A directed graph, also known as a digraph, is a type of graph in which the edges have a direction associated with them. This means that each edge connects a pair of nodes (or vertices) and indicates a one-way relationship from one node to another. In a directed graph, if there is an edge from node A to node B, it implies that the connection flows from A to B, but not necessarily vice versa.
Directed graphs are commonly used to model relationships where direction matters. For example, in social networks, a directed graph can represent followers and followees, where an edge from user A to user B indicates that A follows B. Similarly, in web page linking, a directed edge from page X to page Y signifies that X links to Y.
Mathematically, a directed graph is defined as an ordered pair G = (V, E), where V is a set of vertices (or nodes) and E is a set of directed edges. Each edge is represented as an ordered pair (u, v), indicating a directed connection from vertex u to vertex v. Directed graphs can also have properties such as weights on edges, which can represent distances, costs, or capacities.
Directed graphs are fundamental in various fields including computer science, operations research, and network theory. They are used in algorithms for shortest paths, network flows, and dependency resolution, among many other applications.