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Area of Science:

  • Complex systems
  • Network science
  • Mathematical modeling

Background:

  • Complex social systems are often represented by hypergraphs, where hyperedges denote group interactions.
  • Nestedness, a hierarchical structure within hypergraphs, describes hyperedges contained within larger ones.
  • The impact of this hierarchical nestedness on system dynamics remains largely unexplored.

Purpose of the Study:

  • To propose a random nested-hypergraph model with adjustable nestedness.
  • To investigate the effects of hyperedge nestedness on a higher-order susceptible-infected-susceptible (SIS) process.
  • To develop an analytical framework for understanding these dynamics.

Main Methods:

  • Development of a random nested-hypergraph model.
  • Application of an analytical framework termed the facet approximation.
  • Validation through Monte Carlo simulations.

Main Results:

  • The facet approximation provides accurate predictions for the steady-state fraction of infected nodes.
  • Hyperedge nestedness significantly influences the phase diagram of the SIS process.
  • Analytical results are corroborated by simulation data.

Conclusions:

  • The hierarchical structure of nestedness in hypergraphs is a crucial factor in complex system dynamics.
  • The proposed model and analytical framework offer a novel approach to studying higher-order interactions.
  • Understanding nestedness is key to predicting and managing disease spread in social systems.