Filip Blašković | Searcharxiv

arXiv2026

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

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.

cs.SI↗

arXiv2025

Random walk based snapshot clustering for detecting community dynamics in temporal networks

The evolution of many dynamical systems that describe relationships or interactions between objects can be effectively modeled by temporal networks, which are typically represented as a sequence of static network snapshots. In this paper, we introduce a novel random walk-based approach that can identify clusters of time-snapshots in which network community structures are stable. This allows us to detect significant structural shifts over time, such as the splitting or merging of communities or their births and deaths. We also provide a low-dimensional representation of entire snapshots, placing those with similar community structure close to each other in the feature space. To validate our approach, we develop an agent-based algorithm that generates synthetic datasets with the desired characteristic properties, enabling thorough testing and benchmarking. We further demonstrate the effectiveness and broad applicability of our technique by testing it on various social dynamics models and real-world datasets and comparing its performance to several state-of-the-art algorithms. Our findings highlight the strength of our approach to correctly capture and analyze the dynamics of complex systems.

cs.SI↗