  Community search (CS) aims to identify a set of nodes based on a specified
query, leveraging structural cohesiveness and attribute homogeneity. This task
enjoys various applications, ranging from fraud detection to recommender
systems. In contrast to algorithm-based approaches, graph neural network (GNN)
based methods define communities using ground truth labels, leveraging prior
knowledge to explore patterns from graph structures and node features. However,
existing solutions face three major limitations: 1) GNN-based models primarily
focus on the disjoint community structure, disregarding the nature of nodes
belonging to multiple communities. 2) These model structures suffer from
low-order awareness and severe efficiency issues. 3) The identified community
is subject to the free-rider and boundary effects. In this paper, we propose
Simplified Multi-hop Attention Networks (SMN), which consist of three designs.
First, we introduce a subspace community embedding technique called Sparse
Subspace Filter (SSF). SSF enables the projection of community embeddings into
distinct vector subspaces, accommodating the nature of overlapping and nesting
community structures. In addition, we propose a lightweight model structure and
a hop-wise attention mechanism to capture high-order patterns while improving
model efficiency. Furthermore, two search algorithms are developed to minimize
the latent space's community radius, addressing the challenges of free-rider
and boundary effects. To the best of our knowledge, this is the first
learning-based study of overlapping community search. Extensive experiments
validate the superior performance of SMN compared with the state-of-the-art
approaches. SMN achieves 14.73% improvements in F1-Score and up to 3 orders of
magnitude acceleration in model efficiency.
