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Commit 7327cf8

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1 parent 73db1de commit 7327cf8

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2 files changed

+448
-46
lines changed

2 files changed

+448
-46
lines changed
Lines changed: 361 additions & 2 deletions
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{
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"cells": [],
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"metadata": {},
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"cells": [
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{
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"cell_type": "markdown",
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"id": "839ca9fa-309e-4dbf-a062-3f6a66615873",
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"metadata": {},
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"source": [
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"# Directed Graphs\n",
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"\n",
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"Directed graphs, or digraphs, are a type of graph where edges have a direction associated with them. In other words, each edge in a directed graph is an ordered pair of vertices, indicating a one-way relationship between them. This directional nature distinguishes directed graphs from undirected graphs.\n",
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"\n",
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"In a directed graph, vertices (or nodes) are connected by directed edges, which represent the flow or progression from one vertex to another. This directed relationship implies that an edge from vertex A to vertex B does not necessarily imply the existence of an edge from B to A.\n",
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"\n",
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"Directed graphs are used to model various real-world scenarios, such as dependencies between tasks, network flows, web page links, and social relationships with a sense of direction.\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "5d14c672-55f8-4fb1-a5ce-d4222195e5bf",
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "code",
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"execution_count": 70,
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"id": "483639ea-dabd-4753-836b-3f9b7dd35fa6",
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"metadata": {},
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"outputs": [],
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"source": [
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"class DirectedGraph:\n",
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" def __init__(self, no_of_vertices):\n",
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" self.no_of_vertices = no_of_vertices\n",
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" self.adj_matrix = [[0] * no_of_vertices for _ in range(no_of_vertices)]\n",
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"\n",
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" def add_edge(self, start, end, weight=1):\n",
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" self.adj_matrix[start][end] = weight\n",
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"\n",
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" def remove_edge(self, start, end):\n",
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" self.adj_matrix[start][end] = 0\n",
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"\n",
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" def display(self):\n",
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" for row in self.adj_matrix:\n",
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" print(row)\n",
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"\n",
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" def add_vertex(self):\n",
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" self.no_of_vertices += 1\n",
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" # Add a new row for the new vertex\n",
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" self.adj_matrix.append([0] * self.no_of_vertices)\n",
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" # Add a new column for the new vertex in existing rows\n",
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" for row in self.adj_matrix:\n",
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" row.append(0)\n",
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"\n",
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" def remove_vertex(self, vertex):\n",
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" if vertex < self.no_of_vertices:\n",
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" del self.adj_matrix[vertex]\n",
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" self.no_of_vertices -= 1\n",
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"\n",
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" for row in self.adj_matrix:\n",
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" del row[vertex]\n",
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"\n",
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" def get_neighbors(self, vertex):\n",
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" if vertex < self.no_of_vertices:\n",
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" return [index for index, weight in enumerate(self.adj_matrix[vertex]) if weight > 0]\n",
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" else:\n",
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" return []\n",
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"\n",
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" def has_edge(self, start, end):\n",
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" return self.adj_matrix[start][end] > 0\n",
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"\n",
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" def graph_size(self):\n",
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" return self.no_of_vertices, sum(row.count(1) for row in self.adj_matrix)\n",
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"\n",
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" def clear_graph(self):\n",
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" self.no_of_vertices = 0\n",
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" self.adj_matrix = []\n",
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"\n",
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" def in_degree(self, vertex):\n",
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" in_degree_count = 0\n",
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" for i in range(self.no_of_vertices):\n",
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" in_degree_count += self.adj_matrix[i][vertex]\n",
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" return in_degree_count\n",
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"\n",
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" def out_degree(self, vertex):\n",
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" out_degree_count = 0\n",
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" for i in range(self.no_of_vertices):\n",
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" out_degree_count += self.adj_matrix[vertex][i]\n",
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" return out_degree_count\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 71,
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"id": "58100cfd-be2a-4d7d-8128-79b42c0b7893",
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"metadata": {},
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"outputs": [],
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"source": [
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"graph = DirectedGraph(5)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 72,
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"id": "4eb0c220-439f-4c5a-aeed-832a663e418e",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Directed Graph:\n",
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"[0, 1, 1, 0, 0]\n",
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"[1, 0, 0, 1, 0]\n",
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"[0, 1, 0, 1, 0]\n",
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"[0, 0, 1, 0, 1]\n",
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"[1, 0, 1, 0, 0]\n"
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]
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}
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],
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"source": [
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"graph.add_edge(0, 1)\n",
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"graph.add_edge(0, 2)\n",
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"graph.add_edge(1, 3)\n",
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"graph.add_edge(2, 3)\n",
