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.

arXiv comment14 pages, 9 figures. Generalizes the model in arXiv:1907.00073

References in corpus (28)

• Hyperbolic Geometry of Complex Networks
• High-resolution measurements of face-to-face contact patterns in a primary school
• Activity driven modeling of time varying networks
• Small But Slow World: How Network Topology and Burstiness Slow Down Spreading
• Popularity versus Similarity in Growing Networks
• Contact patterns in a high school: a comparison between data collected using wearable sensors, contact diaries and friendship surveys
• Sustaining the Internet with Hyperbolic Mapping
• Class of correlated random networks with hidden variables
• Impact of non-Poisson activity patterns on spreading processes
• Contact patterns among high school students
• Network Mapping by Replaying Hyperbolic Growth
• Random graph models for dynamic networks
• Hidden geometric correlations in real multiplex networks
• 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
• Network Geometry Inference using Common Neighbors
• Predictability of conversation partners
• Epidemic Spreading on Activity-Driven Networks with Attractiveness
• Persistence in Complex Systems
• Navigable maps of structural brain networks across species
• Activity clocks: spreading dynamics on temporal networks of human contact
• Small worlds and clustering in spatial networks
• Similarity forces and recurrent components in human face-to-face interaction networks
• Link persistence and conditional distances in multiplex networks
• Latent geometry and dynamics of proximity networks
• Dynamic Hidden-Variable Network Models
• Hyperbolic Mapping of Human Proximity Networks
• Dynamics of hot random hyperbolic graphs

Cited by in corpus (1)

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