 A graph is formed by a collection of vertices and edges , where the vertices are <unk> objects that are connected in pairs by edges . In the case of a directed graph , each edge has an orientation , from one vertex to another vertex . A path in a directed graph can be described by a sequence of edges having the property that the ending vertex of each edge in the sequence is the same as the starting vertex of the next edge in the sequence ; a path forms a cycle if the starting vertex of its first edge equals the ending vertex of its last edge . A directed acyclic graph is a directed graph that has no cycles . 
