Definition:Loop-Graph/Loop-Digraph

Definition

A loop-digraph is a digraph 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 loop-digraph is a digraph 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.