Maximum Clique Sensitivity. The number of maximum cliques in a graph can be highly subject to perturbations due, for example, to noise. For example, a graph may contain a single maximum clique C representing a putative network of size k, along with any number of vertices connected to k - 2 vertices in C. In (a), there is a single maximum clique of size k = 5, with "many" other vertices (only three are shown) connected to k - 2 = 3 of its nodes. In (b), noise results in the removal of a single edge, creating many maximum cliques now of size k - 1 = 4.
Eblen et al. BMC Bioinformatics 2012 13(Suppl 10):S5 doi:10.1186/1471-2105-13-S10-S5