Today I read a paper titled “Clique Graphs and Overlapping Communities”
The abstract is:
It is shown how to construct a clique graph in which properties of cliques of a fixed order in a given graph are represented by vertices in a weighted graph.
Various definitions and motivations for these weights are given.
The detection of communities or clusters is used to illustrate how a clique graph may be exploited.
In particular a benchmark network is shown where clique graphs find the overlapping communities accurately while vertex partition methods fail.