Hierarchical community-discovery algorithm combining core nodes and three-order structure model

A community structure in a complex network often exhibits hierarchical characteristics. Current hierarchical community-discovery algorithms generally consider a single node as a community during the initial stage. This approach leads to over-fine clustering granularity, too-deep clustering levels, and other issues. Therefore, this article proposes a hierarchical community-discovery algorithm that combines the core nodes and the three-order structure model. Between neighboring nodes, there is a first-order structure. The core node is identified based on its influence, and the similarity between the core node and its neighboring nodes is defined as the second-order structure. The nodes satisfying the second-order structure are then formed into a friend circle. The similarity between friend circles is defined as the third-order structure. According to this structure, the friend circles are construed as a hierarchical clustering tree (HCT) where one HCT represents a community. The HCT built by this algorithm has relatively fewer levels and exhibits a flat feature. Experimental results on both artificial and real networks show that the algorithm performs well on various indicators. Additionally, the algorithm exhibits near-linear time complexity.