14_networkx_basics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Networkx Basics\n",
    "\n",
    "Tutorial from https://networkx.org/documentation/stable/tutorial.html\n",
    "\n",
    "Use networkx to create a graph. Go through the basics.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.Graph()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "G.add_node(1) # add a node"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "G.add_nodes_from([2,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (3,3))\n",
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "H=nx.path_graph(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (3,3))\n",
    "nx.draw(H) # sw: H is another graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G.add_nodes_from(H) # add Graph H to Graph G.\n",
    "plt.figure(figsize = (3,3))\n",
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "G.add_node(H) # Here G contains H as a node. It represents graphs of graphs. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (3,3))\n",
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G.add_edge(1,2) # sw: add an edge between 1 and 2.\n",
    "plt.figure(figsize = (15,3))\n",
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "e = (2,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G.add_edge(*e) # unpack edge tuple* # sw: add an edge between 2 and 3.\n",
    "plt.figure(figsize = (15,3))\n",
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G.add_edges_from([(1,2),(1,3)])\n",
    "plt.figure(figsize = (15,3))\n",
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G.add_edges_from(H.edges()) # add the edges from Graph H.\n",
    "plt.figure(figsize = (15,3))\n",
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G.remove_node(H) # remove the H node\n",
    "plt.figure(figsize = (15,3))\n",
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G.clear()\n",
    "plt.figure(figsize = (15,3))\n",
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# add things back\n",
    "G.add_edges_from([(1,2),(1,3)])\n",
    "G.add_node(1)\n",
    "G.add_edge(1,2)\n",
    "G.add_node(\"spam\") # adds node \"spam\"\n",
    "G.add_nodes_from(\"spam\") # adds 4 nodes: 's', 'p', 'a', 'm'\n",
    "G.add_edge(3, 'm')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (15,3))\n",
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examining elements of a graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.number_of_nodes()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.number_of_edges()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3, 'spam', 's', 'p', 'a', 'm']"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(G.nodes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(1, 2), (1, 3), (3, 'm')]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(G.edges)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(G.adj[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.degree[1] # the number of edges incident to 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EdgeDataView([(2, 1), ('m', 3)])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.edges([2, 'm']) # report edges of 2 and 'm'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DegreeView({2: 1, 3: 2})"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.degree([2, 3]) # report degrees of the two nodes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Removing elements from a graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "G.remove_node(2)\n",
    "G.remove_nodes_from(\"spam\")\n",
    "G.remove_edge(1, 3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 3, 'spam']"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(G.nodes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Skip a few things..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adding attributes to graphs, nodes, and edges"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'day': 'Friday'}"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Add graph attributes\n",
