Temporal graph measure reveals how epidemics spread differently
A temporal graph dissimilarity measure capturing epidemic spreading behavior
Social and Information NetworksMachine Learning
Summary
Comparing how networks change over time is hard, especially when trying to understand how diseases spread through them. The authors created a way to measure differences between time-varying networks based on the patterns of an epidemic spreading on them, not just their structure. They tested their measure on real and simulated contact networks and showed it can identify meaningful differences related to disease spread without running new simulations every time. This method is fast, smooth to work with mathematically, and can be used in machine learning to help model or generate networks that behave like real ones during outbreaks.
What this means in practice
- •For epidemic modeling teams: Compare temporal contact networks based on how diseases may spread on them without rerunning expensive simulations.
- •For machine learning engineers: Incorporate a differentiable graph distance capturing epidemic behavior as a loss function to train models generating realistic temporal networks.
Authors
Salvatore Freni, Lorenzo Dall'Amico, Francesca Pistilli, Alain Barrat, Tatiana Tommasi, Ciro Cattuto
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.