Lab/Lecture_08/L08_Graphs_with_NetworkX_no_sols.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# NetworkX: Network Analysis in Python\n",
    "----\n",
    "\n",
    "[NetworkX](https://networkx.github.io/) is a Python package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks.\n",
    "\n",
    "- Data structures for graphs, digraphs, and multigraphs\n",
    "- Many standard graph algorithms\n",
    "- Network structure and analysis measures\n",
    "- Generators for classic graphs, random graphs, and synthetic networks\n",
    "- Nodes can be \"anything\" (e.g., text, images, XML records)\n",
    "- Edges can hold arbitrary data (e.g., weights, time-series)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's install necessary libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: networkx in /Users/rossano/Library/Python/3.9/lib/python/site-packages (2.5.1)\n",
      "Requirement already satisfied: decorator<5,>=4.3 in /Users/rossano/Library/Python/3.9/lib/python/site-packages (from networkx) (4.4.2)\n",
      "\u001b[33mWARNING: You are using pip version 22.0.4; however, version 22.1 is available.\n",
      "You should consider upgrading via the '/usr/local/opt/python@3.9/bin/python3.9 -m pip install --upgrade pip' command.\u001b[0m\u001b[33m\n",
      "\u001b[0mRequirement already satisfied: matplotlib in /Users/rossano/Library/Python/3.9/lib/python/site-packages (3.4.2)\n",
      "Requirement already satisfied: pyparsing>=2.2.1 in /usr/local/lib/python3.9/site-packages (from matplotlib) (2.4.7)\n",
      "Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.9/site-packages (from matplotlib) (2.8.1)\n",
      "Requirement already satisfied: cycler>=0.10 in /Users/rossano/Library/Python/3.9/lib/python/site-packages (from matplotlib) (0.10.0)\n",
      "Requirement already satisfied: pillow>=6.2.0 in /Users/rossano/Library/Python/3.9/lib/python/site-packages (from matplotlib) (8.2.0)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in /Users/rossano/Library/Python/3.9/lib/python/site-packages (from matplotlib) (1.3.1)\n",
      "Requirement already satisfied: numpy>=1.16 in /usr/local/lib/python3.9/site-packages (from matplotlib) (1.20.3)\n",
      "Requirement already satisfied: six in /usr/local/lib/python3.9/site-packages (from cycler>=0.10->matplotlib) (1.16.0)\n",
      "\u001b[33mWARNING: You are using pip version 22.0.4; however, version 22.1 is available.\n",
      "You should consider upgrading via the '/usr/local/opt/python@3.9/bin/python3.9 -m pip install --upgrade pip' command.\u001b[0m\u001b[33m\n",
      "\u001b[0mCollecting pygraphviz\n",
      "  Downloading pygraphviz-1.9.zip (119 kB)\n",
      "\u001b[2K     \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m119.9/119.9 KB\u001b[0m \u001b[31m1.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m[31m2.3 MB/s\u001b[0m eta \u001b[36m0:00:01\u001b[0m\n",
      "\u001b[?25h  Preparing metadata (setup.py) ... \u001b[?25ldone\n",
      "\u001b[?25hBuilding wheels for collected packages: pygraphviz\n",
      "  Building wheel for pygraphviz (setup.py) ... \u001b[?25ldone\n",
      "\u001b[?25h  Created wheel for pygraphviz: filename=pygraphviz-1.9-cp39-cp39-macosx_11_0_x86_64.whl size=101741 sha256=7b87ae129d2c86c555490f7cdc9b076c84bd7e8c9866cd9195bb64a7dcf38608\n",
      "  Stored in directory: /Users/rossano/Library/Caches/pip/wheels/db/4e/e9/f6d7ead7327fc2dc4e01c57322770a24a36e0f3a10234aa6df\n",
      "Successfully built pygraphviz\n",
      "Installing collected packages: pygraphviz\n",
      "Successfully installed pygraphviz-1.9\n",
      "\u001b[33mWARNING: You are using pip version 22.0.4; however, version 22.1 is available.\n",
      "You should consider upgrading via the '/usr/local/opt/python@3.9/bin/python3.9 -m pip install --upgrade pip' command.\u001b[0m\u001b[33m\n",
      "\u001b[0m"
     ]
    }
   ],
   "source": [
    "!python3 -m pip install --user networkx\n",
    "#for graph plottinh\n",
    "!python3 -m pip install --user  matplotlib\n",
    "\n",
    "# need graphviz on your machine\n",
    "#!sudo apt-get install graphviz libgraphviz-dev graphviz-dev pkg-config\n",
    "#!brew install graphviz . You may need to do python3 -m pip install --install-option=\"--include-path=/usr/local/include/\" --install-option=\"--library-path=/usr/local/lib/\" pygraphviz\n",
    "\n",
    "!python3 -m pip install --user pygraphviz \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5.1\n"
     ]
    }
   ],
   "source": [
    "import networkx as nx\n",
    "print(nx.__version__)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Some functions to plot graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from networkx.drawing.nx_agraph import graphviz_layout\n",
    "\n",
    "def plot_graph(G):\n",
    "    nx.draw(G, with_labels = True)  \n",
    "    plt.show()\n",
    "    \n",
    "def plot_graph_with_weights(G):\n",
    "    pos = nx.planar_layout(G) # pos = nx.nx_agraph.graphviz_layout(G)\n",
    "    nx.draw_networkx(G,pos)\n",
    "    labels = nx.get_edge_attributes(G,'weight')\n",
    "    nx.draw_networkx_edge_labels(G, pos, edge_labels=labels)\n",
    "    plt.show()\n",
    "\n",
    "def plot_tree(tree):\n",
