When Does Bottom-Up Beat Top-Down in Hierarchical Community Detection?

Maximilien Dreveton, Daichi Kuroda, Matthias Grossglauser, Patrick Thiran

Abstract: Hierarchical community detection consists in finding a tree of communities where deeper levels of the hierarchy reveal finer-grained structures. There are two main classes of algorithms for this task. Divisive (top-down) algorithms recursively partition nodes into smaller communities until a stopping criterion indicates that no further splits are necessary. In contrast, agglomerative (bottom-up) algorithms first identify the smallest community structures and then repeatedly merge the communities by using a linkage method. In this work, we prove that a bottom-up algorithm recovers the hierarchy of a hierarchical stochastic block model (HSBM) when the average degree grows unbounded. We also establish the information-theoretic threshold for exact recovery at intermediate depths of the hierarchy and highlight its significance in understanding the limitations of top-down algorithms. Numerical experiments on both synthetic and real datasets demonstrate the superiority of bottom-up methods. In particular, a notable drawback of top-down algorithms is their tendency to produce dendrograms with inversions. These findings contribute to a better understanding of hierarchical clustering techniques and their applications in network analysis. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

External IDs:doi:10.1080/01621459.2025.2569711