Definition: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:
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 pseudograph 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
- Gary Chartrand: Introductory Graph Theory (1977): $\S 1.6$
