An efficient method for mining the maximal α-quasi-clique-community of a given node in complex networks

Detecting communities in large complex networks is important to understand their structure and to extract features useful for visualization or prediction of various phenomena like the diffusion of information or the dynamic of the network. A community is defined by a set of strongly interconnected nodes. An α-quasi-clique is a group of nodes where each member is connected to more than a proportion α of the other nodes. By construction, an α-quasi-clique has a density greater than α. The size of an α-quasi-clique is limited by the degree of its nodes. In complex networks whose degree distribution follows a power law, usually α-quasi-cliques are small sets of nodes for high values of α. In this paper, we present an efficient method for finding the maximal α-quasi-clique of a given node in the network. Therefore, the resulting communities of our method have two main characteristics: they are α-quasi-cliques (very dense for high α) and they are local to the given node. Detecting the local community of specific nodes is very important for applications dealing with huge networks, when iterating through all nodes would be impractical or when the network is not entirely known. The proposed method, called RANK-NUM-NEIGHS (RNN), is evaluated experimentally on real and computer-generated networks in terms of quality (community size), execution time and stability. We also provide an upper bound on the optimal solution.