Dynamics of cold random hyperbolic graphs with link persistence

TL;DR

This paper analyzes a dynamic model of random hyperbolic graphs with link persistence, showing how persistence influences contact distributions but not their tail behavior, and demonstrates the model's relevance to real temporal networks.

Contribution

It introduces a model capturing link persistence in hyperbolic graphs and analyzes its impact on network dynamics and properties, aligning with real-world temporal networks.

Findings

Persistence affects average contact distributions.

Tail decay remains unaffected by persistence.

Model reproduces properties of real temporal networks.

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.