Multiresolution Local Spectral Attributed Community Search

Community search has become especially important in graph analysis task, which aims to identify latent members of a particular community from a few given nodes. Most of the existing efforts in community search focus on exploring the community structure with a single scale in which the given nodes are located. Despite promising results, the following two insights are often neglected. First, node attributes provide rich and highly related auxiliary information apart from network interactions for characterizing the node properties. Attributes may indicate the community assignment of a node with very few links, which would be difficult to determine from the network structure alone. Second, the multiresolution community affords latent information to depict the hierarchical relation of the network and ensure that one of them is closest to the real one. It is essential for users to understand the underlying structure of the network and explore the community with strong structure and attribute cohesiveness at disparate scales. These aspects motivate us to develop a new community search framework called Multiresolution Local Spectral Attributed Community Search (MLSACS). Specifically, inspired by the local modularity, graph wavelets, and scaling functions, we propose a new Multiresolution Local modularity (MLQ) based on a reconstructed node attribute graph. Furthermore, to detect local communities with cohesive structures and attributes at different scales, a sparse indicator vector is developed based on MLQ by solving a linear programming problem. Extensive experimental results on both synthetic and real-world attributed graphs have demonstrated the detected communities are meaningful and the scale can be changed reasonably.