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Disentangling the Role of Heterogeneity and Hyperedge Overlap in Explosive Contagion on Higher-Order Networks

Federico Malizia1,*, Andrés Guzmán1, Iacopo Iacopini1,2, and István Z. Kiss1,3,†

  • *Contact author: maliziaf@ceu.edu
  • †Contact author: istvan.kiss@nulondon.ac.uk
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Phys. Rev. Lett. 135, 207401 – Published 10 November, 2025

DOI: https://doi.org/10.1103/z3d5-94zb

Abstract

We introduce group-based compartmental modeling (GBCM), a mean-field framework for irreversible contagion in higher-order networks that captures structural heterogeneity and correlations across group sizes. Validated through numerical simulations, GBCM analytically disentangles the role of each interaction order to the global epidemic dynamics, revealing how heterogeneity and inter-order correlations jointly shape the onset of outbreaks and the emergence of explosive dynamics. Crucially, we show that inter-order correlations drive the system along distinct pathways to explosive contagion—emerging universally across both irreversible and reversible spreading processes.

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Phys. Rev. Lett. 135, 207401– Published 10 November, 2025
  • Received 3 February 2025
  • Revised 16 May 2025
  • Accepted 2 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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