Conditional Entropy of Heat Diffusion on Temporal Networks

2026-05-15

AI Summary

This study addresses the problem of change-point detection for structural phase transitions in temporal networks by introducing, for the first time, a theoretical framework based on heat diffusion conditional entropy, which reveals its intrinsic connection to asymmetric temporal paths. Building upon this framework, the authors propose a locally defined conditional entropy measure that exhibits temporal monotonicity, effectively capturing diffusion dynamics within finite time windows. Leveraging this measure, they develop an information-theoretic, non-parametric change-point detection method. Experiments on both synthetic data and a real-world contact network from a French primary school demonstrate that the proposed approach significantly outperforms existing non-parametric baselines, and that the detected change points substantially enhance the quality and interpretability of community structures identified in the resulting subintervals.

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.

Problem

• temporal networks
• change-point detection
• structural phases
• heat diffusion
• conditional entropy

Innovation

• conditional entropy
• heat diffusion
• temporal networks
• change-point detection
• community detection