NX4-Algorithms-I.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithms -I\n",
    "\n",
    "### Distance, Centrality, Community and Traversal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "import matplotlib.cbook\n",
    "warnings.filterwarnings(\"ignore\",category=matplotlib.cbook.mplDeprecation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.karate_club_graph()\n",
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Distance\n",
    "\n",
    "Graph diameter, radius, eccentricity and other properties.\n",
    "\n",
    "- ```center(G[, e, usebounds])``` \tReturns the center of the graph G.\n",
    "- ```diameter(G[, e, usebounds])``` \tReturns the diameter of the graph G.\n",
    "- ```eccentricity(G[, v, sp])``` \tReturns the eccentricity of nodes in G.\n",
    "- ```extrema_bounding(G[, compute])``` \tCompute requested extreme distance metric of undirected graph G\n",
    "- ```periphery(G[, e, usebounds])``` \tReturns the periphery of the graph G.\n",
    "- ```radius(G[, e, usebounds])``` \tReturns the radius of the graph G."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 5)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.radius(G), nx.diameter(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 8, 13, 19, 31]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.center(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 3,\n",
       " 1: 3,\n",
       " 2: 3,\n",
       " 3: 3,\n",
       " 4: 4,\n",
       " 5: 4,\n",
       " 6: 4,\n",
       " 7: 4,\n",
       " 8: 3,\n",
       " 9: 4,\n",
       " 10: 4,\n",
       " 11: 4,\n",
       " 12: 4,\n",
       " 13: 3,\n",
       " 14: 5,\n",
       " 15: 5,\n",
       " 16: 5,\n",
       " 17: 4,\n",
       " 18: 5,\n",
       " 19: 3,\n",
       " 20: 5,\n",
       " 21: 4,\n",
       " 22: 5,\n",
       " 23: 5,\n",
       " 24: 4,\n",
       " 25: 4,\n",
       " 26: 5,\n",
       " 27: 4,\n",
       " 28: 4,\n",
       " 29: 5,\n",
       " 30: 4,\n",
       " 31: 3,\n",
       " 32: 4,\n",
       " 33: 4}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.eccentricity(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.extrema_bounding(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[14, 15, 16, 18, 20, 22, 23, 26, 29]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.periphery(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Centrality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Degree\n",
    "\n",
    "- ```degree_centrality(G)``` \tCompute the degree centrality for nodes.\n",
    "- ```in_degree_centrality(G)``` \tCompute the in-degree centrality for nodes.\n",
    "- ```out_degree_centrality(G)``` \tCompute the out-degree centrality for nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.balanced_tree(r=3, h=2) \n",
    "nx.draw(G, node_size = 500,node_color = 'lightblue', with_labels =True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0.25,\n",
       " 1: 0.3333333333333333,\n",
       " 2: 0.3333333333333333,\n",
       " 3: 0.3333333333333333,\n",
       " 4: 0.08333333333333333,\n",
       " 5: 0.08333333333333333,\n",
       " 6: 0.08333333333333333,\n",
       " 7: 0.08333333333333333,\n",
       " 8: 0.08333333333333333,\n",
       " 9: 0.08333333333333333,\n",
       " 10: 0.08333333333333333,\n",
       " 11: 0.08333333333333333,\n",
       " 12: 0.08333333333333333}"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.degree_centrality(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0.25,\n",
       " 1: 0.3333333333333333,\n",
       " 2: 0.3333333333333333,\n",
       " 3: 0.3333333333333333,\n",
       " 4: 0.08333333333333333,\n",
       " 5: 0.08333333333333333,\n",
       " 6: 0.08333333333333333,\n",
       " 7: 0.08333333333333333,\n",
       " 8: 0.08333333333333333,\n",
       " 9: 0.08333333333333333,\n",
       " 10: 0.08333333333333333,\n",
       " 11: 0.08333333333333333,\n",
       " 12: 0.08333333333333333}"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.in_degree_centrality(nx.to_directed(G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0.25,\n",
       " 1: 0.3333333333333333,\n",
       " 2: 0.3333333333333333,\n",
       " 3: 0.3333333333333333,\n",
       " 4: 0.08333333333333333,\n",
       " 5: 0.08333333333333333,\n",
       " 6: 0.08333333333333333,\n",
       " 7: 0.08333333333333333,\n",
       " 8: 0.08333333333333333,\n",
