This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 BUILT-IN MATHEMATICA SYMBOL

# CompleteGraphQ

 CompleteGraphQ[g] yields True if the graph g is a complete graph, and False otherwise. CompleteGraphQyields True if the subgraph induced by vlist is a complete graph, and False otherwise.
• A graph is complete if there is an edge between every pair of distinct vertices.
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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Test undirected or directed graphs:
Test subgraphs:
CompleteGraphQ gives False for anything that is not a complete graph:
Test large graphs:
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:
New in 8