# Definition:Loop-Graph/Loop-Digraph

< Definition:Loop-Graph(Redirected from Definition:Loop-Digraph)

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## Contents

## Informal Definition

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

### 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.

## Loop-Digraph as a Relation

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

## Also see

- A Hasse diagram is a graphical depiction of an ordered set. However, its representation is stylised such that:
- the loops are not shown;
- relations arising as a result of transitivity are not shown;
- directions are not shown by writing arrows on the edges, but by positioning destination vertices higher on the page.

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): $\S 1.6$: Networks as Mathematical Models