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


Such an edge is called a loop.

Formal Definition

A loop-graph $G$ is a non-empty set $V$ together with a symmetric relation $E$ on $G$.

Thus it can be seen that a loop-graph is a simple graph with the stipulation that the relation $E$ does not need to be antireflexive.


Also known as

Some presentations of this subject omit the hyphen and call this a loop graph.

Loop-graphs and loop-multigraphs are also often known as pseudographs.

However, the precise definition of the latter term varies in the literature, and its precise meaning can be misunderstood. Its use is therefore not recommended.

Also see

  • Results about loop-graphs can be found here.