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This study introduces a dynamic model for random hyperbolic graphs incorporating link persistence. The model shows that while link persistence affects average network behavior, power-law tails in contact distributions remain independent of persistence probability.

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Area of Science:

  • Network Science
  • Complex Systems
  • Statistical Physics

Background:

  • Temporal networks exhibit dynamic changes in connections over time.
  • Random hyperbolic graphs provide a framework for modeling complex network structures.
  • Link persistence, the tendency for connections to endure, is a key factor in network dynamics.

Purpose of the Study:

  • To analyze a dynamic model of random hyperbolic graphs with link persistence.
  • To investigate the impact of link persistence on network properties, particularly contact and intercontact distributions.
  • To evaluate the model's ability to replicate real-world temporal network dynamics.

Main Methods:

  • Development of a dynamic random hyperbolic graph model with a persistence probability parameter (ω).
  • Analytical investigation of contact and intercontact distributions under varying persistence probabilities.
  • Comparison of model-generated network properties with empirical data from real temporal networks.

Main Results:

  • Link persistence (ω) influences the average values of contact and intercontact distributions.
  • The power-law decay of the tails of these distributions is independent of the persistence probability (ω).
  • The proposed model effectively reproduces several dynamical properties observed in real temporal networks.

Conclusions:

  • The dynamic random hyperbolic graph model with link persistence offers a realistic approach to network modeling.
  • Link persistence significantly impacts average network behavior but not the fundamental power-law scaling in distribution tails.
  • The findings enhance the understanding of temporal network dynamics and the role of enduring connections.