Definition:Arborescence/Definition 3

Definition
Let $G = (V, A)$ be a directed graph.

Let $r \in V$.

Then $G$ is an arborescence of root $r$, an $r$-arborescence, or just an arborescence 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 $v$.

Note
reverses the orientation of the arcs, so that they all point toward the root. It also calls this an oriented tree.