# A temporal graph dissimilarity measure capturing epidemic spreading behavior

arXiv: https://arxiv.org/abs/2610.16456 · HTML: https://mlsanity.com/paper/2610.16456/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 68 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 26 of 26)

- [Graph Neural Networks for temporal graphs: State of the art, open challenges, and opportunities](https://mlsanity.com/paper/2302.01018/) (2023)
- [Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys](https://mlsanity.com/paper/1506.03645/) (2015)
- [Spectral redemption: clustering sparse networks](https://mlsanity.com/paper/1306.5550/) (2013)
- [NetLSD: Hearing the Shape of a Graph](https://mlsanity.com/paper/1805.10712/) (2018)
- [Metrics for Graph Comparison: A Practitioner's Guide](https://mlsanity.com/paper/1904.07414/) (2019)
- [A survey of dynamic graph neural networks](https://mlsanity.com/paper/2404.18211/) (2024)
- [DELTACON: A Principled Massive-Graph Similarity Function](https://mlsanity.com/paper/1304.4657/) (2013)
- [Memory in network flows and its effects on spreading dynamics and community detection](https://mlsanity.com/paper/1305.4807/) (2013)
- [Contact patterns among high school students](https://mlsanity.com/paper/1409.5318/) (2014)
- [Can co-location be used as a proxy for face-to-face contacts?](https://mlsanity.com/paper/1712.06346/) (2017)
- [DYMOND: DYnamic MOtif-NoDes Network Generative Model](https://mlsanity.com/paper/2308.00770/) (2023)
- [A Framework for Evaluating Epidemic Forecasts](https://mlsanity.com/paper/1703.09828/) (2017)
- [An information-theoretic, all-scales approach to comparing networks](https://mlsanity.com/paper/1804.03665/) (2018)
- [Measuring large-scale social networks with high resolution](https://mlsanity.com/paper/1401.7233/) (2014)
- [A unified framework for spectral clustering in sparse graphs](https://mlsanity.com/paper/2003.09198/) (2020)
- [A Primer on Temporal Graph Learning](https://mlsanity.com/paper/2401.03988/) (2024)
- [Automatic feature selection and weighting in molecular systems using Differentiable Information Imbalance](https://mlsanity.com/paper/2411.00851/) (2024)
- [How memory generates heterogeneous dynamics in temporal networks](https://mlsanity.com/paper/1409.1805/) (2014)
- [An embedding-based distance for temporal graphs](https://mlsanity.com/paper/2401.12843/) (2024)
- [Time varying networks and the weakness of strong ties](https://mlsanity.com/paper/1303.5966/) (2013)
- [Bursty Human Dynamics](https://mlsanity.com/paper/1803.02580/) (2018)
- [Quantitative Evaluation of Snapshot Graphs for the Analysis of Temporal Networks](https://mlsanity.com/paper/2110.13466/) (2021)
- [Generating fine-grained surrogate temporal networks](https://mlsanity.com/paper/2205.08820/) (2022)
- [Learning distributed representations with efficient SoftMax normalization](https://mlsanity.com/paper/2303.17475/) (2023)
- [Compensating for population sampling in simulations of epidemic spread on temporal contact networks](https://mlsanity.com/paper/1503.04066/) (2015)
- [Modeling memory in time-respecting paths on temporal networks](https://mlsanity.com/paper/2511.17108/) (2025)

## Abstract (arXiv)

Comparing temporal networks is a challenging problem in network analysis. Commonly adopted methods compare structural properties of temporal graphs and can be highly sensitive to the pre-selected features. However, temporal networks are the support of dynamical processes, and a process may take place in statistically indistinguishable ways on structurally different temporal graphs. In particular, a dissimilarity measure that compares temporal graphs based on how spreading processes unfold on them is highly desirable. In this work, we first define the Time-Shift DTW, a dissimilarity between epidemic curves that accounts for both differences in their shape and temporal shifts. We then introduce Epidemic-Aware Temporal Graph Dissimilarity (EATGD), a deterministic and differentiable dissimilarity between temporal graphs that combines an embedding-based temporal graph distance with a set of topological and temporal features. Its parameters are calibrated using stochastic SIR simulations to maximize the correlation with the Time-Shift DTW, after which graph comparisons require no further epidemic simulations. Using empirical human proximity networks from the SocioPatterns collaboration and synthetic temporal graphs, we show that EATGD captures epidemic-based graph dissimilarity and generalizes across heterogeneous network settings. Its differentiability and computational efficiency make EATGD suitable for integration into machine-learning pipelines and provide a potential loss function for training generative models to reproduce epidemic dynamics without requiring an exact reconstruction of fine-grained network structure.