvSAw88oPj4+Mu+xjtLluiFefM03+fTo36/0jp5TpOkco9H\nLyUm6sXFi/XEnDnd/r3g0ggxAESA7777LnCASENDgwoKCmTbth588EH17t37d89/Z8kSlc2bpzWn\nTqkr95LaIyknKUnziXHIEWIAiDD79+8PHCBSW1ur3Nxc2bat6dOnKzk5WTU1NSrIztbn50X4jKSn\nJH2ic1vwEEn/W9L08153j6SspCSt3LhR48aNC+n3FMsIMQBEsMOHD6uiokKO42jLli2aOnWqfjx4\nUMX/+If++3l/vZ+StFjSY5JulbRK0n+RtEvSbee93l88Hv2juFj/4Tgh/C5iGyEGgChx/Phx/fWv\nf9WCZ57RwY6OTn8mfL4xkv6XpOLzX0PSkIQE1R84wNXUIXLll+ABAMLSDTfcoNZTp/Sfe/W6bISP\nSNot6U8XvoakYo9Hy8rLgzEiOkGIASCK1NfWanxr6yWfc1bSnyXNlpTRyeOZPp/qd+7s/uHQKUIM\nAFHkZHOzUi7xuF/nItxb0v+5yHNSJLU0NXX3aLiIy38QDQAQMZJTU9Vyicf/q6Rjkqok9bjIc1ok\npaRd7s1tdBc2YgCIIhmjR6s6IaHTx/5d0reSVkjqdYnXqElMVMaoUUGYDp3hqmkAiCKNjY26Y+BA\n7Wtt/c0FWwckDZKUoP+/CXsk/V+d+xjTr7hqOvTYiAEgitx8882akZur9y64WcRtkjp07vPELb/8\nc0K/jbAkvefxKD8vjwiHEBsxAESZzk7W6gpO1jKDjRgAokxmZqZeXLxYOUlJ2tPFX/PrWdMvLl5M\nhEOMEANAFHpizhzNX7xYWUlJ+ovHo4t9GOm4pFc8HmVxwwdjeGsaAKLY1q1b9VpJiSqrqlTs8SjT\n5wvcj7jml/sR5+fl6ZmFC9mEDSHEABADjh49qmXl5arfuVMtTU1KSUtTxqhRemT2bC7MMowQAwBg\nED8jBgDAIEIMAIBBhBgAAIMIMQAABhFiAAAMIsQAABhEiAEAMIgQAwBgECEGAMAgQgwAgEGEGAAA\ngwgxAAAGEWIAAAwixAAAGESIAQAwiBADAGAQIQYAwCBCDACAQYQYAACDCDEAAAYRYgAADCLEAAAY\nRIgBADCIEAMAYBAhBgDAIEIMAIBBhBgAAIMIMQAABhFiAAAMIsQAABhEiAEAMIgQAwBgECEGAMAg\nQgwAgEGEGAAAgwgxAAAGEWIAAAwixAAAGESIAQAwiBADAGAQIQYAwCBCDACAQYQYAACDCDEAAAYR\nYgAADCLEAAAYRIgBADCIEAMAYBAhBgDAIEIMAIBBhBgAAIP+H0gIU1WqnhyGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff648a95a20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "open_triangles=get_open_triangles(G,5)\n",
    "print(\"There are {} open triangles:\".format(len(open_triangles)))\n",
    "print(open_triangles)\n",
    "draw(open_triangles)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1+"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}