    "    pos = graphviz_layout(tree, prog='dot')\n",
    "    nx.draw(tree, pos, with_labels=True)\n",
    "    plt.show()\n",
    "    \n",
    "def plot_graph_and_highlight_dijistra(G, path):\n",
    "    pos = graphviz_layout(G)\n",
    "    nx.draw(G, pos, with_labels = True)\n",
    "\n",
    "    nx.draw_networkx_nodes(G, pos, nodelist=path,node_color='r', with_labels=True)\n",
    "    path_edges = list(zip(path, path[1:]))\n",
    "    nx.draw_networkx_edges(G, pos, edgelist=path_edges, edge_color='r', width=4)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## Create a Graph\n",
    "\n",
    "A graph is a __collection of nodes and edges__, *i.e.*, G = (V, E). Let us create an empty graph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by creating an empty graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.Graph()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's __populate__ the graph. We can add one node at time using *G.add_node()* or add any iterable collections (lists, strings etc..) with *G.add_nodes_from*. \n",
    "\n",
    "We are now using strings as nodes's names, but nodes can be any hashable object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "G.add_node('a')\n",
    "my_list = ['b', 'c', 'd']\n",
    "G.add_nodes_from(my_list)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can __inspect the nodes__ in a graph using *G.nodes()*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NodeView(('a', 'b', 'c', 'd'))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.nodes()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_graph(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let us __add edges__ to the graph. \n",
    "\n",
    "We can add one edge at time with *G.add_edge()*, specifying the nodes between whom we want the edge to stay. As for nodes, we can pass an iterable colletion to *G.add_edges_from()*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EdgeView([('a', 'b'), ('a', 'c'), ('b', 'd'), ('c', 'd')])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.add_edges_from([('a', 'b'), ('a', 'c'), ('c', 'd'), ('b', 'd')])\n",
    "G.edges()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we add edges between nodes that does not exist, __nodes are automatically added__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "G.add_edge(\"a\", \"e\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_graph(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Remove__ nodes and/or edges using the *G.remove_node()* or the *G.remove_nodes_from()*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "ename": "NetworkXError",
     "evalue": "The node e is not in the graph.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[0;32m~/Library/Python/3.9/lib/python/site-packages/networkx/classes/graph.py\u001b[0m in \u001b[0;36mremove_node\u001b[0;34m(self, n)\u001b[0m\n\u001b[1;32m    612\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 613\u001b[0;31m             \u001b[0mnbrs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0madj\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# list handles self-loops (allows mutation)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    614\u001b[0m             \u001b[0;32mdel\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_node\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyError\u001b[0m: 'e'",
      "\nThe above exception was the direct cause of the following exception:\n",
      "\u001b[0;31mNetworkXError\u001b[0m                             Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/qf/q75c3cv57x16cs02gmcb55mh0000gn/T/ipykernel_64387/7760498.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mG\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mremove_node\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'e'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mplot_graph\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mG\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Library/Python/3.9/lib/python/site-packages/networkx/classes/graph.py\u001b[0m in \u001b[0;36mremove_node\u001b[0;34m(self, n)\u001b[0m\n\u001b[1;32m    614\u001b[0m             \u001b[0;32mdel\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_node\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    615\u001b[0m         \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# NetworkXError if n not in self\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 616\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mNetworkXError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34mf\"The node {n} is not in the graph.\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    617\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mu\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mnbrs\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    618\u001b[0m             \u001b[0;32mdel\u001b[0m \u001b[0madj\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mu\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m]\u001b[0m  \u001b[0;31m# remove all edges n-u in graph\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNetworkXError\u001b[0m: The node e is not in the graph."
