Definition:Path (Graph Theory)/Digraph

Definition
Let $D = \struct {V, E}$ be a directed graph.

A path $P$ in $D$ is:
 * a sequence of vertices $v_1, v_2, \ldots, v_n$ in $V$ and a sequence of arcs $e_1, e_2, \ldots{}, e_{n - 1}$ in $E$ such that:
 * $P$ begins with $v_1$ and ends with $v_n$
 * in which each arc $e_j$ is incident from $v_j$ and incident to $v_{j + 1}$
 * all arcs are distinct
 * all vertices (except perhaps the first and last ones) are distinct.

A path between two vertices $u$ and $v$ is called a path from $u$ to $v$.