Abstract
Empirical complex systems can be characterized not only by pairwise interactions, but also by higher-order (group) interactions influencing collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks’ apparent superior descriptive power—compared to classical pairwise networks—comes with a much increased model complexity and computational cost, challenging their application. Consequently, it is of paramount importance to establish a quantitative method to determine when such a modeling framework is advantageous with respect to pairwise models, and to which extent it provides a valuable description of empirical systems. Here, we propose an information-theoretic framework, accounting for how structures affect diffusion behaviors, quantifying the entropic cost and distinguishability of higher-order interactions to assess their reducibility to lower-order structures while preserving relevant functional information. Empirical analyses indicate that some systems retain essential higher-order structure, whereas in some technological and biological networks it collapses to pairwise interactions. With controlled randomization procedures, we investigate the role of nestedness and degree heterogeneity in this reducibility process. Our findings contribute to ongoing efforts to minimize the dimensionality of models for complex systems.
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Data availability
All data is publicly available from XGI-data: https://zenodo.org/communities/xgi/about.
Code availability
Code for reproducing our results is available online from the repository https://github.com/maximelucas/hypergraph_reducibility and on Zenodo https://doi.org/10.5281/zenodo.1783306072. It uses the XGI package26.
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Acknowledgements
M.L. thanks Marco Nurisso for useful feedback on the manuscript and Nicholas Landry for discussions about the configuration model and his publicly available implementations of it and of the simplicial fraction measure. M.L. is a Postdoctoral Researcher of the Fonds de la Recherche Scientifique-FNRS. F.B. and L.G. acknowledge support from the Air Force Office of Scientific Research under award number FA8655-22-1-7025. F.B. acknowledges support from the Austrian Science Fund (FWF) through projects 10.55776/PAT1052824 and 10.55776/PAT1652425. L.G. acknowledges support from the Villum Foundation (project no. 57396) at the University of Copenhagen. M.D.D acknowledge MUR funding within the FIS (DD n. 1219 31-07-2023) Project no. FIS00000158 (CUP C53C23000660001).
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All authors designed the study. M.L., L.G., and A.G. performed the theoretical analysis. M.L. and L.G. performed the numerical simulations. All authors discussed the results. M.L. wrote the original draft and all authors reviewed and edited it. F.B. and M.D.D. supervised the project.
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Lucas, M., Gallo, L., Ghavasieh, A. et al. Reducibility of higher-order networks from dynamics. Nat Commun (2026). https://doi.org/10.1038/s41467-025-68273-4
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DOI: https://doi.org/10.1038/s41467-025-68273-4
