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arXiv · 2610.16456

A temporal graph dissimilarity measure capturing epidemic spreading behavior

Salvatore Freni·Lorenzo Dall'Amico·Francesca Pistilli·Alain Barrat·Tatiana Tommasi·Ciro Cattuto
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Abstract

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.

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Salvatore Freni, Lorenzo Dall'Amico, Francesca Pistilli, Alain Barrat, Tatiana Tommasi, Ciro Cattuto. 2026-10-12. A temporal graph dissimilarity measure capturing epidemic spreading behavior. https://arxiv.org/abs/2610.16456

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