Directed graph

A directed graph is a pair $G=(V,E)$ with $E\subseteq V\times V$. An ordered edge $(u,v)$, written $u\to v$, has source $u$ and target $v$. This convention allows loops and allows both $u\to v$ and $v\to u$; additional hypotheses can exclude them. There are no parallel copies of an edge when $E$ is a set.