Efficient multi-scale community search method based on spectral graph wavelet

Community search is an important problem in network analysis, which has attracted much attention in recent years. As a query-oriented variant of community detection problem, community search starts with some given nodes, pays more attention to local network structures, and gets personalized resultant communities quickly. The existing community search method typically returns a single target community containing query nodes by default. This is a strict requirement and does not allow much flexibility. In many real-world applications, however, query nodes are expected to be located in multiple communities with different semantics. To address this limitation of existing methods, an efficient spectral-based Multi-Scale Community Search method (MSCS) is proposed, which can simultaneously identify the multi-scale target local communities to which query node belong. In MSCS, each node is equipped with a graph Fourier multiplier operator. The access of the graph Fourier multiplier operator helps nodes to obtain feature representations at various community scales. In addition, an efficient algorithm is proposed for avoiding the large number of matrix operations due to spectral methods. Comprehensive experimental evaluations on a variety of real-world datasets demonstrate the effectiveness and efficiency of the proposed method.