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The Kclique Densest Subgraph Problem
"... Numerous graph mining applications rely on detecting subgraphs which are large nearcliques. Since formulations that are geared towards finding large nearcliques are NPhard and frequently inapproximable due to connections with the Maximum Clique problem, the polytime solvable densest subgraph pr ..."
Abstract

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Numerous graph mining applications rely on detecting subgraphs which are large nearcliques. Since formulations that are geared towards finding large nearcliques are NPhard and frequently inapproximable due to connections with the Maximum Clique problem, the polytime 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 problem fails in detecting large nearcliques in networks. In this work, we introduce the kclique densest subgraph problem, k ≥ 2. This generalizes the well studied densest 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)