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Directed higher-order networks capture complex system interactions. This study introduces a percolation model to assess their robustness, finding that network heterogeneity weakens resilience while higher-order edges enhance it.

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Area of Science:

  • Complex Systems Science
  • Network Science
  • Statistical Physics

Background:

  • Pairwise interactions are insufficient for complex systems like social and biological networks.
  • Directed higher-order networks explicitly encode multinode interactions, revealing rich critical phenomena.
  • The robustness of directed higher-order networks remains under-explored.

Purpose of the Study:

  • To propose a theoretical percolation model for analyzing the robustness of directed higher-order networks.
  • To investigate how network properties influence robustness and critical phenomena.
  • To provide a theoretical framework for predicting network behavior under attack or failure.

Main Methods:

  • Developed a theoretical percolation model for directed higher-order networks.
  • Employed Monte Carlo simulations on artificial and real-world network data.
  • Analyzed the size of giant connected components and percolation thresholds.

Main Results:

  • Percolation thresholds are significantly influenced by network heterogeneity, specifically in hyperdegree distribution and hyperedge cardinality.
  • Increased heterogeneity in hyperdegree or hyperedge cardinality distributions weakens network robustness.
  • The presence of higher-order directed edges was found to enhance system robustness.

Conclusions:

  • The proposed theoretical model accurately predicts percolation behavior in directed higher-order networks.
  • Network heterogeneity is a critical factor determining the vulnerability of complex systems.
  • Understanding higher-order interactions is crucial for designing robust complex systems.