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Nonmonotonic percolation threshold in correlated networks and hypergraphs

L. D. Valdez* and C. E. La Rocca

  • *Contact author: ldvaldes@mdp.edu.ar
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Phys. Rev. E 114, 014313 – Published 27 July, 2026

DOI: https://doi.org/10.1103/bvsj-7pmq

Abstract

We study the effect of assortative and disassortative mixing on the robustness of networks under random node failures. For ordinary (dyadic) networks, by using the generating function technique and stochastic simulations, we show that the relationship between the Pearson assortativity coefficient r and the percolation threshold pc is not always monotonic. More specifically, in certain regions of the parameter space of our model, moderately disassortative networks can be more fragile than either strongly disassortative or uncorrelated networks. We observe this nonmonotonic behavior for trimodal networks as well as for networks with Poisson and power-law degree distributions. We then extend our analysis to hypergraphs with correlations between node hyperdegree and hyperedge cardinality. For this case, we find that positively correlated hypergraphs tend to be more fragile than negatively correlated ones. Additionally, as in the dyadic case, the relationship between r and pc is nonmonotonic, and the most fragile configuration does not correspond to the most assortative hypergraph.

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Outline

Information

Phys. Rev. E 114, 014313– Published 27 July, 2026
  • Received 15 April 2026
  • Accepted 10 July 2026
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