Random hyperbolic graphs in d+1 dimensions

Journal article (2024)

Authors

G.J.A. Budel Network Architectures and Services - EEMCS
M.A. Kitsak Network Architectures and Services - EEMCS
Rodrigo Aldecoa Northeastern University
Konstantin Zuev California Institute of Technology Division of Engineering and Applied Science
Dmitri Krioukov Northeastern University
Research Group
Network Architectures and Services (EEMCS) (TU Delft)
More Info
expand_more

Published Date

2024

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Quantum & Computer Engineering

Research Group

Network Architectures and Services

Abstract

We consider random hyperbolic graphs in hyperbolic spaces of any dimension d+1≥2. We present a rescaling of model parameters that casts the random hyperbolic graph model of any dimension to a unified mathematical framework, leaving the degree distribution invariant with respect to the dimension. Unlike the degree distribution, clustering does depend on the dimension, decreasing to 0 at d→∞. We analyze all of the other limiting regimes of the model, and we release a software package that generates random hyperbolic graphs and their limits in hyperbolic spaces of any dimension.