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.

社区搜索在图分析任务中变得尤为重要，其目的是从几个给定的节点中识别特定社区的潜在成员。现有的社区搜索工作大多集中于探索给定节点所在的单一尺度的社区结构。尽管结果令人鼓舞，但以下两个见解经常被忽视。首先，除了用于表征节点属性的网络交互之外，节点属性还提供丰富且高度相关的辅助信息。属性可以指示具有很少链接的节点的社区分配，这很难仅从网络结构来确定。其次，多分辨率社区提供潜在信息来描述网络的层次关系，并确保其中之一最接近真实网络。用户必须了解网络的底层结构，并探索不同尺度上具有强结构和属性凝聚力的社区。这些方面促使我们开发一种新的社区搜索框架，称为多分辨率局部光谱属性社区搜索（MLSACS）。具体来说，受局部模块化、图小波和缩放函数的启发，我们提出了一种基于重构节点属性图的新的多分辨率局部模块化（MLQ）。此外，为了检测不同尺度上具有内聚结构和属性的本地社区，通过解决线性规划问题，基于 MLQ 开发了稀疏指示向量。对合成和真实世界属性图的广泛实验结果表明，检测到的社区是有意义的，并且可以合理地改变规模。