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Percolation in random hypergraphs with anchor nodes.

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Anchor nodes unify hypergraph percolation processes. Their removal impacts hyperedge existence, influencing phase transitions from second-order to higher-order, crucial for understanding network robustness.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Hypergraph Theory

Background:

  • Hypergraph percolation is crucial for understanding complex systems.
  • Existing models lack a unified framework for different percolation processes.
  • Anchor nodes offer a novel approach to unify and analyze these processes.

Purpose of the Study:

  • Introduce and define anchor nodes in hypergraphs.
  • Develop a unified analytical framework for hypergraph percolation.
  • Investigate the impact of anchor nodes on percolation thresholds and phase transitions.

Main Methods:

  • Utilize a bipartite factor graph representation.
  • Employ message-passing theory for analytical calculations.
  • Analyze percolation thresholds, critical exponents, and cluster sizes.

Main Results:

  • Anchor nodes unify distinct hypergraph percolation models.
  • Heterogeneous hypergraphs show increased sensitivity to anchor nodes.
  • Anchor node presence dictates phase transitions (second-order vs. higher-order).
  • Crossover phenomena emerge based on anchor node fraction and hyperedge cardinality.

Conclusions:

  • Anchor nodes provide a versatile framework for hypergraph percolation.
  • Hypergraph robustness is mediated by anchor nodes in multiplex networks.
  • Findings offer insights into network structure and phase transitions.