AA3-TreeandGraph.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tree and Graph Algorithms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tree  and graph Search"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Breadth First Search simplified"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "graph = {'A': set(['B', 'C']),\n",
    "         'B': set(['A', 'D', 'E']),\n",
    "         'C': set(['A', 'F']),\n",
    "         'D': set(['B']),\n",
    "         'E': set(['B', 'F']),\n",
    "         'F': set(['C', 'E'])}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A': {'B', 'C'},\n",
       " 'B': {'A', 'D', 'E'},\n",
       " 'C': {'A', 'F'},\n",
       " 'D': {'B'},\n",
       " 'E': {'B', 'F'},\n",
       " 'F': {'C', 'E'}}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![alt](http://eddmann.com/uploads/depth-first-search-and-breadth-first-search-in-python/graph.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bfs(graph, start):\n",
    "    visited, queue = set(), [start]\n",
    "    while queue:\n",
    "        vertex = queue.pop(0)\n",
    "        if vertex not in visited:\n",
    "            visited.add(vertex)\n",
    "            queue.extend(graph[vertex] - visited)\n",
    "    return visited"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A', 'B', 'C', 'D', 'E', 'F'}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bfs(graph, 'A')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Depth First Search simplified"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dfs(graph, start):\n",
    "    visited, stack = set(), [start]\n",
    "    while stack:\n",
    "        vertex = stack.pop()\n",
    "        if vertex not in visited:\n",
    "            visited.add(vertex)\n",
    "            stack.extend(graph[vertex] - visited)\n",
    "    return visited\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A', 'B', 'C', 'D', 'E', 'F'}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfs(graph, 'A')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A', 'B', 'C', 'D', 'E', 'F'}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfs(graph, 'C')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Minimal Spanning Tree (Prism's Method)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys \n",
    "\n",
    "class Graph(): \n",
    "\n",
    "    def __init__(self, vertices): \n",
    "            self.V = vertices \n",
    "            self.graph = [[0 for column in range(vertices)] \n",
    "                         for row in range(vertices)] \n",
    "            \n",
    "            \n",
    "    def printMST(self, parent): \n",
    "        print (\"Edge \\tWeight\")\n",
    "        for i in range(1, self.V): \n",
    "            print(parent[i],\"-\",i,\"\\t\",self.graph[i][parent[i]]) \n",
    "            \n",
    "            \n",
    "    def minKey(self, key, mstSet):  \n",
    "            min = sys.maxsize \n",
    "            for v in range(self.V): \n",
    "                if key[v] < min and mstSet[v] == False: \n",
    "                    min = key[v] \n",
    "                    min_index = v \n",
    "            return min_index \n",
    "\n",
    "        \n",
    "    def primMST(self): \n",
    "        key = [sys.maxsize] * self.V \n",
    "        parent = [None] * self.V \n",
    "        key[0] = 0\n",
    "        mstSet = [False] * self.V \n",
    "        parent[0] = -1 \n",
    "        for cout in range(self.V): \n",
    "            u = self.minKey(key, mstSet) \n",
    "            mstSet[u] = True\n",
    "            for v in range(self.V): \n",
    "                if self.graph[u][v] > 0 and \\\n",
