# Definition:Loop-Graph/Loop-Digraph

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

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## 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.

## Also see

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

- Definition:Hasse Diagram: a depiction of an ordered set as a loop-digraph with a stylised representation such that:
- the loops are not shown
- relation arising as a result of transitivity are not shown
- directions are not shown by writing arrows on the arcs, but by positioning destination vertices higher on the page.