Dynamics of cold random hyperbolic graphs with link persistence

Abstract

We consider and analyze a dynamic model of random hyperbolic graphs with link persistence. In the model, both connections and disconnections can be propagated from the current to the next snapshot with probability $\omega \in [0,1)$. Otherwise, with probability $1-\omega$, connections are reestablished according to the random hyperbolic graphs model. We show that while the persistence probability $\omega$ affects the averages of the contact and intercontact distributions, it does not affect the tails of these distributions, which decay as power laws with exponents that do not depend on $\omega$. We also consider examples of real temporal networks, and we show that the considered model can adequately reproduce several of their dynamical properties. Our results advance our understanding of the realistic modeling of temporal networks and of the effects of link persistence on temporal network properties.

14 pages, 9 figures. Generalizes the model in arXiv:1907.00073

References in corpus (9)

• Hyperbolic Geometry of Complex Networks
• Activity driven modeling of time varying networks
• Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
• Sustaining the Internet with Hyperbolic Mapping
• Contact patterns among high school students
• An infectious disease model on empirical networks of human contact: bridging the gap between dynamic network data and contact matrices
• Curvature and temperature of complex networks
• Persistence in Complex Systems
• Dynamics of hot random hyperbolic graphs

Cited by in corpus (1)

• $({\omega }_1,{\omega }_2)$-temporal random hyperbolic graphs