    "                    mstSet[v] == False and \\\n",
    "                    key[v] > self.graph[u][v]: \n",
    "                        key[v] = self.graph[u][v] \n",
    "                        parent[v] = u \n",
    "        self.printMST(parent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = Graph(5) \n",
    "g.graph = [ [0, 2, 0, 6, 0], \n",
    "        [2, 0, 3, 8, 5], \n",
    "        [0, 3, 0, 0, 7], \n",
    "        [6, 8, 0, 0, 9], \n",
    "        [0, 5, 7, 9, 0]] "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Edge \tWeight\n",
      "0 - 1 \t 2\n",
      "1 - 2 \t 3\n",
      "0 - 3 \t 6\n",
      "1 - 4 \t 5\n"
     ]
    }
   ],
   "source": [
    "g.primMST(); "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### NetworkX implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "import matplotlib.cbook\n",
    "warnings.filterwarnings(\"ignore\",category=matplotlib.cbook.mplDeprecation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Traversal\n",
    "\n",
    "##### 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": 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": [
    "G = nx.balanced_tree(3,3)\n",
    "nx.draw(G, node_size = 500, node_color = \"lightgreen\", with_labels = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 1), (1, 4), (4, 13), (4, 14), (4, 15), (1, 5), (5, 16), (5, 17), (5, 18), (1, 6), (6, 19), (6, 20), (6, 21), (0, 2), (2, 7), (7, 22), (7, 23), (7, 24), (2, 8), (8, 25), (8, 26), (8, 27), (2, 9), (9, 28), (9, 29), (9, 30), (0, 3), (3, 10), (10, 31), (10, 32), (10, 33), (3, 11), (11, 34), (11, 35), (11, 36), (3, 12), (12, 37), (12, 38), (12, 39)]\n"
     ]
    }
   ],
   "source": [
    "L = list(nx.dfs_edges(G, source=0, depth_limit=5))\n",
    "print(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 0,\n",
       " 4: 1,\n",
       " 13: 4,\n",
       " 14: 4,\n",
       " 15: 4,\n",
       " 5: 1,\n",
       " 16: 5,\n",
       " 17: 5,\n",
       " 18: 5,\n",
       " 6: 1,\n",
       " 19: 6,\n",
       " 20: 6,\n",
       " 21: 6,\n",
       " 2: 0,\n",
       " 7: 2,\n",
       " 22: 7,\n",
       " 23: 7,\n",
       " 24: 7,\n",
       " 8: 2,\n",
       " 25: 8,\n",
       " 26: 8,\n",
       " 27: 8,\n",
       " 9: 2,\n",
       " 28: 9,\n",
       " 29: 9,\n",
       " 30: 9,\n",
       " 3: 0,\n",
       " 10: 3,\n",
       " 31: 10,\n",
       " 32: 10,\n",
       " 33: 10,\n",
       " 11: 3,\n",
       " 34: 11,\n",
       " 35: 11,\n",
       " 36: 11,\n",
       " 12: 3,\n",
       " 37: 12,\n",
       " 38: 12,\n",
       " 39: 12}"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.dfs_predecessors(G, source=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: [1, 2, 3],\n",
       " 1: [4, 5, 6],\n",
       " 4: [13, 14, 15],\n",
       " 5: [16, 17, 18],\n",
       " 6: [19, 20, 21],\n",
       " 2: [7, 8, 9],\n",
       " 7: [22, 23, 24],\n",
       " 8: [25, 26, 27],\n",
       " 9: [28, 29, 30],\n",
       " 3: [10, 11, 12],\n",
       " 10: [31, 32, 33],\n",
       " 11: [34, 35, 36],\n",
       " 12: [37, 38, 39]}"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nx.dfs_successors(G, source=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0,\n",
       " 1,\n",
       " 4,\n",
       " 13,\n",
       " 14,\n",
       " 15,\n",
       " 5,\n",
       " 16,\n",
       " 17,\n",
       " 18,\n",
       " 6,\n",
       " 19,\n",
       " 20,\n",
       " 21,\n",
       " 2,\n",
       " 7,\n",
       " 22,\n",
       " 23,\n",
       " 24,\n",
       " 8,\n",
       " 25,\n",
       " 26,\n",
       " 27,\n",
       " 9,\n",
       " 28,\n",
       " 29,\n",
       " 30,\n",
       " 3,\n",
       " 10,\n",