       " 9: 0.08333333333333333,\n",
       " 10: 0.08333333333333333,\n",
       " 11: 0.08333333333333333,\n",
       " 12: 0.08333333333333333}"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.out_degree_centrality(nx.to_directed(G))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Eigenvector Centality\n",
    "\n",
    "- ```eigenvector_centrality(G[, max_iter, tol, …])``` \tCompute the eigenvector centrality for the graph G.\n",
    "- ```eigenvector_centrality_numpy(G[, weight, …])``` \tCompute the eigenvector centrality for the graph G.\n",
    "- ```katz_centrality(G[, alpha, beta, max_iter, …])``` \tCompute the Katz centrality for the nodes of the graph G.\n",
    "- ```katz_centrality_numpy(G[, alpha, beta, …])``` \tCompute the Katz centrality for the graph G."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0.49999972705204543,\n",
       " 1: 0.40824851115143324,\n",
       " 2: 0.40824851115143324,\n",
       " 3: 0.40824851115143324,\n",
       " 4: 0.16666657745857444,\n",
       " 5: 0.16666657745857444,\n",
       " 6: 0.16666657745857444,\n",
       " 7: 0.16666657745857444,\n",
       " 8: 0.16666657745857444,\n",
       " 9: 0.16666657745857444,\n",
       " 10: 0.16666657745857444,\n",
       " 11: 0.16666657745857444,\n",
       " 12: 0.16666657745857444}"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.eigenvector_centrality(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0.31855094383728,\n",
       " 1: 0.3279200842087277,\n",
       " 2: 0.3279200842087277,\n",
       " 3: 0.3279200842087277,\n",
       " 4: 0.2529669612371458,\n",
       " 5: 0.2529669612371458,\n",
       " 6: 0.2529669612371458,\n",
       " 7: 0.2529669612371458,\n",
       " 8: 0.2529669612371458,\n",
       " 9: 0.2529669612371458,\n",
       " 10: 0.2529669612371458,\n",
       " 11: 0.2529669612371458,\n",
       " 12: 0.2529669612371458}"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.katz_centrality(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Betweenness Centrality\n",
    "\n",
    "- ```betweenness_centrality(G[, k, normalized, …])``` \tCompute the shortest-path betweenness centrality for nodes.\n",
    "- ```edge_betweenness_centrality(G[, k, …])``` \tCompute betweenness centrality for edges.\n",
    "- ```betweenness_centrality_subset(G, sources, …)``` \tCompute betweenness centrality for a subset of nodes.\n",
    "- ```edge_betweenness_centrality_subset(G, …[, …])``` \tCompute betweenness centrality for edges for a subset of nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: 0.7272727272727273,\n",
       " 1: 0.4545454545454546,\n",
       " 2: 0.4545454545454546,\n",
       " 3: 0.4545454545454546,\n",
       " 4: 0.0,\n",
       " 5: 0.0,\n",
       " 6: 0.0,\n",
       " 7: 0.0,\n",
       " 8: 0.0,\n",
       " 9: 0.0,\n",
       " 10: 0.0,\n",
       " 11: 0.0,\n",
       " 12: 0.0}"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.betweenness_centrality(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Community\n",
    "\n",
    "Functions for computing and measuring community structure.\n",
    "\n",
    "The functions in this class are not imported into the top-level networkx namespace. You can access these functions by importing the ```networkx.algorithms.community``` module, then accessing the functions as attributes of community. For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from networkx.algorithms import community\n",
    "\n",
    "G = nx.barbell_graph(5, 1)\n",
    "nx.draw(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[0, 1, 2, 3, 4], [5], [6, 7, 8, 9, 10]]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "communities_generator = community.girvan_newman(G)\n",
    "\n",
    "top_level_communities = next(communities_generator)\n",
    "next_level_communities = next(communities_generator)\n",
    "\n",
    "sorted(map(sorted, next_level_communities))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### K-Clique Communty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.relaxed_caveman_graph(5,10,0.1)\n",
    "nx.draw(G, node_size = 40,node_color = 'blue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[frozenset({0, 1, 2, 3, 4, 5, 6, 7, 8, 9}), frozenset({10, 11, 12, 13, 14, 15, 16, 17, 18, 19}), frozenset({20, 21, 22, 23, 24, 25, 26, 27, 28, 29}), frozenset({32, 33, 34, 35, 36, 37, 38, 39, 30, 31}), frozenset({40, 41, 42, 43, 44, 45, 46, 47, 48, 49})]\n"