     ]
    }
   ],
   "source": [
    "G.remove_node('e')\n",
    "plot_graph(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Graph properties\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NewtorkX provides direct access to several __graph properties__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Nodes:  4\n",
      "Number of Edges:  4\n"
     ]
    }
   ],
   "source": [
    "# Number of nodes\n",
    "print(\"Number of Nodes: \", G.order()) # equivalent to len(G) and G.number_of_nodes()\n",
    "# Number of edges\n",
    "print(\"Number of Edges: \", G.number_of_edges())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nodes can be listed with G.nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "NodeView(('a', 'b', 'c', 'd'))"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.nodes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can assign nodes some attributes, e.g., a color."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "for node in G.nodes:\n",
    "    G.nodes[node]['color'] = 'white'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('a', {'color': 'white'}),\n",
       " ('b', {'color': 'white'}),\n",
       " ('c', {'color': 'white'}),\n",
       " ('d', {'color': 'white'})]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(G.nodes.data())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'white'"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.nodes['a']['color']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can explore the **neighbours** and the **degree** of the nodes in a graph using the facilities *G.adj* and *G.degree*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'a': {'b': {}, 'c': {}}, 'b': {'a': {}, 'd': {}}, 'c': {'a': {}, 'd': {}}, 'd': {'c': {}, 'b': {}}}\n",
      "{'b': {}, 'c': {}}\n"
     ]
    }
   ],
   "source": [
    "print(G.adj)\n",
    "print(G.adj['a'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Graph are __subscriptable__ objects and we can access neighbours directly with the [ ] operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'b': {}, 'c': {}}\n",
      "{'b': {}, 'c': {}}\n"
     ]
    }
   ],
   "source": [
    "print(G.adj['a'])\n",
    "print(G['a'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We may want to add some edges properties."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "G['a']['c']['color'] = 'green'\n",
    "G['a']['b']['color'] = 'black'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use *G.adj* as a dictionary and __iterate__ over it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a {'b': {'color': 'black'}, 'c': {'color': 'green'}}\n",
      "b {'a': {'color': 'black'}, 'd': {}}\n",
      "c {'a': {'color': 'green'}, 'd': {}}\n",
      "d {'c': {}, 'b': {}}\n"
     ]
    }
   ],
   "source": [
    "for node, datadict in G.adj.items():\n",
    "    # datadict is a dictionary whose keys are node neighbours and whose value, in turn, is a dictionary \n",
    "    # reporting 'property:value' of the edge between node and key\n",
    "    \n",
    "    print(node, datadict) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The degree property reports the number of edges for each node."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[('a', 2), ('b', 2), ('c', 2), ('d', 2)]\n"
     ]
    }
   ],
   "source": [
    "print(G.degree)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "EdgeDataView([('a', 'b', {'color': 'black'}), ('a', 'c', {'color': 'green'}), ('b', 'd', {}), ('c', 'd', {}), (1, 2, {'weight': 1.0})])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G.add_edge(1,2, weight = 1.0)\n",
    "G.edges().data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Directed Graphs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Networkx supports directed graphs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "DG = nx.DiGraph()\n",
    "#we add nodes and edges as a list oftriplets (or_node, dest_node, weight)\n",
    "DG.add_weighted_edges_from([(1, 2, 0.5), (3, 1, 0.75), (3, 2, 0.4)]) \n",
    "plot_graph_with_weights(DG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Successor of node 1: Node 2\n",
      "Predecssor of node 1 : Node 3\n"
     ]
    }
   ],
   "source": [
    "print(\"Successor of node 1: Node\", list(DG.successors(1))[0]) #Equivalent to DG.neighbors for directed graphs\n",
    "print(\"Predecssor of node 1 : Node\", list(DG.predecessors(1))[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can __convert__ directed graphs to undirected one and viceversa.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = nx.to_undirected(DG)\n",
