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)
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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+1ā‰„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 dā†’āˆž. 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.