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arXiv · 2409.11984

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

Gary Froyland·Manu Kalia·Péter Koltai
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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.

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Gary Froyland, Manu Kalia, Péter Koltai. 2024-09-18. Multi-set spectral clustering of time-evolving networks using the supra-Laplacian. https://arxiv.org/abs/2409.11984

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