Recognize Clique Communities

By definition, a clique is a very rigid and sensitive network structure. Removing an edge from a k-clique transforms it into two interwound, partially overlapping, adjacent (k-1)-cliques. In the figure, subgraphs Alpha--Delta and Alpha--Charlie, Echo are 4-cliques each, but the whole network is not a 5-clique, because the edge Delta--Echo is missing (I show it as a dashed line).

images/CliqueCommunity.png

Intuitively, you may feel that all k nodes somehow belong together and the missing edge could have been a victim of a measurement or data entry error or improper slicing (Slice Weighted Networks) or conversion from a directed graph. Nonetheless, ...

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