     ]
    }
   ],
   "source": [
    "from networkx.algorithms.community import k_clique_communities\n",
    "c = list(k_clique_communities(G,k=4))\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[frozenset({0, 1, 2, 3, 4, 5, 6, 7, 8, 9}), frozenset({10, 11, 12, 13, 14, 15, 16, 17, 18, 19}), frozenset({20, 21, 22, 23, 24, 25, 26, 27, 28, 29}), frozenset({32, 33, 34, 35, 36, 37, 38, 39, 30, 31}), frozenset({40, 41, 42, 43, 44, 45, 46, 47, 48, 49})]\n"
     ]
    }
   ],
   "source": [
    "from networkx.algorithms.community import greedy_modularity_communities\n",
    "c = list(greedy_modularity_communities(G))\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, {10, 11, 12, 13, 14, 15, 16, 17, 18, 19}, {20, 21, 22, 23, 24, 25, 26, 27, 28, 29}, {32, 33, 34, 35, 36, 37, 38, 39, 30, 31}, {40, 41, 42, 43, 44, 45, 46, 47, 48, 49}]\n"
     ]
    }
   ],
   "source": [
    "from networkx.algorithms.community import asyn_lpa_communities\n",
    "c = list(asyn_lpa_communities(G))\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{10, 11, 12, 13, 14, 15, 16, 17, 18, 19}, {32, 33, 34, 35, 36, 37, 38, 39, 30, 31}, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, {40, 41, 42, 43, 44, 45, 46, 47, 48, 49}, {20, 21, 22, 23, 24, 25, 26, 27, 28, 29}]\n"
     ]
    }
   ],
   "source": [
    "from networkx.algorithms.community import label_propagation_communities\n",
    "c = list(label_propagation_communities(G))\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[{16, 17, 19, 11}, {10, 12, 13, 14, 15, 18}, {32, 33, 34, 35, 36, 37, 38, 39, 30, 31}, {0, 1, 2, 3, 4, 5, 6, 7, 40, 9, 8, 43, 44, 45, 46, 47, 48, 49, 41, 42}, {20, 21, 22, 23, 24, 25, 26, 27, 28, 29}]\n"
     ]
    }
   ],
   "source": [
    "from networkx.algorithms.community import asyn_fluidc\n",
    "c = list(asyn_fluidc(G,k=5))\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3 Traversal\n",
    "\n",
    "#### 3.1 Depth First Search\n",
    "\n",
    "Basic algorithms for depth-first searching the nodes of a graph.\n",
    "\n",
    "- ```dfs_edges(G[, source, depth_limit])``` \tIterate over edges in a depth-first-search (DFS).\n",
    "- ```dfs_tree(G[, source, depth_limit])``` \tReturns oriented tree constructed from a depth-first-search from source.\n",
    "- ```dfs_predecessors(G[, source, depth_limit])``` \tReturns dictionary of predecessors in depth-first-search from source.\n",
    "- ```dfs_successors(G[, source, depth_limit])``` \tReturns dictionary of successors in depth-first-search from source.\n",
    "- ```dfs_preorder_nodes(G[, source, depth_limit])``` \tGenerate nodes in a depth-first-search pre-ordering starting at source.\n",
    "- ```dfs_postorder_nodes(G[, source, depth_limit])``` \tGenerate nodes in a depth-first-search post-ordering starting at source.\n",
    "- ```dfs_labeled_edges(G[, source, depth_limit])``` \tIterate over edges in a depth-first-search (DFS) labeled by type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.random_tree(20) \n",
    "nx.draw(G, node_size = 200,node_color = 'lightblue',with_labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 14), (14, 19), (19, 1), (1, 10), (10, 12)]\n"
     ]
    }
   ],
   "source": [
    "L = list(nx.dfs_edges(G, source=0, depth_limit=5))\n",
    "print(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "TG = nx.dfs_tree(G)\n",
    "nx.draw(G, node_size = 200,node_color = 'lightblue',with_labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 19,\n",
       " 2: 12,\n",
       " 3: 11,\n",
       " 4: 18,\n",
       " 5: 13,\n",
       " 6: 8,\n",
       " 7: 5,\n",
       " 8: 4,\n",
       " 9: 12,\n",
       " 10: 1,\n",
       " 11: 2,\n",
       " 12: 10,\n",
       " 13: 16,\n",
       " 14: 0,\n",
       " 15: 5,\n",
       " 16: 18,\n",
       " 17: 3,\n",
       " 18: 11,\n",
       " 19: 14}"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.dfs_predecessors(G, source=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: [14],\n",
       " 1: [10],\n",
       " 2: [11],\n",
       " 3: [17],\n",
       " 4: [8],\n",
       " 5: [7, 15],\n",
       " 8: [6],\n",
       " 10: [12],\n",
       " 11: [3, 18],\n",
       " 12: [9, 2],\n",
       " 13: [5],\n",
       " 14: [19],\n",
       " 16: [13],\n",
       " 18: [4, 16],\n",
