Kaleidoscopic reorganization of network communities across different scales

TL;DR

This paper reveals that community structures in networks undergo complex reorganization across scales, involving simultaneous splitting and merging, challenging traditional hierarchical assumptions and suggesting a paradigm shift in network analysis.

Contribution

It introduces a mathematical framework and empirical analysis demonstrating nontrivial, scale-dependent community reorganization involving splitting and merging processes.

Findings

Community reorganization involves simultaneous splitting and merging.

Traditional hierarchical models are insufficient to describe real network communities.

Scale-dependent reorganization affects community detection and understanding.

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.