Loop-Digraph as a Relation

Theorem
A loop-digraph is the same thing as a relational structure.

Proof
A loop-digraph is a graph such that:


 * it is not necessarily antireflexive


 * it is not necessarily symmetric.

Hence a loop-digraph is an ordered pair:
 * $G = \struct {V, E}$

such that:
 * $V$ is a set of objects
 * $E$ is a relation on $V$.

This defines a relational structure.