Conditional Entropy of Heat Diffusion on Temporal Networks

TL;DR

This paper extends the concept of conditional entropy of heat diffusion to temporal networks, providing a new information-theoretic approach for change-point detection and community analysis in evolving complex systems.

Contribution

It introduces a novel temporal conditional entropy measure, analyzes its properties, and demonstrates its effectiveness for change-point detection and community detection in real-world networks.

Findings

The proposed entropy measure is monotone in time, analogous to the second law of thermodynamics.

The local entropy variant effectively detects change points in continuous-time networks.

Application to a real-world school contact network shows improved community detection.

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.