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Temporal percolation in activity-driven networks.

Michele Starnini1, Romualdo Pastor-Satorras1

  • 1Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary
This summary is machine-generated.

We analyzed temporal network percolation using the activity-driven network model. Our findings provide precise calculations for the percolation time, crucial for understanding network connectivity and epidemic spread.

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Area of Science:

  • Network Science
  • Statistical Physics
  • Complex Systems

Background:

  • Temporal networks exhibit dynamic connectivity, impacting information diffusion and system robustness.
  • Understanding the emergence of giant connected components in these networks is critical.
  • The activity-driven network model provides a framework for studying dynamic network behavior.

Purpose of the Study:

  • To investigate the temporal percolation properties of activity-driven networks.
  • To derive analytical expressions for the percolation time (Tp).
  • To explore the impact of degree correlations on percolation thresholds.

Main Methods:

  • Analytical framework based on mapping to hidden variables networks.
  • Utilizing generating function formalism for degree-uncorrelated networks.
  • Analyzing the general case of networks with degree correlations.
  • Numerical simulations to validate analytical predictions.

Main Results:

  • Expressions for percolation time (Tp) were derived for activity-driven networks.
  • Identified parameter regions where correlated thresholds converge to uncorrelated cases.
  • Analytical predictions were confirmed by numerical simulations.
  • Demonstrated a mapping between epidemic spreading (SIR model) and percolation.

Conclusions:

  • The study provides a robust analytical framework for temporal percolation in activity-driven networks.
  • The derived expressions for percolation time offer insights into network connectivity dynamics.
  • The mapping to epidemic spreading facilitates a deeper understanding of disease transmission on temporal networks.