       " 19: [1]}"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.dfs_successors(G, source=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 14, 19, 1, 10, 12, 9, 2, 11, 3, 17, 18, 4, 8, 6, 16, 13, 5, 7, 15]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(nx.dfs_preorder_nodes(G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 17, 3, 6, 8, 4, 7, 15, 5, 13, 16, 18, 11, 2, 12, 10, 1, 19, 14, 0]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(nx.dfs_postorder_nodes(G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 0, 'forward'),\n",
       " (0, 14, 'forward'),\n",
       " (14, 0, 'nontree'),\n",
       " (14, 19, 'forward'),\n",
       " (19, 14, 'nontree'),\n",
       " (19, 1, 'forward'),\n",
       " (1, 10, 'forward'),\n",
       " (10, 12, 'forward'),\n",
       " (12, 9, 'forward'),\n",
       " (9, 12, 'nontree'),\n",
       " (12, 9, 'reverse'),\n",
       " (12, 2, 'forward'),\n",
       " (2, 11, 'forward'),\n",
       " (11, 3, 'forward'),\n",
       " (3, 17, 'forward'),\n",
       " (17, 3, 'nontree'),\n",
       " (3, 17, 'reverse'),\n",
       " (3, 11, 'nontree'),\n",
       " (11, 3, 'reverse'),\n",
       " (11, 18, 'forward'),\n",
       " (18, 4, 'forward'),\n",
       " (4, 8, 'forward'),\n",
       " (8, 6, 'forward'),\n",
       " (6, 8, 'nontree'),\n",
       " (8, 6, 'reverse'),\n",
       " (8, 4, 'nontree'),\n",
       " (4, 8, 'reverse'),\n",
       " (4, 18, 'nontree'),\n",
       " (18, 4, 'reverse'),\n",
       " (18, 16, 'forward'),\n",
       " (16, 13, 'forward'),\n",
       " (13, 5, 'forward'),\n",
       " (5, 7, 'forward'),\n",
       " (7, 5, 'nontree'),\n",
       " (5, 7, 'reverse'),\n",
       " (5, 15, 'forward'),\n",
       " (15, 5, 'nontree'),\n",
       " (5, 15, 'reverse'),\n",
       " (5, 13, 'nontree'),\n",
       " (13, 5, 'reverse'),\n",
       " (13, 16, 'nontree'),\n",
       " (16, 13, 'reverse'),\n",
       " (16, 18, 'nontree'),\n",
       " (18, 16, 'reverse'),\n",
       " (18, 11, 'nontree'),\n",
       " (11, 18, 'reverse'),\n",
       " (11, 2, 'nontree'),\n",
       " (2, 11, 'reverse'),\n",
       " (2, 12, 'nontree'),\n",
       " (12, 2, 'reverse'),\n",
       " (12, 10, 'nontree'),\n",
       " (10, 12, 'reverse'),\n",
       " (10, 1, 'nontree'),\n",
       " (1, 10, 'reverse'),\n",
       " (1, 19, 'nontree'),\n",
       " (19, 1, 'reverse'),\n",
       " (14, 19, 'reverse'),\n",
       " (0, 14, 'reverse'),\n",
       " (0, 0, 'reverse')]"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(nx.dfs_labeled_edges(G))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-----------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.2 Breadth-first search\n",
    "\n",
    "Basic algorithms for breadth-first searching the nodes of a graph.\n",
    "\n",
    "- ```bfs_edges(G, source[, reverse, depth_limit])``` \tIterate over edges in a breadth-first-search starting at source.\n",
    "- ```bfs_tree(G, source[, reverse, depth_limit])``` \tReturns an oriented tree constructed from of a breadth-first-search starting at source.\n",
    "- ```bfs_predecessors(G, source[, depth_limit])``` \tReturns an iterator of predecessors in breadth-first-search from source.\n",
    "- ```bfs_successors(G, source[, depth_limit])``` \tReturns an iterator of successors in breadth-first-search from so"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 14), (14, 19), (19, 1), (1, 10), (10, 12), (12, 9), (12, 2), (2, 11), (11, 3), (11, 18), (3, 17), (18, 4), (18, 16), (4, 8), (16, 13), (8, 6), (13, 5), (5, 7), (5, 15)]\n"
     ]
    }
   ],
   "source": [
    "print(list(nx.bfs_edges(G,0)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "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(nx.bfs_tree(G,0), node_color = 'lightblue', node_size = 200, with_labels = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(14, 0), (19, 14), (1, 19), (10, 1), (12, 10), (9, 12), (2, 12), (11, 2), (3, 11), (18, 11), (17, 3), (4, 18), (16, 18), (8, 4), (13, 16), (6, 8), (5, 13), (7, 5), (15, 5)]\n"
     ]
    }
   ],
   "source": [
    "print(list(nx.bfs_predecessors(G,0)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, [14]), (14, [19]), (19, [1]), (1, [10]), (10, [12]), (12, [9, 2]), (2, [11]), (11, [3, 18]), (3, [17]), (18, [4, 16]), (4, [8]), (16, [13]), (8, [6]), (13, [5]), (5, [7, 15])]\n"
     ]
    }
   ],
   "source": [
    "print(list(nx.bfs_successors(G,0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}