yields True if the graph g is a complete graph, and False otherwise.
yields 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.
- CompleteGraphQ works with undirected graphs, directed graphs, multigraphs, and mixed graphs.
Examplesopen allclose all
Test undirected or directed graphs:
CompleteGraphQ gives False for anything that is not a complete graph:
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):
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:
Wolfram Research (2010), CompleteGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/CompleteGraphQ.html (updated 2014).
Wolfram Language. 2010. "CompleteGraphQ." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. https://reference.wolfram.com/language/ref/CompleteGraphQ.html.
Wolfram Language. (2010). CompleteGraphQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CompleteGraphQ.html