Editing Directed acyclic graph (section)

{{short description|Directed graph with no directed cycles}}
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[[File:Tred-G.svg|thumb|Example of a directed acyclic graph]]
In [[mathematics]], particularly [[graph theory]], and [[computer science]], a '''directed acyclic graph''' ('''DAG''') is a [[directed graph]] with no [[Cycle graph#Directed cycle graph|directed cycles]]. That is, it consists of [[Vertex (graph theory)|vertices]] and [[edge (graph theory)|edges]] (also called ''arcs''), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only if it can be [[topological ordering|topologically ordered]], by arranging the vertices as a linear ordering that is consistent with all edge directions. DAGs have numerous scientific and computational applications, ranging from biology (evolution, family trees, epidemiology) to information science (citation networks) to computation (scheduling).

Directed acyclic graphs are also called '''acyclic directed graphs'''<ref name="thul"/> or '''acyclic digraphs'''.<ref name="bang"/>