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We developed a new theory for hypergraph k-core percolation, showing it differs from factor graph percolation. This new model, crucial for understanding complex systems like supply chains and biological networks, offers distinct insights into network resilience.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Hypergraphs represent higher-order interactions, distinct from traditional networks.
  • Factor graphs offer a bipartite representation of hypergraphs.
  • Existing k-core percolation theories on factor graphs differ from hypergraph dynamics.

Purpose of the Study:

  • To formulate and analyze hypergraph k-core percolation theory.
  • To investigate the distinct percolation behaviors between hypergraphs and factor graphs.
  • To develop pruning processes to reconcile these differences.

Main Methods:

  • Formulation of hypergraph k-core percolation theory assuming hyperedge integrity requires all nodes to be intact.
  • Development of a message-passing theory for hypergraph k-core percolation.
  • Combination with critical phenomena theory for network analysis.
  • Definition of second-neighbor pruning processes acting on nodes or hyperedges.

Main Results:

  • Hypergraph k-core percolation shows significant differences compared to factor graph k-core percolation.
  • The proposed pruning processes on hypergraphs yield distinct percolation behaviors.
  • When pruning acts exclusively on hyperedges, the phase diagram simplifies to that of factor graph k-cores.

Conclusions:

  • Hypergraph k-core percolation is fundamentally different from factor graph percolation.
  • Second-neighbor pruning processes highlight these distinctions.
  • The study provides a unified framework for understanding percolation in higher-order networks.