A 有向グラフ, 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 有向エッジ ページXからページYへのリンクは、XがYにリンクしていることを意味します。
数学的には、有向グラフは次のように定義されます。 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 路線上のエッジは、距離、コスト、容量を表すことができます。
有向グラフは、さまざまな分野で基本的な役割を果たしています コンピュータ科学, 運用研究, and ネットワーク理論. They are used in algorithms for shortest paths, network flows, and dependency resolution, among many other applications.