The clique graph of a given graph is the graph intersection of the family of cliques of . A graph is a clique graph iff it contains a family of complete subgraphs whose graph union is , such that whenever every pair of such complete graphs in some subfamily has a nonempty graph intersection, the intersection of all members of is not empty (Harary 1994, p. 20).

# Clique Graph

## See also

Clique, Clique Number, Complete Graph## Explore with Wolfram|Alpha

## References

Harary, F.*Graph Theory.*Reading, MA: Addison-Wesley, 1994.

## Referenced on Wolfram|Alpha

Clique Graph## Cite this as:

Weisstein, Eric W. "Clique Graph." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/CliqueGraph.html