This resource function is obsolete. Use the built-in symbol SimpleGraphQ instead.

Function Repository Resource:

SimplicalGraphQ

Test whether a graph is simplical

Contributed by: Jon McLoone

ResourceFunction["SimplicalGraphQ"][gr]

tests whether the graph gr is simplical.

Details

A graph is simplical if no edge starts and ends at the same vertex, and no two edges have the same pair of vertices.

If more than one edge joins the same pair of vertices then the graph is not simplical:

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Self-connected vertices are not simplical:

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The Petersen graph is simplicial:

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