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Hot random hyperbolic graphs exhibit unrealistic power-law decays for intercontact durations, making them unsuitable for modeling real temporal networks. This contrasts with cold random hyperbolic graphs and suggests limitations for the configuration model as a null temporal network model.

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Area of Science:

  • Complex Networks
  • Statistical Physics
  • Network Dynamics

Background:

  • Random hyperbolic graphs are a class of complex networks with rich structural properties.
  • Understanding temporal network dynamics is crucial for modeling real-world systems.

Purpose of the Study:

  • To derive the dynamical properties, specifically contact and intercontact duration distributions, of random hyperbolic graphs in the hot regime (T>1).
  • To assess the adequacy of hot random hyperbolic graphs as models for real temporal networks.

Main Methods:

  • Derivation of contact and intercontact duration distributions using mathematical analysis.
  • Analysis of power-law and exponential decay behaviors based on network temperature (T) and degree distribution properties.
  • Comparison with cold random hyperbolic graphs (T<1) and the configuration model.

Main Results:

  • In the hot regime, contact distributions exhibit power-law decays (exponent 2+T>3) for long durations and exponential-like decays for short durations.
  • Intercontact distributions show unrealistic power-law decays (exponent <1) for T∈(1,2) and linear decays for T>2.
  • These dynamics are largely independent of the degree distribution, provided certain moment conditions are met.

Conclusions:

  • Hot random hyperbolic graphs, despite exhibiting power-law distributions, are inadequate for modeling real temporal networks due to unrealistic intercontact duration exponents.
  • The findings highlight the importance of network temperature in temporal network modeling.
  • The configuration model is also suggested to be an inadequate null temporal network model in this context.