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.