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Numerous graph mining applications rely on detecting subgraphs which are large near-cliques. Since formulations that are geared towards finding large near-cliques are 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 problem fails in detecting large near-cliques in networks.
Charalampos E. Tsourakakis (Mon,) studied this question.