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Conditional Entropy of Heat Diffusion on Temporal Networks
Samuel Koove · 2026-05-23 · via cs.LG updates on arXiv.org

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Abstract:Many complex systems can be modeled by temporal networks, whose organization often evolves through distinct structural phases. Detecting the change points that delimit these phases is both important and challenging. In this work, we extend the conditional entropy of heat diffusion from static graphs to temporal networks and study its properties. We provide an upper bound and explain how discrepancies from it arise from the presence of asymmetric temporal paths. Moreover, we show that this quantity is monotone in time, yielding an information-theoretic analog of the second law of thermodynamics for inhomogeneous diffusion on temporal networks. We then introduce a local version of conditional entropy, designed to probe diffusion over finite temporal windows, and show that it provides an informative signal for change-point detection in continuous-time temporal networks. We evaluate the proposed methodology on synthetic benchmarks, including comparative experiments with existing nonparametric baselines in the snapshot setting, and then apply it to a real-world temporal contact network from a French primary school. Finally, we show how to use detected change points to perform community detection on targeted sub-intervals, improving the quality and interpretability of the clustering results.
Subjects: Social and Information Networks (cs.SI); Statistical Mechanics (cond-mat.stat-mech); Information Theory (cs.IT); Machine Learning (cs.LG); Data Analysis, Statistics and Probability (physics.data-an)
MSC classes: 82C31 (Primary), 68T99, 60J27, 94C15 (Secondary)
Cite as: arXiv:2605.21514 [cs.SI]
  (or arXiv:2605.21514v1 [cs.SI] for this version)
  https://doi.org/10.48550/arXiv.2605.21514

arXiv-issued DOI via DataCite

Submission history

From: Samuel Koovely [view email]
[v1] Fri, 15 May 2026 10:47:44 UTC (1,134 KB)