 In mathematics and computer science , a directed acyclic graph ( DAG / <unk> / ) , is a finite directed graph with no directed cycles . That is , it consists of <unk> many vertices and edges , with each edge directed from one vertex to another , such that there is no way to start at any vertex v and follow a consistently @-@ directed sequence of edges that eventually loops back to v again . <unk> , a DAG is a directed graph that has a topological ordering , a sequence of the vertices such that every edge is directed from earlier to later in the sequence . 
