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Percolation and Topological Properties of Temporal Higher-Order Networks.

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We introduce a new framework to model complex systems with temporal higher-order interactions. This approach accurately estimates percolation times, revealing underestimations when higher-order structures are ignored in social networks.

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Area of Science:

  • Complex Systems Science
  • Network Science
  • Statistical Physics

Background:

  • Many complex systems feature temporal non-pairwise interactions, necessitating advanced modeling techniques.
  • Higher-order network models provide a framework for representing these intricate relationships.
  • Understanding temporal dynamics and topological properties is crucial for characterizing system behavior.

Purpose of the Study:

  • To develop a hidden variable formalism for the analytical characterization of higher-order network models.
  • To apply this framework to a temporal higher-order activity-driven model.
  • To analytically estimate percolation times in both synthetic and empirical hypergraphs.

Main Methods:

  • Development of a hidden variable formalism for general higher-order network models.
  • Application to a temporal higher-order activity-driven model.
  • Derivation of analytical expressions for topological properties and percolation times.

Main Results:

  • Analytical expressions for topological properties of time-integrated hypergraphs were derived.
  • Estimates for percolation times of uncorrelated and correlated hypergraphs were obtained.
  • Significant underestimation of percolation time in empirical social networks was quantified when higher-order effects were neglected.

Conclusions:

  • The proposed hidden variable formalism effectively characterizes temporal higher-order network models.
  • The framework provides accurate analytical estimates for percolation times.
  • Neglecting the higher-order nature of interactions leads to underestimation of critical phenomena like percolation in real-world systems.