| Directed Graphs
				Many applications of graph theory require a definition of a graph for
				which edges are directed: allowing there to be an edge
				from  to  but
				not necessarily an edge from  to  . 
				Here is a formal definition:
				 
				A directed graph (often called a
				digraph for brevity's sake)
				 is a pair  where  is a set of elements called vertices and  is a subset of the set of all ordered pairs  , where  and  are vertices. (An
				element of  is called an edge of  ). For more information on edges and vertices
				please click here |