Directed graphs are graphs in which each edge (u,v) has an orientation. That is, the edge (u,v) (from u to v) is different than the edge (v,u) (from v to u). Thus, the edge set is a subset of V× V -- the ordered pairs of vertices.
Paths and cycles in directed graphs must traverse edges in the forward direction. That is, if a path has vertices v1, v2, ... vk, then each edge (vi, vi+1) must exist.
BreadthFirstSearch (BFS) extends straightforwardly to directed graphs.
DepthFirstSearch (DFS) also works in directed graphs, but it becomes more interesting.
See DFSInDiGraphs .