\begin{definition}[Definition:Arborescence/Definition 3]
Let $G = \struct {V, A}$ be a directed graph.
Let $r \in V$.
$G$ is an '''arborescence of root $r$''' {{iff}}:
: $(1): \quad$ Each vertex $v \ne r$ is the final vertex of exactly one arc.
: $(2): \quad$ $r$ is not the final vertex of any arc.
: $(3): \quad$ For each $v \in V$ such that $v \ne r$ there is a directed walk from $r$ to $v$.
\end{definition}