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We analyzed forward reachable sets (FRS) in dynamic networks, finding their growth depends on network structure and edge duration. This work offers insights into epidemic modeling and network dynamics.

Keywords:
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Area of Science:

  • Network Science
  • Complex Systems
  • Mathematical Biology

Background:

  • Formal analysis of emergent structural properties in dynamic networks remains an underdeveloped area.
  • Forward reachable sets (FRS) are a key measure for understanding information propagation and connectivity in dynamic networks.
  • Existing methods often do not account for temporal dynamics or detailed network structures.

Purpose of the Study:

  • To formally analyze the emergent structural properties of dynamic networks using forward reachable sets (FRS).
  • To investigate the influence of degree distribution and edge duration on FRS growth in temporal networks.
  • To provide a theoretical framework applicable to epidemic modeling and other dynamic network processes.

Main Methods:

  • Developed a stochastic framework to derive closed-form expressions for the mean and variance of FRS exponential growth rates.
  • Incorporated both edge and node dynamics within the temporal network model.
  • Utilized simulation and approximation to explore finite population effects and variations across degree distributions (Poisson, Bernoulli).

Main Results:

  • Derived closed-form expressions for the growth rate of FRS in temporal networks with edge and node dynamics.
  • Identified thresholds for FRS growth in networks exhibiting node dynamics.
  • Demonstrated how FRS properties are influenced by edge duration and cross-sectional degree distributions.

Conclusions:

  • The study provides a robust theoretical foundation for analyzing FRS in dynamic networks.
  • Findings offer a direct link to epidemic modeling, where FRS size serves as an upper bound for epidemic spread.
  • The derived mathematical framework enhances understanding of network structure-dynamics interplay.