Enumerating Top-k Quasi-Cliques

Abstract

Quasi-cliques are dense incomplete subgraphs of a graph that generalize the notion of cliques. Enumerating quasicliques 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 NPhard (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.

Noise Resistant Multidimensional Data Fusion via Quasi-Cliques on Hypergraphs

“…In other words, if we remove from a γ-quasi-clique a node v with a degree lower than the average degree, the resulting graph is still at least a γ-quasi-clique. Note that this is consistent with the observation that a quasi-clique contains denser sub-graphs [23].…”

“…PRESQ seed stage begins close to the original clique, while the growing stage pushes the result closer. For k = 2, our proposal is similar to existing quasi-clique finding algorithms [23], [24], so these results are to be expected.…”

“…Finding quasi-cliques seeds Some initial experiments with FIND2 showed that as-is, the algorithm was able to find relatively high arity EDDs regardless of the missing edges. It makes sense since, generally, a quasi-clique contains smaller but denser sub-graphs [23] and a clique is denser than a quasi-clique.…”

Noise Resistant Multidimensional Data Fusion via Quasi-Cliques on Hypergraphs

“…Growing the quasi-clique seeds This is similar to KER-NELQC's idea [23], but based on a quasi-clique enumeration algorithm. Given a quasi-clique seed from the first stage, candidates are grown following a tree-shaped, depth-first traversal [24]:…”

Scalable Mining of Maximal Quasi-Cliques: An Algorithm-System Codesign Approach

“…Other than Sanei-Mehri et al [34], quasi-cliques have seldom been considered in a big graph setting. Quick [29] was only tested on two small graphs: a yeast interaction network with 4932 vertices (proteins) and 17201 edges (interactions), and an E. coli interaction network with 1846 vertices and 5929 edges.…”