directed graph

A directed graph or digraph is a pair $G=(V,E)$ where $V$ is a set of vertices and $E$ is a subset of $V\times V$ called edges or arcs.

If $E$ is symmetric (i.e., $(u,v)\in E$ if and only if $(v,u)\in E$), then the digraph is isomorphic to an ordinary (that is, undirected) graph.

Digraphs are generally drawn in a similar manner to graphs with arrows on the edges to indicate a sense of direction. For example, the digraph

$$(\{a,b,c,d\},\{(a,b),(b,d),(b,c),(c,b),(c,c),(c,d)\})$$

may be drawn as