       " 31,\n",
       " 32,\n",
       " 33,\n",
       " 11,\n",
       " 34,\n",
       " 35,\n",
       " 36,\n",
       " 12,\n",
       " 37,\n",
       " 38,\n",
       " 39]"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(nx.dfs_preorder_nodes(G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[13,\n",
       " 14,\n",
       " 15,\n",
       " 4,\n",
       " 16,\n",
       " 17,\n",
       " 18,\n",
       " 5,\n",
       " 19,\n",
       " 20,\n",
       " 21,\n",
       " 6,\n",
       " 1,\n",
       " 22,\n",
       " 23,\n",
       " 24,\n",
       " 7,\n",
       " 25,\n",
       " 26,\n",
       " 27,\n",
       " 8,\n",
       " 28,\n",
       " 29,\n",
       " 30,\n",
       " 9,\n",
       " 2,\n",
       " 31,\n",
       " 32,\n",
       " 33,\n",
       " 10,\n",
       " 34,\n",
       " 35,\n",
       " 36,\n",
       " 11,\n",
       " 37,\n",
       " 38,\n",
       " 39,\n",
       " 12,\n",
       " 3,\n",
       " 0]"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(nx.dfs_postorder_nodes(G))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0, 0, 'forward'),\n",
       " (0, 1, 'forward'),\n",
       " (1, 0, 'nontree'),\n",
       " (1, 4, 'forward'),\n",
       " (4, 1, 'nontree'),\n",
       " (4, 13, 'forward'),\n",
       " (13, 4, 'nontree'),\n",
       " (4, 13, 'reverse'),\n",
       " (4, 14, 'forward'),\n",
       " (14, 4, 'nontree'),\n",
       " (4, 14, 'reverse'),\n",
       " (4, 15, 'forward'),\n",
       " (15, 4, 'nontree'),\n",
       " (4, 15, 'reverse'),\n",
       " (1, 4, 'reverse'),\n",
       " (1, 5, 'forward'),\n",
       " (5, 1, 'nontree'),\n",
       " (5, 16, 'forward'),\n",
       " (16, 5, 'nontree'),\n",
       " (5, 16, 'reverse'),\n",
       " (5, 17, 'forward'),\n",
       " (17, 5, 'nontree'),\n",
       " (5, 17, 'reverse'),\n",
       " (5, 18, 'forward'),\n",
       " (18, 5, 'nontree'),\n",
       " (5, 18, 'reverse'),\n",
       " (1, 5, 'reverse'),\n",
       " (1, 6, 'forward'),\n",
       " (6, 1, 'nontree'),\n",
       " (6, 19, 'forward'),\n",
       " (19, 6, 'nontree'),\n",
       " (6, 19, 'reverse'),\n",
       " (6, 20, 'forward'),\n",
       " (20, 6, 'nontree'),\n",
       " (6, 20, 'reverse'),\n",
       " (6, 21, 'forward'),\n",
       " (21, 6, 'nontree'),\n",
       " (6, 21, 'reverse'),\n",
       " (1, 6, 'reverse'),\n",
       " (0, 1, 'reverse'),\n",
       " (0, 2, 'forward'),\n",
       " (2, 0, 'nontree'),\n",
       " (2, 7, 'forward'),\n",
       " (7, 2, 'nontree'),\n",
       " (7, 22, 'forward'),\n",
       " (22, 7, 'nontree'),\n",
       " (7, 22, 'reverse'),\n",
       " (7, 23, 'forward'),\n",
       " (23, 7, 'nontree'),\n",
       " (7, 23, 'reverse'),\n",
       " (7, 24, 'forward'),\n",
       " (24, 7, 'nontree'),\n",
       " (7, 24, 'reverse'),\n",
       " (2, 7, 'reverse'),\n",
       " (2, 8, 'forward'),\n",
       " (8, 2, 'nontree'),\n",
       " (8, 25, 'forward'),\n",
       " (25, 8, 'nontree'),\n",
       " (8, 25, 'reverse'),\n",
       " (8, 26, 'forward'),\n",
       " (26, 8, 'nontree'),\n",
       " (8, 26, 'reverse'),\n",
       " (8, 27, 'forward'),\n",
       " (27, 8, 'nontree'),\n",
       " (8, 27, 'reverse'),\n",
       " (2, 8, 'reverse'),\n",
       " (2, 9, 'forward'),\n",
       " (9, 2, 'nontree'),\n",
       " (9, 28, 'forward'),\n",
       " (28, 9, 'nontree'),\n",
       " (9, 28, 'reverse'),\n",
       " (9, 29, 'forward'),\n",
       " (29, 9, 'nontree'),\n",
       " (9, 29, 'reverse'),\n",
       " (9, 30, 'forward'),\n",
       " (30, 9, 'nontree'),\n",
       " (9, 30, 'reverse'),\n",
       " (2, 9, 'reverse'),\n",
       " (0, 2, 'reverse'),\n",
