|
| 1 | +{ |
| 2 | + "cells": [ |
| 3 | + { |
| 4 | + "cell_type": "markdown", |
| 5 | + "id": "ff457e68-2fa9-4848-bc5e-7ceedac64bf6", |
| 6 | + "metadata": {}, |
| 7 | + "source": [ |
| 8 | + "# Undirected Graphs\n", |
| 9 | + "\n", |
| 10 | + "In contrast to directed graphs, undirected graphs are a type of graph where edges have no inherent direction. The edges in an undirected graph represent symmetric relationships between vertices, meaning they connect vertices in both directions.\n", |
| 11 | + "\n", |
| 12 | + "In undirected graphs, the relationships are mutual; if there is an edge between vertex A and vertex B, it implies the existence of an edge from B to A. Undirected graphs are often used to model symmetric relationships like friendships in a social network, communication links in a computer network, or connections between locations in a map.\n", |
| 13 | + "\n", |
| 14 | + "Undirected graphs are simpler in structure compared to directed graphs, and they are widely employed in various fields, including computer science, social network analysis, and transportation planning.\n", |
| 15 | + "\n", |
| 16 | + "These two types of graphs, directed and undirected, serve as fundamental representations for modeling relationships and connections in a wide range of applications.\n" |
| 17 | + ] |
| 18 | + }, |
| 19 | + { |
| 20 | + "cell_type": "code", |
| 21 | + "execution_count": 11, |
| 22 | + "id": "2525d8d3-cf7b-4b34-a38a-bc7ac2d5f683", |
| 23 | + "metadata": {}, |
| 24 | + "outputs": [], |
| 25 | + "source": [ |
| 26 | + "class UndirectedGraph:\n", |
| 27 | + " def __init__(self, no_of_vertices):\n", |
| 28 | + " self.no_of_vertices = no_of_vertices\n", |
| 29 | + " self.adj_matrix = [[0] * no_of_vertices for _ in range(no_of_vertices)]\n", |
| 30 | + "\n", |
| 31 | + " def add_edge(self, vertex1, vertex2, weight=1):\n", |
| 32 | + " self.adj_matrix[vertex1][vertex2] = weight\n", |
| 33 | + " self.adj_matrix[vertex2][vertex1] = weight # For undirected graph\n", |
| 34 | + "\n", |
| 35 | + " def remove_edge(self, vertex1, vertex2):\n", |
| 36 | + " self.adj_matrix[vertex1][vertex2] = 0\n", |
| 37 | + " self.adj_matrix[vertex2][vertex1] = 0\n", |
| 38 | + "\n", |
| 39 | + " def display(self):\n", |
| 40 | + " for row in self.adj_matrix:\n", |
| 41 | + " print(row)\n", |
| 42 | + "\n", |
| 43 | + " def add_vertex(self):\n", |
| 44 | + " self.no_of_vertices += 1\n", |
| 45 | + " # Add a new row for the new vertex\n", |
| 46 | + " self.adj_matrix.append([0] * self.no_of_vertices)\n", |
| 47 | + " # Add a new column for the new vertex in existing rows\n", |
| 48 | + " for row in self.adj_matrix:\n", |
| 49 | + " row.append(0)\n", |
| 50 | + "\n", |
| 51 | + " def remove_vertex(self, vertex):\n", |
| 52 | + " if vertex < self.no_of_vertices:\n", |
| 53 | + " del self.adj_matrix[vertex]\n", |
| 54 | + " self.no_of_vertices -= 1\n", |
| 55 | + "\n", |
| 56 | + " for row in self.adj_matrix:\n", |
| 57 | + " del row[vertex]\n", |
| 58 | + "\n", |
| 59 | + " def get_neighbors(self, vertex):\n", |
| 60 | + " if vertex < self.no_of_vertices:\n", |
| 61 | + " return [index for index, weight in enumerate(self.adj_matrix[vertex]) if weight > 0]\n", |
| 62 | + " else:\n", |
| 63 | + " return []\n", |
| 64 | + "\n", |
| 65 | + " def has_edge(self, vertex1, vertex2):\n", |
| 66 | + " return self.adj_matrix[vertex1][vertex2] > 0 or self.adj_matrix[vertex2][vertex1] > 0\n", |
| 67 | + "\n", |
| 68 | + " def graph_size(self):\n", |
| 69 | + " return self.no_of_vertices, sum(row.count(1) for row in self.adj_matrix)\n", |
