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This study introduces a generalized bootstrap percolation model on hypergraphs to understand network robustness against cascading failures. Higher-order interactions significantly influence network behavior, affecting the giant active component

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Bootstrap percolation models analyze network robustness against cascading failures.
  • Real-world data reveals higher-order interactions beyond pairwise relationships, often modeled by hypergraphs.
  • Existing models often overlook these higher-order interactions.

Purpose of the Study:

  • To propose and analyze a generalized bootstrap percolation model on hypergraphs.
  • To investigate the impact of higher-order interactions on network robustness and phase transitions.
  • To understand how infection thresholds and the proportion of higher-order edges affect network behavior.

Main Methods:

  • Development of a generalized bootstrap percolation model incorporating higher-order interactions via hypergraphs.
  • Numerical simulations to observe network behavior under varying conditions.
  • Theoretical analysis to derive percolation thresholds and characterize phase transitions.

Main Results:

  • The bootstrap percolation threshold and phase transition type are dependent on the infection threshold and the proportion of higher-order edges.
  • A significant infection threshold leads to continuous growth of the giant active component (GAC) with increasing occupation probability.
  • A small infection threshold causes the GAC size to transition from continuous to discontinuous growth as initial activation probability increases.
  • Increasing higher-order edges reduces the percolation threshold, enhancing network robustness.
  • Higher-order edges increase activation opportunities, shifting GAC growth from continuous to discontinuous.

Conclusions:

  • The generalized hypergraph bootstrap percolation model effectively captures the influence of higher-order interactions on network robustness.
  • Network robustness is enhanced by increasing the proportion of higher-order edges.
  • The interplay between infection threshold and higher-order edge proportion dictates the nature of phase transitions in these networks.