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.

$\blacksquare$

Sources

• 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): Chapter $1$: Mathematical Models: $\S 1.6$: Networks as Mathematical Models: Problem $42$