In mathematics, and more specifically in graph theory, a polytree[1] (also called directed tree,[2] oriented tree[3] or singly connected network[4]) is a directed acyclic graph whose underlying undirected graph is a tree. In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is both connected and acyclic.
A polyforest (or directed forest or oriented forest) is a directed acyclic graph whose underlying undirected graph is a forest. In other words, if we replace its directed edges with undirected edges, we obtain an undirected graph that is acyclic.
A polytree is an example of an oriented graph.
The term polytree was coined in 1987 by Rebane and Pearl.[5]