@MISC{Tsourakakis_thek-clique, author = {Charalampos E. Tsourakakis}, title = {The K-clique Densest Subgraph Problem}, year = {} }

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Abstract

Numerous graph mining applications rely on detecting sub-graphs which are large near-cliques. Since formulations that are geared towards finding large near-cliques are NP-hard and frequently inapproximable due to connections with the Maximum Clique problem, the poly-time solvable densest subgraph problem which maximizes the average degree over all possible subgraphs “lies at the core of large scale data mining”[10]. However, frequently the densest subgraph prob-lem fails in detecting large near-cliques in networks. In this work, we introduce the k-clique densest subgraph problem, k ≥ 2. This generalizes the well studied dens-est subgraph problem which is obtained as a special case for k = 2. For k = 3 we obtain a novel formulation which we refer to as the triangle densest subgraph problem: given a graph G(V,E), find a subset of vertices S ∗ such that τ(S∗) = max S⊆V t(S)