Definition:Path in Digraph/Successor

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

Let $P$ be a path in $D$ such that the vertices of $P$ are $v_1, v_2, \ldots, v_n$.

Let $v_j$ be a vertex of $P$ such that $j < n$.

Then the successor (vertex) of $v_j$ is the vertex $v_{j + 1}$.

That is, if $v \to w$ is an arc in $P$, $w$ is the successor (vertex) of $v$.

Also see

 * Definition:Predecessor Vertex