A graph in which each graph edge is replaced by a directed graph edge, also called a digraph. A directed graph having no multiple edges or loops (corresponding to a binary adjacency matrix with 0s on the diagonal) is called a simple directed graph. A complete graph in which each edge is bidirected is called a complete directed graph. A directed graph having no symmetric pair of directed edges (i.e., no bidirected edges) is called an oriented graph. A complete oriented graph (i.e., a directed graph in which each pair of nodes is joined by a single edge having a unique direction) is called a tournament.
If 
is an undirected connected graph,
then one can always direct the circuit graph edges
of 
and leave the separating
edges undirected so that there is a directed path from any node to another. Such
a graph is said to be transitive if the adjacency relation
is transitive.
A graph may be tested in the Wolfram Language to see if it is a directed graph using DirectedGraphQ[g].
