Abstract Complex networks contain complete subgraphs such as nodes, edges, triangles, etc., referred to simplices and cliques of different orders. Notably, cavities consisting higher-order play an important role in brain functions. Since searching for maximum is NP-complete problem, we use k-core decomposition determine the computability a given network. For computable network, design search me...

A regular graph is superregular if it has no vertices or if the subgraphs induced by the neighbors and by the nonneighbors of each vertex are superreg-ular. The superregular graphs are precisely the disjoint union of m isomorphic cliques, the Cartesian product of two isomorphic cliques, the ve-cycle, and the complements of these graphs.

We address the problem of un-supervised soft-clustering called micro-clustering. The aim of the problem is to enumerate all groups composed of records strongly related to each other, while standard clustering methods separate records at sparse parts. The problem formulation of micro-clustering is non-trivial. Clique mining in a similarity graph is a typical approach, but it results in a huge nu...

Identifying communities in social networks is a problem of great interest. One popular type of community is where every member of the community knows all others, which can be viewed as a clique in the graph representing the social network. In several real life situations, finding small cliques may not be interesting as they are large in number and low in information content. Hence, in this pape...

Several recent papers have described probability models which used graph and hypergraphs to represent relationships among the variables. Two related computing algorithms are commonly used to manipulate such models: the peeling algorithm which eliminates variables one at a time to find the marginal distribution of a single variable, and the fusion and propagation algorithm which simultaneously s...