Multi-set spectral clustering of time-evolving networks using the supra-Laplacian

TL;DR

This paper introduces a spectral clustering method for time-evolving networks using the supra-Laplacian, effectively capturing dynamic community structures and outperforming existing algorithms like Leiden.

Contribution

It develops a novel spectral clustering framework based on the supra-Laplacian for multiplex and non-multiplex networks, with specialized post-processing techniques.

Findings

Outperforms Leiden algorithm in dynamic network clustering

Effectively detects evolving communities in time-varying networks

Quantifies increasing political polarization over time

Abstract

Complex time-varying networks are prominent models for a wide variety of spatiotemporal phenomena. The functioning of networks depends crucially on their connectivity, yet reliable techniques for learning communities in time-evolving networks remain elusive. We adapt successful spectral techniques from continuous-time dynamics on manifolds to the graph setting to fill this gap. We consider the supra-Laplacian for graphs and develop a spectral theory to underpin the corresponding algorithmic realisations. We develop spectral clustering approaches for both multiplex and non-multiplex networks, based on the eigenvectors of the supra-Laplacian and specialised Sparse EigenBasis Approximation (SEBA) post-processing of these eigenvectors. We demonstrate that our approach can outperform the Leiden algorithm applied both in spacetime and layer-by-layer, and we analyse voting data from the US senate (where senators come and go as congresses evolve) to quantify increasing polarisation in time.