| 70 | + "\n", |
| 71 | + " def clear_graph(self):\n", |
| 72 | + " self.no_of_vertices = 0\n", |
| 73 | + " self.adj_matrix = []\n" |
| 74 | + ] |
| 75 | + }, |
| 76 | + { |
| 77 | + "cell_type": "code", |
| 78 | + "execution_count": 12, |
| 79 | + "id": "93c1bc88-0d14-48b5-be60-e35cd9b25d7c", |
| 80 | + "metadata": {}, |
| 81 | + "outputs": [], |
| 82 | + "source": [ |
| 83 | + "graph = UndirectedGraph(5)" |
| 84 | + ] |
| 85 | + }, |
| 86 | + { |
| 87 | + "cell_type": "code", |
| 88 | + "execution_count": 13, |
| 89 | + "id": "ddf3c951-2efa-4a53-b2c8-4753b01342f1", |
| 90 | + "metadata": {}, |
| 91 | + "outputs": [ |
| 92 | + { |
| 93 | + "name": "stdout", |
| 94 | + "output_type": "stream", |
| 95 | + "text": [ |
| 96 | + "Undirected Graph:\n", |
| 97 | + "[0, 2, 1, 0, 0]\n", |
| 98 | + "[2, 0, 0, 3, 0]\n", |
| 99 | + "[1, 0, 0, 2, 0]\n", |
| 100 | + "[0, 3, 2, 0, 1]\n", |
| 101 | + "[0, 0, 0, 1, 0]\n" |
| 102 | + ] |
| 103 | + } |
| 104 | + ], |
| 105 | + "source": [ |
| 106 | + "graph.add_edge(0, 1, 2)\n", |
| 107 | + "graph.add_edge(0, 2, 1)\n", |
| 108 | + "graph.add_edge(1, 3, 3)\n", |
| 109 | + "graph.add_edge(2, 3, 2)\n", |
| 110 | + "graph.add_edge(3, 4, 1)\n", |
| 111 | + "\n", |
| 112 | + "print(\"Undirected Graph:\")\n", |
| 113 | + "graph.display()" |
| 114 | + ] |
| 115 | + }, |
| 116 | + { |
| 117 | + "cell_type": "code", |
| 118 | + "execution_count": 14, |
| 119 | + "id": "1b29be66-e589-47b0-860b-6385eed7c6f0", |
| 120 | + "metadata": {}, |
| 121 | + "outputs": [ |
| 122 | + { |
| 123 | + "name": "stdout", |
| 124 | + "output_type": "stream", |
| 125 | + "text": [ |
| 126 | + "\n", |
| 127 | + "Undirected Graph after removing edge (1, 3):\n", |
| 128 | + "[0, 2, 1, 0, 0]\n", |
| 129 | + "[2, 0, 0, 0, 0]\n", |
| 130 | + "[1, 0, 0, 2, 0]\n", |
| 131 | + "[0, 0, 2, 0, 1]\n", |
| 132 | + "[0, 0, 0, 1, 0]\n" |
| 133 | + ] |
| 134 | + } |
| 135 | + ], |
| 136 | + "source": [ |
| 137 | + "graph.remove_edge(1, 3)\n", |
| 138 | + "\n", |
| 139 | + "print(\"\\nUndirected Graph after removing edge (1, 3):\")\n", |
| 140 | + "graph.display()" |
| 141 | + ] |
| 142 | + }, |
| 143 | + { |
| 144 | + "cell_type": "code", |
| 145 | + "execution_count": 15, |
| 146 | + "id": "c39ec39b-d0fe-431e-9ba1-54d80adc5ed5", |
| 147 | + "metadata": {}, |
| 148 | + "outputs": [ |
| 149 | + { |
| 150 | + "name": "stdout", |
| 151 | + "output_type": "stream", |
| 152 | + "text": [ |
| 153 | + "\n", |
| 154 | + "Undirected Graph after adding a vertex:\n", |
| 155 | + "[0, 2, 1, 0, 0, 0]\n", |
| 156 | + "[2, 0, 0, 0, 0, 0]\n", |
| 157 | + "[1, 0, 0, 2, 0, 0]\n", |
| 158 | + "[0, 0, 2, 0, 1, 0]\n", |
| 159 | + "[0, 0, 0, 1, 0, 0]\n", |
| 160 | + "[0, 0, 0, 0, 0, 0, 0]\n" |
| 161 | + ] |
| 162 | + } |
| 163 | + ], |
| 164 | + "source": [ |
| 165 | + "graph.add_vertex()\n", |
| 166 | + "\n", |
| 167 | + "print(\"\\nUndirected Graph after adding a vertex:\")\n", |
| 168 | + "graph.display()" |
| 169 | + ] |
| 170 | + }, |
| 171 | + { |
| 172 | + "cell_type": "code", |
| 173 | + "execution_count": 16, |
| 174 | + "id": "d8e1a783-d7c0-442b-ba41-2b3736e66184", |
| 175 | + "metadata": {}, |
| 176 | + "outputs": [ |
| 177 | + { |
| 178 | + "name": "stdout", |
| 179 | + "output_type": "stream", |
| 180 | + "text": [ |
| 181 | + "\n", |
| 182 | + "Undirected Graph after removing vertex 1:\n", |
| 183 | + "[0, 1, 0, 0, 0]\n", |
| 184 | + "[1, 0, 2, 0, 0]\n", |
| 185 | + "[0, 2, 0, 1, 0]\n", |
| 186 | + "[0, 0, 1, 0, 0]\n", |
| 187 | + "[0, 0, 0, 0, 0, 0]\n" |
