# Definition:Loop-Graph/Loop-Digraph

(Redirected from Definition:Loop-Digraph)

## Definition

A loop-digraph is a directed graph which allows an arc to start and end at the same vertex:

### Loop

Such an arc is called a loop.

### Formal Definition

A loop-digraph $D$ is a non-empty set $V$ together with a relation $E$ on $D$.

Thus it can be seen that a loop-digraph is a directed graph with the stipulation that the relation $E$ does not need to be antireflexive.