Beginner Explanation
Imagine a directed graph like a one-way street map. Each intersection is a point (or node), and the streets that connect them are arrows (or edges) showing which way you can go. If there’s an arrow from point A to point B, it means you can travel from A to B, but not necessarily back from B to A. This helps us understand how things relate to each other, like how a friend can send you a message, but you might not be able to send them one back right away.Technical Explanation
A directed graph (or digraph) consists of nodes connected by edges that have a direction, indicated by arrows. Each edge is an ordered pair of nodes, represented as (u, v), meaning there’s a directed edge from node u to node v. In Python, you can represent a directed graph using dictionaries or libraries like NetworkX. For example: “`python import networkx as nx G = nx.DiGraph() G.add_edges_from([(1, 2), (2, 3), (1, 3)]) “` This creates a directed graph with edges from 1 to 2, 2 to 3, and 1 to 3. Directed graphs are useful for modeling relationships where direction matters, such as web page links or social media connections.Academic Context
Directed graphs are a fundamental concept in graph theory, a branch of mathematics and computer science. They are defined formally as a pair G = (V, E), where V is a set of vertices (or nodes) and E is a set of directed edges (ordered pairs of vertices). Directed graphs are crucial in various applications, including network theory, algorithm design, and data structure optimization. Key papers in this area include ‘Graph Theory’ by Diestel and ‘Introduction to Graph Theory’ by Bondy and Murty, which delve into the properties and applications of directed graphs in depth.Code Examples
Example 1:
import networkx as nx
G = nx.DiGraph()
G.add_edges_from([(1, 2), (2, 3), (1, 3)])Example 2:
import networkx as nx
G = nx.DiGraph()
G.add_edges_from([(1, 2), (2, 3), (1, 3)])
```
This creates a directed graph with edges from 1 to 2, 2 to 3, and 1 to 3. Directed graphs are useful for modeling relationships where direction matters, such as web page links or social media connections.View Source: https://arxiv.org/abs/2511.16066v1