BUILT-IN MATHEMATICA SYMBOL

CompleteGraphQ

CompleteGraphQ[g]
yields True if the graph g is a complete graph, and False otherwise.

CompleteGraphQ

yields True if the subgraph induced by vlist is a complete graph, and False otherwise.

MORE INFORMATION

A graph is complete if there is an edge between every pair of distinct vertices.

EXAMPLES

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Basic Examples (2)

Test whether a graph is complete:

Petersen graph is not a complete graph:

Test whether a graph is complete:

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Petersen graph is not a complete graph:

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Scope (4)

Test undirected or directed graphs:

Test subgraphs:

CompleteGraphQ gives False for anything that is not a complete graph:

Test large graphs:

Properties & Relations (11)

A complete graph has no self-loops:

A TreeGraph is not a complete graph:

The only complete path graphs are triangles (undirected):

And the directed path:

A complete graph on

vertices has

edges:

The complete graph

is a cycle graph

:

The complete graph

is a wheel graph

:

The complete graph

is the line graph of the star graph

:

A complete graph is an

-regular graph:

The GraphComplement of a complete graph is an empty graph:

For a complete graph, all entries outside the diagonal are 1s in the AdjacencyMatrix:

Complete graphs are their own cliques: