Arborescence (graph theory)

In graph theory, an arborescence is a directed graph having a distinguished vertex u (called the root) such that, for any other vertex v, there is exactly one directed path from u to v. An arborescence is thus the directed-graph form of a rooted tree, understood here as an undirected graph. An arborescence is also a directed rooted tree in which all edges point away from the root; a number of other equivalent characterizations exist.

Every arborescence is a directed acyclic graph (DAG), but not every DAG is an arborescence.