Enumerating Top-k Quasi-Cliques

Seyed-Vahid Sanei-Mehri; Apurba Das; Srikanta Tirthapura

doi:10.1109/bigdata.2018.8622352

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arXiv · 1808.09531

Enumerating Top-k Quasi-Cliques

Seyed-Vahid Sanei-Mehri·Apurba Das·Srikanta Tirthapura

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Abstract

Quasi-cliques are dense incomplete subgraphs of a graph that generalize the notion of cliques. Enumerating quasi-cliques from a graph is a robust way to detect densely connected structures with applications to bio-informatics and social network analysis. However, enumerating quasi-cliques in a graph is a challenging problem, even harder than the problem of enumerating cliques. We consider the enumeration of top-k degree-based quasi-cliques, and make the following contributions: (1) We show that even the problem of detecting if a given quasi-clique is maximal (i.e. not contained within another quasi-clique) is NP-hard (2) We present a novel heuristic algorithm KernelQC to enumerate the k largest quasi-cliques in a graph. Our method is based on identifying kernels of extremely dense subgraphs within a graph, following by growing subgraphs around these kernels, to arrive at quasi-cliques with the required densities (3) Experimental results show that our algorithm accurately enumerates quasi-cliques from a graph, is much faster than current state-of-the-art methods for quasi-clique enumeration (often more than three orders of magnitude faster), and can scale to larger graphs than current methods.

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Seyed-Vahid Sanei-Mehri, Apurba Das, Srikanta Tirthapura. 2018-08-28. Enumerating Top-k Quasi-Cliques. https://doi.org/10.1109/bigdata.2018.8622352

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