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Local community detection has attracted much research attention recently, andmany methods have been proposed for the single local community detection thatfinds a community containing the given set of query nodes. However, nodes maybelong to several communities in the network, and detecting all the communitiesfor the query node set, termed as the multiple local community detection(MLCD), is more important as it could uncover more potential information. MLCDis also more challenging because when a query node belongs to multiplecommunities, it always locates in the complicated overlapping region and themarginal region of communities. Accordingly, detecting multiple communities forsuch nodes by applying seed expansion methods is insufficient.  In this work, we address the MLCD based on higher-order structural importance(HoSI). First, to effectively estimate the influence of higher-orderstructures, we propose a new variant of random walk called Active Random Walkto measure the HoSI score between nodes. Then, we propose two new metrics toevaluate the HoSI score of a subgraph to a node and the HoSI score of a node,respectively. Based on the proposed metrics, we present a novel algorithmcalled HoSIM to detect multiple local communities for a single query node.HoSIM enforces a three-stage processing, namely subgraph sampling, core memberidentification, and local community detection. The key idea is utilizing HoSIto find and identify the core members of communities relevant to the query nodeand optimize the generated communities. Extensive experiments illustrate theeffectiveness of HoSIM.

HoSIM: Higher-order Structural Importance based Method for Multiple Local Community Detection