# Conditional Entropy of Heat Diffusion on Temporal Networks

arXiv: https://arxiv.org/abs/2605.21514 · HTML: https://mlsanity.com/paper/2605.21514/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 58 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 22 of 22)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning](https://mlsanity.com/paper/2007.16002/) (2020)
- [Learning heat diffusion graphs](https://mlsanity.com/paper/1611.01456/) (2016)
- [Statistical clustering of temporal networks through a dynamic stochastic block model](https://mlsanity.com/paper/1506.07464/) (2015)
- [Random walks and diffusion on networks](https://mlsanity.com/paper/1612.03281/) (2016)
- [Laplacian Change Point Detection for Dynamic Graphs](https://mlsanity.com/paper/2007.01229/) (2020)
- [Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks](https://mlsanity.com/paper/1502.04381/) (2015)
- [Stream Graphs and Link Streams for the Modeling of Interactions over Time](https://mlsanity.com/paper/1710.04073/) (2017)
- [Fast Change Point Detection on Dynamic Social Networks](https://mlsanity.com/paper/1705.07325/) (2017)
- [Change Point Estimation in a Dynamic Stochastic Block Model](https://mlsanity.com/paper/1812.03090/) (2018)
- [Flow stability for dynamic community detection](https://mlsanity.com/paper/2101.06131/) (2021)
- [Laplacian Change Point Detection for Single and Multi-view Dynamic Graphs](https://mlsanity.com/paper/2302.01204/) (2023)
- [Change Point Detection in Correlation Networks](https://mlsanity.com/paper/1410.0761/) (2014)
- [Graph similarity learning for change-point detection in dynamic networks](https://mlsanity.com/paper/2203.15470/) (2022)
- [Thermodynamic characterization of networks using graph polynomials](https://mlsanity.com/paper/1512.01418/) (2015)
- [Broken detailed balance and entropy production in directed networks](https://mlsanity.com/paper/2402.19157/) (2024)
- [Scalar embedding of temporal network trajectories](https://mlsanity.com/paper/2412.02715/) (2024)
- [Laplacian paths in complex networks: information core emerges from entropic transitions](https://mlsanity.com/paper/2202.06669/) (2022)
- [Analysing Multiscale Clusterings with Persistent Homology](https://mlsanity.com/paper/2305.04281/) (2023)
- [Random walk based snapshot clustering for detecting community dynamics in temporal networks](https://mlsanity.com/paper/2412.12187/) (2024)
- [Challenges in Community Discovery on Temporal Networks](https://mlsanity.com/paper/1907.11435/) (2019)
- [MCbiF: Measuring Topological Autocorrelation in Multiscale Clusterings via 2-Parameter Persistent Homology](https://mlsanity.com/paper/2510.14710/) (2025)

## Abstract (arXiv)

Diffusion-based information-theoretic approaches provide new theoretical and practical tools to study complex networks. So far, they have not been generalized to temporal networks. In this work, we show that common entropic measures based on modeling diffusion on graphs, such as the entropy rate and the spectral entropy, do not generalize straightforwardly to temporal networks due to the process's non-stationarity and temporal asymmetries. Instead, we propose the conditional entropy of heat diffusion as an entropic measure for continuous-time temporal networks and study its properties. 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 provide an upper bound and suggest a lower bound on its evolution and explain how discrepancies from it arise due to asymmetric temporal paths. 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. Finally, we show how to use detected change points to guide community detection on targeted sub-intervals, improving the quality and interpretability of the clustering results.