| 188 | + ] |
| 189 | + } |
| 190 | + ], |
| 191 | + "source": [ |
| 192 | + "graph.remove_vertex(1)\n", |
| 193 | + "\n", |
| 194 | + "print(\"\\nUndirected Graph after removing vertex 1:\")\n", |
| 195 | + "graph.display()" |
| 196 | + ] |
| 197 | + }, |
| 198 | + { |
| 199 | + "cell_type": "code", |
| 200 | + "execution_count": 17, |
| 201 | + "id": "cde71770-2e32-4444-96ea-20452decdd90", |
| 202 | + "metadata": {}, |
| 203 | + "outputs": [ |
| 204 | + { |
| 205 | + "name": "stdout", |
| 206 | + "output_type": "stream", |
| 207 | + "text": [ |
| 208 | + "\n", |
| 209 | + "Neighbors of vertex 0: [1]\n" |
| 210 | + ] |
| 211 | + } |
| 212 | + ], |
| 213 | + "source": [ |
| 214 | + "neighbors = graph.get_neighbors(0)\n", |
| 215 | + "print(\"\\nNeighbors of vertex 0:\", neighbors)" |
| 216 | + ] |
| 217 | + }, |
| 218 | + { |
| 219 | + "cell_type": "code", |
| 220 | + "execution_count": 18, |
| 221 | + "id": "6a4b61b7-1881-432d-b63a-9c0a8ca33a56", |
| 222 | + "metadata": {}, |
| 223 | + "outputs": [ |
| 224 | + { |
| 225 | + "name": "stdout", |
| 226 | + "output_type": "stream", |
| 227 | + "text": [ |
| 228 | + "\n", |
| 229 | + "Does edge (0, 2) exist? False\n" |
| 230 | + ] |
| 231 | + } |
| 232 | + ], |
| 233 | + "source": [ |
| 234 | + "has_edge = graph.has_edge(0, 2)\n", |
| 235 | + "print(\"\\nDoes edge (0, 2) exist?\", has_edge)" |
| 236 | + ] |
| 237 | + }, |
| 238 | + { |
| 239 | + "cell_type": "code", |
| 240 | + "execution_count": 19, |
| 241 | + "id": "75cd8bc2-2800-4c49-b7b1-ff28e5bbd82c", |
| 242 | + "metadata": {}, |
| 243 | + "outputs": [ |
| 244 | + { |
| 245 | + "name": "stdout", |
| 246 | + "output_type": "stream", |
| 247 | + "text": [ |
| 248 | + "\n", |
| 249 | + "Graph Size (Vertices, Edges): (5, 4)\n" |
| 250 | + ] |
| 251 | + } |
| 252 | + ], |
| 253 | + "source": [ |
| 254 | + "size = graph.graph_size()\n", |
| 255 | + "print(\"\\nGraph Size (Vertices, Edges):\", size)" |
| 256 | + ] |
| 257 | + }, |
| 258 | + { |
| 259 | + "cell_type": "code", |
| 260 | + "execution_count": 20, |
| 261 | + "id": "bed90a7d-1cbb-469c-8ea0-f5da0b5fee85", |
| 262 | + "metadata": {}, |
| 263 | + "outputs": [ |
| 264 | + { |
| 265 | + "name": "stdout", |
| 266 | + "output_type": "stream", |
| 267 | + "text": [ |
| 268 | + "\n", |
| 269 | + "Undirected Graph after clearing:\n" |
| 270 | + ] |
| 271 | + } |
| 272 | + ], |
| 273 | + "source": [ |
| 274 | + "graph.clear_graph()\n", |
| 275 | + "\n", |
| 276 | + "print(\"\\nUndirected Graph after clearing:\")\n", |
| 277 | + "graph.display()" |
| 278 | + ] |
| 279 | + }, |
| 280 | + { |
| 281 | + "cell_type": "code", |
| 282 | + "execution_count": null, |
| 283 | + "id": "de72da94-99ed-4ab2-9e79-cfb1de482577", |
| 284 | + "metadata": {}, |
| 285 | + "outputs": [], |
| 286 | + "source": [] |
| 287 | + } |
| 288 | + ], |
| 289 | + "metadata": { |
| 290 | + "kernelspec": { |
| 291 | + "display_name": "Python 3 (ipykernel)", |
| 292 | + "language": "python", |
| 293 | + "name": "python3" |
| 294 | + }, |
| 295 | + "language_info": { |
| 296 | + "codemirror_mode": { |
| 297 | + "name": "ipython", |
| 298 | + "version": 3 |
| 299 | + }, |
| 300 | + "file_extension": ".py", |
| 301 | + "mimetype": "text/x-python", |
| 302 | + "name": "python", |
| 303 | + "nbconvert_exporter": "python", |
| 304 | + "pygments_lexer": "ipython3", |
| 305 | + "version": "3.10.6" |
| 306 | + } |
| 307 | + }, |
| 308 | + "nbformat": 4, |
| 309 | + "nbformat_minor": 5 |
| 310 | +} |
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