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Higher-Order Components Dictate Higher-Order Contagion Dynamics in Hypergraphs.

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The giant higher-order component (HOC) is essential for collective behavior in hypergraphs. Its presence is required for higher-order contagion to spread globally from a single seed.

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Area of Science:

  • Complex systems
  • Network science
  • Hypergraph theory

Background:

  • Collective behavior in networks relies on a giant component.
  • Hypergraphs possess higher-order components (HOCs), defined by shared nodes between hyperedges.
  • The role of giant HOCs in hypergraph collective behavior remains unclear.

Purpose of the Study:

  • To investigate the impact of the giant HOC on higher-order contagion dynamics.
  • To determine if the giant HOC is necessary for global contagion spread in hypergraphs.

Main Methods:

  • Analysis of higher-order contagion dynamics on real-world hypergraphs.
  • Utilizing synthetic random hypergraphs with tunable giant HOCs.
  • Analytical calculations of giant HOC properties.

Main Results:

  • The giant HOC fundamentally alters contagion outbreak patterns.
  • Global invasion of higher-order contagion requires the presence of the giant HOC.
  • Findings confirmed using synthetic hypergraph models.

Conclusions:

  • The giant HOC is a critical factor for collective behavior on hypergraphs.
  • Understanding giant HOCs is crucial for modeling contagion and information spread in complex systems.