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"graph.add_edge(3, 4)\n",
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"\n",
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"# Adding more edges\n",
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"graph.add_edge(4, 0)\n",
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"graph.add_edge(2, 1)\n",
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"graph.add_edge(4, 2)\n",
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"graph.add_edge(1, 0)\n",
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"graph.add_edge(3, 2)\n",
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"\n",
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"print(\"Directed Graph:\")\n",
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"graph.display()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 73,
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"id": "002d4290-251f-46ac-b0f6-9502925d0d0d",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"In-Degree of Vertex 0: 2\n",
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"Out-Degree of Vertex 0: 2\n"
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]
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}
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],
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"source": [
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"vertex = 0\n",
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"in_degree = graph.in_degree(vertex)\n",
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"out_degree = graph.out_degree(vertex)\n",
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"\n",
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"print(f'In-Degree of Vertex {vertex}: {in_degree}')\n",
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"print(f'Out-Degree of Vertex {vertex}: {out_degree}')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 74,
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"id": "211b51e8-34d1-444b-b434-5d9a50ff23ba",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"Directed Graph after removing edge (1, 3):\n",
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"[0, 1, 1, 0, 0]\n",
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"[1, 0, 0, 0, 0]\n",
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"[0, 1, 0, 1, 0]\n",
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"[0, 0, 1, 0, 1]\n",
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"[1, 0, 1, 0, 0]\n"
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]
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}
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],
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"source": [
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"graph.remove_edge(1, 3)\n",
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"\n",
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"print(\"\\nDirected Graph after removing edge (1, 3):\")\n",
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"graph.display()\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 75,
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"id": "42924b20-1dae-4820-aee1-bc9896d197af",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"Directed Graph after adding a vertex:\n",
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"[0, 1, 1, 0, 0, 0]\n",
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"[1, 0, 0, 0, 0, 0]\n",
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"[0, 1, 0, 1, 0, 0]\n",
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"[0, 0, 1, 0, 1, 0]\n",
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"[1, 0, 1, 0, 0, 0]\n",
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"[0, 0, 0, 0, 0, 0, 0]\n"
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]
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}
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],
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"source": [
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"graph.add_vertex()\n",
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"\n",
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"print(\"\\nDirected Graph after adding a vertex:\")\n",
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"graph.display()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 76,
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"id": "6ec08462-1653-4475-aab3-77aae9210643",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"Directed Graph after removing vertex 1:\n",
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"[0, 1, 0, 0, 0]\n",
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"[0, 0, 1, 0, 0]\n",
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"[0, 1, 0, 1, 0]\n",
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"[1, 1, 0, 0, 0]\n",
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"[0, 0, 0, 0, 0, 0]\n"
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]
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}
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],
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"source": [
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"graph.remove_vertex(1)\n",
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"\n",
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"print(\"\\nDirected Graph after removing vertex 1:\")\n",
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"graph.display()\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 77,
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"id": "8d7ae565-d5d4-4143-9faa-f880ed1e7b70",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"Neighbors of vertex 0: [1]\n"
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]
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}
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],
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"source": [
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"neighbors = graph.get_neighbors(0)\n",
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"print(\"\\nNeighbors of vertex 0:\", neighbors)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 78,
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"id": "1c20d315-b99b-48e5-984c-f12b65347f9d",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"Does edge (0, 2) exist? False\n"
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]
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}
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],
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"source": [
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"has_edge = graph.has_edge(0, 2)\n",
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"print(\"\\nDoes edge (0, 2) exist?\", has_edge)\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 79,
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"id": "54a286fa-e389-472f-a489-74a08906c45d",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"Graph Size (Vertices, Edges): (5, 6)\n"
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]
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}
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],
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"source": [
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"size = graph.graph_size()\n",
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"print(\"\\nGraph Size (Vertices, Edges):\", size)\n",
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"\n",
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"graph.clear_graph()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "6b654b5a-d8bd-433c-8455-54dab63cc151",
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"metadata": {},
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"outputs": [],
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"source": []
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},
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{
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"cell_type": "code",
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"execution_count": 80,
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"id": "949100d1-c70a-43f9-b88b-3ec4340ab86c",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"Directed Graph after clearing:\n"
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]
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}
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],
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"source": [
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"print(\"\\nDirected Graph after clearing:\")\n",
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"graph.display()\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "ab15b137-e360-4fef-9445-f5dac0b69bbb",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.10.6"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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