  Local community detection has attracted much research attention recently, and
many methods have been proposed for the single local community detection that
finds a community containing the given set of query nodes. However, nodes may
belong to several communities in the network, and detecting all the communities
for the query node set, termed as the multiple local community detection
(MLCD), is more important as it could uncover more potential information. MLCD
is also more challenging because when a query node belongs to multiple
communities, it always locates in the complicated overlapping region and the
marginal region of communities. Accordingly, detecting multiple communities for
such 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-order
structures, we propose a new variant of random walk called Active Random Walk
to measure the HoSI score between nodes. Then, we propose two new metrics to
evaluate 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 algorithm
called HoSIM to detect multiple local communities for a single query node.
HoSIM enforces a three-stage processing, namely subgraph sampling, core member
identification, and local community detection. The key idea is utilizing HoSI
to find and identify the core members of communities relevant to the query node
and optimize the generated communities. Extensive experiments illustrate the
effectiveness of HoSIM.
