Definition:Loop-Graph/Loop-Digraph

Informal 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 pseudograph is a directed graph with the stipulation that the relation $$E$$ does not need to be antireflexive.

Loop-Digraph as a Relation
It can be seen by direct comparison that a loop-digraph is the same thing as a relational structure.