       " (0, 3, 'forward'),\n",
       " (3, 0, 'nontree'),\n",
       " (3, 10, 'forward'),\n",
       " (10, 3, 'nontree'),\n",
       " (10, 31, 'forward'),\n",
       " (31, 10, 'nontree'),\n",
       " (10, 31, 'reverse'),\n",
       " (10, 32, 'forward'),\n",
       " (32, 10, 'nontree'),\n",
       " (10, 32, 'reverse'),\n",
       " (10, 33, 'forward'),\n",
       " (33, 10, 'nontree'),\n",
       " (10, 33, 'reverse'),\n",
       " (3, 10, 'reverse'),\n",
       " (3, 11, 'forward'),\n",
       " (11, 3, 'nontree'),\n",
       " (11, 34, 'forward'),\n",
       " (34, 11, 'nontree'),\n",
       " (11, 34, 'reverse'),\n",
       " (11, 35, 'forward'),\n",
       " (35, 11, 'nontree'),\n",
       " (11, 35, 'reverse'),\n",
       " (11, 36, 'forward'),\n",
       " (36, 11, 'nontree'),\n",
       " (11, 36, 'reverse'),\n",
       " (3, 11, 'reverse'),\n",
       " (3, 12, 'forward'),\n",
       " (12, 3, 'nontree'),\n",
       " (12, 37, 'forward'),\n",
       " (37, 12, 'nontree'),\n",
       " (12, 37, 'reverse'),\n",
       " (12, 38, 'forward'),\n",
       " (38, 12, 'nontree'),\n",
       " (12, 38, 'reverse'),\n",
       " (12, 39, 'forward'),\n",
       " (39, 12, 'nontree'),\n",
       " (12, 39, 'reverse'),\n",
       " (3, 12, 'reverse'),\n",
       " (0, 3, 'reverse'),\n",
       " (0, 0, 'reverse')]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(nx.dfs_labeled_edges(G))"
   ]
  },
  {
   "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": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, 1), (0, 2), (0, 3), (1, 4), (1, 5), (1, 6), (2, 7), (2, 8), (2, 9), (3, 10), (3, 11), (3, 12), (4, 13), (4, 14), (4, 15), (5, 16), (5, 17), (5, 18), (6, 19), (6, 20), (6, 21), (7, 22), (7, 23), (7, 24), (8, 25), (8, 26), (8, 27), (9, 28), (9, 29), (9, 30), (10, 31), (10, 32), (10, 33), (11, 34), (11, 35), (11, 36), (12, 37), (12, 38), (12, 39)]\n"
     ]
    }
   ],
   "source": [
    "print(list(nx.bfs_edges(G,0)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "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, node_size = 500, node_color = \"lightgreen\", with_labels = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(1, 0), (2, 0), (3, 0), (4, 1), (5, 1), (6, 1), (7, 2), (8, 2), (9, 2), (10, 3), (11, 3), (12, 3), (13, 4), (14, 4), (15, 4), (16, 5), (17, 5), (18, 5), (19, 6), (20, 6), (21, 6), (22, 7), (23, 7), (24, 7), (25, 8), (26, 8), (27, 8), (28, 9), (29, 9), (30, 9), (31, 10), (32, 10), (33, 10), (34, 11), (35, 11), (36, 11), (37, 12), (38, 12), (39, 12)]\n"
     ]
    }
   ],
   "source": [
    "print(list(nx.bfs_predecessors(G,0)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(0, [1, 2, 3]), (1, [4, 5, 6]), (2, [7, 8, 9]), (3, [10, 11, 12]), (4, [13, 14, 15]), (5, [16, 17, 18]), (6, [19, 20, 21]), (7, [22, 23, 24]), (8, [25, 26, 27]), (9, [28, 29, 30]), (10, [31, 32, 33]), (11, [34, 35, 36]), (12, [37, 38, 39])]\n"
     ]
    }
   ],
   "source": [
    "print(list(nx.bfs_successors(G,0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "--------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References:\n",
    "1. Latest Algorithm Collection GitHub:https://github.com/TheAlgorithms/Python\n",
    "2. AI search GitHub book:https://github.com/aimacode\n",
    "3. Algorithm Online Book: https://algs4.cs.princeton.edu/home/\n",
    "4. NetworkX documents: https://networkx.github.io/documentation/latest/index.html\n",
    "5. Network Science Online Book: http://networksciencebook.com/"
   ]
  }
 ],
 "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"
  },
  "widgets": {
   "state": {},
   "version": "1.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}