Spectral clustering of time-evolving networks using spatio-temporal random walks
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.
Versions
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BibTeX
@misc{blaskovic2026spectral,
title = {{Spectral clustering of time-evolving networks using spatio-temporal random walks}},
author = {Filip Blašković and Tim O. F. Conrad and Stefan Klus and Nataša Djurdjevac Conrad},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.27850},
eprint = {2606.27850},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.27850},
}
RIS
TY - UNPB
TI - Spectral clustering of time-evolving networks using spatio-temporal random walks
AU - Filip Blašković
AU - Tim O. F. Conrad
AU - Stefan Klus
AU - Nataša Djurdjevac Conrad
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2606.27850
UR - https://arxiv.org/abs/2606.27850
AB - 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.
ER -