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For questions about directed graphs. In a directed graph, each edge is an ordered pair of vertices; we think of it as pointing from one to the other. Use with the (graph-theory) tag.

Directed graphs, or digraphs, are used to represent asymmetric relationships between a collection of objects.

Formally, a directed graph is defined as consisting of:

  • a set of vertices;
  • set of ordered pairs of vertices, called arcs or directed edges.

In diagrams, vertices are represented by points, and each directed edge is represented by an arrow from its first vertex to its second.

Some special classes of directed graphs include:

  • Tournaments: directed graphs in which, for every pair of vertices, an edge exists in exactly one direction between them.
  • Directed acyclic graphs (DAGs), which contain no directed cycles.