    "DG = nx.to_directed(G)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Graph Operations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Networkx supports most common graph operations. Some examples are \n",
    "<ul>\n",
    "<li>Union</li>\n",
    "<li>Intersection</li>\n",
    "<li>Complement</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a first graph G\n",
    "G = nx.Graph()\n",
    "G.add_edges_from([(\"a\", \"b\"), (\"b\", \"c\"), (\"c\", \"d\")])\n",
    "\n",
    "# Create a second graph H\n",
    "H = nx.Graph()\n",
    "H.add_edges_from([(\"e\", \"f\"), (\"f\", \"g\"), (\"g\", \"h\") ])\n",
    "\n",
    "# Perform the union operation\n",
    "I = nx.union(G, H)\n",
    "plot_graph(I)"
   ]
  },
  {
   "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": [
    "# Now link the two connected components\n",
    "I.add_edges_from([(\"a\",\"e\"), (\"b\", \"g\")])\n",
    "plot_graph(I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create a third graph\n",
    "L = nx.Graph()\n",
    "\n",
    "# To perform intersection between two graphs, they must have the same nodes\n",
    "# First we copy all the nodes in I into L\n",
    "L.add_nodes_from(I.nodes())\n",
    "\n",
    "# Then we add some edge in L\n",
    "L.add_edges_from([(\"e\", \"f\"), (\"f\", \"g\")])\n",
    "\n",
    "M = nx.intersection(I, L)\n",
    "\n",
    "# Only the shared edges between I, L wil survive this operation\n",
    "plot_graph(M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Graph Search\n",
    "\n",
    "Several algorithm are already implemented in NetworkX, take a look [here](https://networkx.github.io/documentation/stable/reference/algorithms/index.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Breadth First Search (BFS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With Networkx it is easy to perform  graph search. Let us start with __BFS__. \n",
    "\n",
    "We will use a __Petersen__ graph as an example, a graph with 10 nodes and 15 edges."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of nodes 10\n",
      "Number of edges 15\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "petersen = nx.petersen_graph()\n",
    "print(\"Number of nodes\", petersen.order())\n",
    "print(\"Number of edges\", petersen.number_of_edges())\n",
    "plot_graph(petersen)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Networkx offers several __methods__ to perform BFS. Observe that in the method definition, the arguments in square brackets [ ]  are optional.\n",
    "\n",
    "- bfs_edges(G, source, [reverse, depth_limit]):  returns an iterator over edges in a breadth-first-search starting at source, until depth_limit\n",
    "- bfs_tree(G, source, [reverse, depth_limit]): returns an oriented tree constructed from of a breadth-first-search starting at source\n",
    "- bfs_predecessors(G, source, [depth_limit]): returns an iterator of predecessors in breadth-first-search from source\n",
    "- bfs_successors(G, source, [depth_limit]): returns an iterator of successors in breadth-first-search from source         "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result of BFS on edges: [(0, 1), (0, 4), (0, 5), (1, 2), (1, 6), (4, 3), (4, 9), (5, 7), (5, 8)]\n"
     ]
    }
   ],
   "source": [
    "# We use 0 as source node. \n",
    "edges_bfs = list(nx.bfs_edges(petersen, 0))\n",
    "print(\"Result of BFS on edges:\", edges_bfs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Another helpful way to understand is the tree that comes out from its execution. This can be done by using bfs_tree\n",
    "tree_bfs = nx.bfs_tree(petersen, 0)\n",
    "\n",
    "# Now we plot the resulting tree\n",
    "plot_tree(tree_bfs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "### Depth First Search (DFS)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As for BFS,  Networkx offers several __methods__ to perform DFS. Observe that,as previously explained, in the method definition, the arguments in square brackets [ ]  are optional.\n",
    "<ul>\n",
    "  <li> dfs_edges(G, source, [reverse, depth_limit]):  returns an iterator over edges in a depth-first-search starting at source, until max_depth </li>\n",
    "<li>dfs_tree(G, source, [reverse, depth_limit]): returns an oriented tree constructed from of a depth-first-search starting at source(</li>\n",
    "<li>dfs_predecessors(G, source, [depth_limit]): returns an iterator of predecessors in depth-first-search from source</li>\n",
    "    <li>dfs_successors(G, source, [depth_limit]): returns an iterator of successors in depth-first-search from source </li>    \n",
    "    \n",
