arborescence

Let $G = (V, E)$ be a directed graph and fix a root vertex $r \in V$ . An arborescence of $G$ rooted at $r$ , $T$ is

$T$ is a subgraph of $G$ where if we forget the direction of the edges, is a spanning tree
For all $v \in V$ , there is a directed path from $r \to v$ .

For a graph, the directed matrix tree theorem gives you the number of arborescences.