Enumerating Top-k Quasi-Cliques

TL;DR

This paper introduces KernelQC, a heuristic algorithm for efficiently enumerating the top-k degree-based quasi-cliques in large graphs, significantly outperforming existing methods in speed and scalability.

Contribution

The paper presents a novel heuristic approach, KernelQC, for enumerating the largest quasi-cliques by identifying dense kernels and expanding around them, addressing the NP-hardness of maximal quasi-clique detection.

Findings

KernelQC accurately enumerates quasi-cliques.

It is over three orders of magnitude faster than existing methods.

The algorithm scales well to large graphs.

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.