Arborescence (graph theory)

In graph theory, an arborescence is a directed graph where there exists a vertex r (called the root) such that, for any other vertex v, there is exactly one directed walk from r to v (noting that the root r is unique).

[1] An arborescence is thus the directed-graph form of a rooted tree, understood here as an undirected graph.

[7] There is a large number of synonyms for arborescence in graph theory, including directed rooted tree,[3][7] out-arborescence,[8] out-tree,[9] and even branching being used to denote the same concept.

[10][11][12] Furthermore, some authors define an arborescence to be a spanning directed tree of a given digraph.

[12] It's also possible to define a useful notion by reversing all the edges of an arborescence, i.e. making them all point in the direction of the root rather than away from it.