Spectral clustering of time-evolving networks using spatio-temporal random walks

2026-06-26

AI Summary

This study addresses the problem of identifying and tracking dynamic community structures in temporally evolving networks. It proposes a unified framework based on multi-view canonical correlation analysis (mCCA), which constructs time-reversible random walks on an extended spatiotemporal network and applies spectral analysis to the associated transition operator. Communities are characterized as metastable states of the underlying dynamical process, effectively distinguishing genuine structural features from artifacts induced by snapshot coupling. By integrating spatiotemporal modeling, spectral clustering, and model-order reduction, the method accurately captures community evolution while significantly improving computational efficiency.

Abstract

Temporal (or time-evolving) networks provide a natural framework for modeling complex systems with time-dependent interactions, where understanding the evolution of community structures is a central challenge. While random walk-based approaches to community detection in static networks are well established through the spectral analysis of associated transfer operators, extending these ideas to temporal networks is nontrivial due to the inherent time-dependence of the underlying dynamics. In this work, we develop a general framework for community detection in temporal networks that is based on multi-view canonical correlation analysis (mCCA). We show that the proposed formulation admits a spectral characterization via a time-reversible random walk on an augmented space-time network, providing a clear dynamical interpretation of temporal communities as metastable structures of the process. Furthermore, we analyze key spectral properties of the resulting transfer operators and the interplay between spatial and temporal effects, which allows us to distinguish between structural features and artifacts induced by the snapshot coupling. Finally, we derive a reduced-order model, which preserves the essential spectral properties while significantly improving computational efficiency. We show that the proposed approach effectively detects communities in temporal networks and captures their evolution.

Problem

• temporal networks
• community detection
• time-evolving networks
• spectral clustering
• community evolution

Innovation

• temporal networks
• spectral clustering
• spatio-temporal random walks
• multi-view CCA
• metastable communities