Definition:Loop-Graph/Loop-Digraph

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Informal Definition

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

LoopDigraph.png


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 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