🤖 AI Summary
Existing community detection methods commonly assume static community sizes, overlooking their dynamic splitting and merging across resolution scales. This work reveals a non-monotonic “kaleidoscopic” reorganization phenomenon in real-world networks—where simultaneous splitting and merging occur at the same scale—challenging the conventional unidirectional hierarchical assumption. Method: We formally characterize scale-dependent community reorganization, particularly cases where the number of communities locally decreases, integrating mathematical analysis of modularity, empirical validation on real networks, and interpretable synthetic modeling. Contribution/Results: We establish the first formal framework for such multi-scale, bidirectional reorganization, shifting the paradigm from static, single-scale community detection to dynamic, multi-scale structural reconstruction. Empirical results confirm the ubiquity and irreducibility of this phenomenon—it cannot be decomposed into pure splitting or merging alone—thereby providing a theoretical foundation and a novel evaluation dimension for multi-scale community detection.
📝 Abstract
The notion of structural heterogeneity is pervasive in real networks, and their community organization is no exception. Still, a vast majority of community detection methods assume neatly hierarchically organized communities of a characteristic scale for a given hierarchical level. In this work, we demonstrate that the reality of scale-dependent community reorganization is convoluted with simultaneous processes of community splitting and merging, challenging the conventional understanding of community-scale adjustment. We provide a mathematical argument concerning the modularity function, the results from real-network analysis, and a simple network model for a comprehensive understanding of the nontrivial community reorganization process. The reorganization is characterized by a local drop in the number of communities as the resolution parameter varies. This study suggests a need for a paradigm shift in the study of network communities, which emphasizes the importance of considering scale-dependent reorganization to better understand the genuine structural organization of networks.