Graph_Network_practice.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7b8185a5",
   "metadata": {},
   "source": [
    "Amanda Rodgers\n",
    "Graph Network Practice\n",
    "2024-07-17"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "59f7229d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: networkx in /opt/anaconda3/lib/python3.11/site-packages (3.1)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "pip install networkx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "212d313f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create graph\n",
    "import networkx as nx\n",
    "\n",
    "# Create an empty graph\n",
    "G = nx.Graph()\n",
    "\n",
    "# Add nodes\n",
    "G.add_node(1)\n",
    "G.add_nodes_from([2, 3, 4])\n",
    "\n",
    "# Add edges\n",
    "G.add_edge(1, 2)\n",
    "G.add_edges_from([(2, 3), (3, 4), (4, 1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6dfbcd60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Draw the graph\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "nx.draw(G, with_labels=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "946a91ee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shortest path from 1 to 3: [1, 2, 3]\n",
      "Degree centrality: {1: 0.6666666666666666, 2: 0.6666666666666666, 3: 0.6666666666666666, 4: 0.6666666666666666}\n"
     ]
    }
   ],
   "source": [
    "# Graph algorithms\n",
    "\n",
    "# Shortest path\n",
    "path = nx.shortest_path(G, source=1, target=3)\n",
    "print(\"Shortest path from 1 to 3:\", path)\n",
    "\n",
    "# Degree Centrality\n",
    "centrality = nx.degree_centrality(G)\n",
    "print(\"Degree centrality:\", centrality)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8bb9d1d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reading and writing graph\n",
    "# Write graph to a file\n",
    "nx.write_adjlist(G, \"graph.adjlist\")\n",
    "\n",
    "# Read graph from a file\n",
    "G_loaded = nx.read_adjlist(\"graph.adjlist\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}