Enumerating Maximal Clique Sets with K-plex Constraint by using Meta-cliques

Many variants of pseudo-cliques have been introduced as relaxation models of cliques to detect communities in real world networks. For most types of pseudo-cliques, enumeration algorithms can be designed just similar to maximal clique enumerator. However, the problem of enumerating pseudo-cliques are computationally hard, because the number of maximal pseudo-cliques is huge in general. Furthermore, because of the weak requirement of k-plex, sparse communities are also allowed depending on the parameter k. To obtain a class of more dense pseudo cliques and to improve the computational performance, we introdue a derived graph whose vertices are cliques in the original input graph. Then our target must be cliques or pseudo cliques of the derived graph under an additional constraint requiring high density in the original graph. An enumerator for this new class is designed and its computational efficientcy is experimentally verfied.