    "</ul>\n",
    "Let us now observe the difference between BFS and DFS\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Result of dfs on edges: [(0, 1), (1, 2), (2, 3), (3, 4), (4, 9), (9, 6), (6, 8), (8, 5), (5, 7)]\n"
     ]
    }
   ],
   "source": [
    "# We use 0 as source node. \n",
    "edges_dfs = list(nx.dfs_edges(petersen, 0))\n",
    "print(\"Result of dfs on edges:\",edges_dfs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "tree_dfs = nx.dfs_tree(petersen, 0)\n",
    "\n",
    "# Now we plot the resulting tree\n",
    "plot_tree(tree_dfs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "### Shortest path with Dijkstra algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now move to the Dijkstra algorithm to find the shortest path between two points.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import random, choice\n",
    "from networkx.utils import pairwise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0, 3]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.Graph()\n",
    "\n",
    "n_nodes = 15\n",
    "\n",
    "# Generate nodes from 0 to n_nodes-1\n",
    "nodes = np.arange(n_nodes)\n",
    "G.add_nodes_from(nodes)\n",
    "\n",
    "# Build a path from nodes[0] to nodes[-1] to be sure it exists\n",
    "for p1, p2 in pairwise(nodes):\n",
    "    G.add_edge(p1, p2, weight=np.linalg.norm(p1-p2))\n",
    "\n",
    "    \n",
    "# Add other random edges\n",
    "new_edges = 25\n",
    "for _ in range(new_edges):\n",
    "    p1, p2 = choice(nodes), choice(nodes)\n",
    "    if p1 != nodes[0] and p2!= nodes[-1]:#avoid direct link\n",
    "        G.add_edge(p1, p2, weight=np.linalg.norm(p1-p2))\n",
    "    \n",
    "    \n",
    "plot_graph(G)\n",
    "\n",
    "\n",
    "# Compute Dijistra path\n",
    "path =  nx.dijkstra_path(G, nodes[0], nodes[3])\n",
    "print(path)\n",
    "plot_graph_and_highlight_dijistra(G, path)"
   ]
  },
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    "---\n",
    "### Exercise: Strongly Connected Components\n",
    "The goal of this exercise is to implement the following algorithm to compute the strongly connected components of a directed graph $G$. [See here](https://www.hackerearth.com/practice/algorithms/graphs/strongly-connected-components/tutorial/). \n",
    "\n",
    "In a directed graph a component is strongly connected if there is a directed path from any vertex to every other vertex of the component. The problem asks to is to partition the graph into maximal strongly connected components.\n",
    "\n",
    "NetworkX provides a method to compute the strongly connected components of a graph [here](https://networkx.github.io/documentation/stable/reference/algorithms/generated/networkx.algorithms.components.strongly_connected_components.html#networkx.algorithms.components.strongly_connected_components). \n",
    "\n",
    "Your goal is to implement the Kosaraju's Linear time algorithm to find Strongly Connected Component. \n",
    "The algorithm is described [here](https://www.hackerearth.com/practice/algorithms/graphs/strongly-connected-components/tutorial).\n",
    "\n",
    "It works in three steps. \n",
    "\n",
    "- Do a DFS on the original graph, keeping track of the DFS finish times of each node. This can be done with a stack, when some  finishes put the source vertex on the stack. This way node with highest finishing time will be on top of the stack.\n",
    "- Reverse the original graph, i.e., if there is an edge $(u,v)$ in the original graph, add the edge $(v,u)$ in the reversed one.\n",
    "-  Do DFS on the reversed graph, with the source vertex as the vertex on top of the stack. When DFS finishes, all nodes visited will form one Strongly Connected Component. If any more nodes remain unvisited, this means there are more Strongly Connected Component's, so pop vertices from top of the stack until a valid unvisited node is found. This will have the highest finishing time of all currently unvisited nodes.\n",
    "\n",
    "Take a look at [DFS traversal documentation](https://networkx.github.io/documentation/stable/reference/algorithms/traversal.html#module-networkx.algorithms.traversal.depth_first_search).\n",
    "Note that the finishing time of a node can be inferred from its position in the DFS tree. \n",
    "\n",
    "\n",
    "\n",
    "![alt text](scc.webp \"Example\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Your implementation goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Test your implementation here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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