    "G = nx.Graph(day=\"Friday\")\n",
    "G.graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'day': 'Monday'}"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.graph['day'] = \"Monday\"\n",
    "G.graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'time': '5pm'}\n",
      "[(1, {'time': '5pm', 'room': 714}), (3, {'time': '2pm'})]\n"
     ]
    }
   ],
   "source": [
    "# Add node attributes\n",
    "G.add_node(1, time='5pm') # sw: add node 1 with attribute 'time' = '5pm'\n",
    "G.add_nodes_from([3], time='2pm') # sw: add node 3 with attribute 'time' = '2pm'\n",
    "print(G.nodes[1])\n",
    "G.nodes[1]['room'] = 714\n",
    "print(G.nodes.data())\n",
    "# sw: it leads to a hierarchy of dictionaries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(1, {'time': '5pm', 'room': 714}), (3, {'time': '2pm'}), (2, {}), (4, {}), (5, {})]\n",
      "[(1, 2, {'weight': 4.7, 'color': 'blue'}), (3, 4, {'color': 'red'}), (3, 2, {'weight': 8}), (4, 5, {'color': 'red'})]\n"
     ]
    }
   ],
   "source": [
    "# add edge attributes\n",
    "G.add_edge(1, 2, weight=4.7) # sw: add edge between 1 and 2 with 'weight' = 4.7\n",
    "G.add_edges_from([(3, 4), (4, 5)], color='red')\n",
    "G.add_edges_from([(1, 2, {'color': 'blue'}), (2, 3, {'weight': 8})])\n",
    "print(G.nodes.data())\n",
    "print(G.edges.data())\n",
    "# sw: both nodes and edges have a lot of info. \n",
    "# Networks are much more complex than simple adjacency matrices.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (15,3))\n",
    "nx.draw(G)\n",
    "# sw: visualization of the graph is very simple. But the dictionary is much more complex!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "G[1][2]['weight'] = 4.7\n",
    "G.edges[3, 4]['weight'] = 4.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(1, {'time': '5pm', 'room': 714}), (3, {'time': '2pm'}), (2, {}), (4, {}), (5, {})]\n",
      "[(1, 2, {'weight': 4.7, 'color': 'blue'}), (3, 4, {'color': 'red', 'weight': 4.2}), (3, 2, {'weight': 8}), (4, 5, {'color': 'red'})]\n"
     ]
    }
   ],
   "source": [
    "print(G.nodes.data())\n",
    "print(G.edges.data())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (15,3))\n",
    "nx.draw(G) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Directed graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DG = nx.DiGraph()\n",
    "\n",
    "DG.add_weighted_edges_from([(1, 2, 0.5), (3, 1, 0.75)])\n",
    "\n",
    "DG.out_degree(1, weight='weight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.25"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "DG.degree(1, weight='weight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2]"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(DG.successors(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2]"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(DG.neighbors(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (15,3))\n",
    "nx.draw(DG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "H = nx.Graph(G)  # create an undirected graph H from a directed graph G\n",
    "plt.figure(figsize = (15,3))\n",
    "nx.draw(H)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multigraphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Mxesvbo9Sqb37S6WIN/Zuz+yreiOEEQAAACi0vzq0J6qVgbburVYG4tihPQlP1FvCCAAAABTYK7u2xtTEWAwPtpYIhgfLMTUxFvtHt3ZnsB5J5vhZAAAAILMmx3dHRMTx6VrUG6vRbK5/ban04D9FpibGHt6XZaVmc6PHBQAAAIri8tx8nDh/Pc5dvR2liKg37j/8rFopRzMenCly7NCezP+nyPeEEQAAAOAx3y4ux5kv5qL2zd1YqK/ESHUwxnY+HUcOjGb6oNW1CCMAAABAYTl8FQAAACgsYQQAAAAoLGEEAAAAKCxhBAAAACgsYQQAAAAoLGEEAAAAKKz/AzTAQ4lpC7GEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x216 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MG = nx.MultiGraph()\n",
