Clustering Time-Evolving Networks Using the Spatio-Temporal Graph Laplacian

TL;DR

This paper introduces a novel spectral clustering method for time-evolving graphs by extending the graph Laplacian with a spatio-temporal framework, enabling better analysis of dynamic community structures.

Contribution

It generalizes spectral clustering to dynamic graphs using a new spatio-temporal Laplacian based on canonical correlation analysis, connecting to dynamical systems theory.

Findings

Effective in capturing evolving community structures

Outperforms existing methods on benchmark graphs

Provides clear interpretation of cluster evolution

Abstract

Time-evolving graphs arise frequently when modeling complex dynamical systems such as social networks, traffic flow, and biological processes. Developing techniques to identify and analyze communities in these time-varying graph structures is an important challenge. In this work, we generalize existing spectral clustering algorithms from static to dynamic graphs using canonical correlation analysis (CCA) to capture the temporal evolution of clusters. Based on this extended canonical correlation framework, we define the spatio-temporal graph Laplacian and investigate its spectral properties. We connect these concepts to dynamical systems theory via transfer operators, and illustrate the advantages of our method on benchmark graphs by comparison with existing methods. We show that the spatio-temporal graph Laplacian allows for a clear interpretation of cluster structure evolution over time for directed and undirected graphs.