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…
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