    "MG.add_weighted_edges_from([(1, 2, 0.5), (1, 2, 0.75), (2, 3, 0.5)]) # add weights to edges\n",
    "dict(MG.degree(weight='weight'))\n",
    "plt.figure(figsize = (15,3))\n",
    "nx.draw(MG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 2, 3]"
      ]
     },
     "execution_count": 141,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GG = nx.Graph()\n",
    "for n, nbrs in MG.adjacency():\n",
    "   for nbr, edict in nbrs.items():\n",
    "       minvalue = min([d['weight'] for d in edict.values()])\n",
    "       GG.add_edge(n, nbr, weight = minvalue)\n",
    "\n",
    "nx.shortest_path(GG, 1, 3) # identify the shortest path."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 1.0, 2: 0.5, 3: 0.5}"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Drawing graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_random(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAb4AAAEuCAYAAADx63eqAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Il7ecAAAACXBIWXMAAAsTAAALEwEAmpwYAAAJ9ElEQVR4nO3dv2pbdxTA8XNtGSuQCENrSMCBDqbW1ECydIuzena3PoH7CJ79CMkTdPTsNc7WJYFkiRI8FCJIwAkYxWAJyb4dgkuDGre1ftcNnM9nle65Z/uiP/feqq7rOgAgibn/ewEAuErCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCqtpk/w/ngUu0/70Xs3iMFwEp12K7o3O/HTvZX45vpi06cHgM9UTd2r8/mbo3i4fxBPXh9GRMRocvbna+3WXNQRsb62HFv3V+PO7aUmVgCAKY2E79fffo+dvV4MJ6dx0fSqimi35mN7oxs///hd6TUAYErxrzo/Re9lnIzP/vG9dR1xMj6Nnb2XERHiB0Djiv655fmbo9jZ6/2r6P3VyfgsdvZ68aJ/VHIdAJhSNHwP9w9iODm91LHDyWk82j8ouQ4ATCkWvvfHo3jy+vDC3/QuUtcRj18dxofjUamVAGBKsfDtPu3PPKOKiN1ns88BgC8pFr7eu8FnlyxcxnByFr23HwttBADTioVvMJwUmjMuMgcA/k6x8HXaZa6M6LQXiswBgL9TLHzdm51YbM02rt2ai+6tG4U2AoBpxcK3eW9l5hl1RGzenX0OAHxJsfB9e30x7n+/HFV1ueOrKuLB2rIbVwPQqKIXsP+yvhrt1vyljm235mNrfbXkOgAwpWj47txeiu2Nblxb+G9jry3MxfZGN35YWSq5DgBMKX6T6vMbTXs6AwBfo8aex/eifxSP9g/i8avDqOLTxennzp/H92BtObbWV33SA+DKNBa+cx+OR7H7rB+9tx9jMBxHp70Q3Vs3YvOuJ7ADcPUaDx8AfE2K/rkFAL52wgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCrCB0AqwgdAKsIHQCqt/3sBAPJ6fzyK3af96L0bxGA4iU67Fd2bnfjp3kp8c32xkXNWdV3XjUwGgC94/uYoHu4fxJPXhxERMZqc/flauzUXdUSsry3H1v3VuHN7qei5hQ+AK/Xrb7/Hzl4vhpPTuKhAVRXRbs3H9kY3fv7xu2Ln91UnAFfmU/Rexsn47B/fW9cRJ+PT2Nl7GRFRLH7+3ALAlXj+5ih29nr/Knp/dTI+i529XrzoHxXZQ/gAuBIP9w9iODm91LHDyWk82j8osofwAdC498ejePL68MLf9C5S1xGPXx3Gh+PRzLsIHwCN233an3lGFRG7z2afI3wANK73bvDZJQuXMZycRe/tx5l3ET4AGjcYTgrNGc88Q/gAaFynXebquU57YeYZwgdA47o3O7HYmi057dZcdG/dmHkX4QOgcZv3VmaeUUfE5t3Z5wgfAI379vpi3P9+OarqcsdXVcSDteUiN64WPgCuxC/rq9FuzV/q2HZrPrbWV4vsIXwAXIk7t5die6Mb1xb+W3quLczF9kY3flhZKrKHm1QDcGXObzT9fz6dwWOJALhyL/pH8Wj/IB6/OowqPl2cfu78eXwP1pZja3212Ce9c8IHwP/mw/Eodp/1o/f2YwyG4+i0F6J760Zs3vUEdgAowp9bAEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASEX4AEhF+ABIRfgASKXV9AneH49i92k/eu8GMRhOotNuRfdmJ366txLfXF9s+vQA8Jmqruu6icHP3xzFw/2DePL6MCIiRpOzP19rt+aijoj1teXYur8ad24vNbECAExpJHy//vZ77Oz1Yjg5jYumV1VEuzUf2xvd+PnH70qvAQBTin/V+Sl6L+NkfPaP763riJPxaezsvYyIED8AGlf0zy3P3xzFzl7vX0Xvr07GZ7Gz14sX/aOS6wDAlKLhe7h/EMPJ6aWOHU5O49H+Qcl1AGBKsfC9Px7Fk9eHF/6md5G6jnj86jA+HI9KrQQAU4qFb/dpf+YZVUTsPpt9DgB8SbHw9d4NPrtk4TKGk7Povf1YaCMAmFYsfIPhpNCccZE5APB3ioWv0y5zZUSnvVBkDgD8nWLh697sxGJrtnHt1lx0b90otBEATCsWvs17KzPPqCNi8+7scwDgS4qF79vri3H/++WoqssdX1URD9aW3bgagEYVvYD9l/XVaLfmL3VsuzUfW+urJdcBgClFw3fn9lJsb3Tj2sJ/G3ttYS62N7rxw8pSyXUAYErxm1Sf32ja0xkA+Bo19jy+F/2jeLR/EI9fHUYVny5OP3f+PL4Ha8uxtb7qkx4AV6ax8J37cDyK3Wf96L39GIPhODrthejeuhGbdz2BHYCr13j4AOBrUvTPLQDwtRM+AFIRPgBSET4AUhE+AFIRPgBSET4AUhE+AFIRPgBS+QNBvxd4TVgHygAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_circular(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw_spectral(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}