Random hyperbolic graphs in d+1 dimensions
G.J.A. Budel (TU Delft - Network Architectures and Services)
Maksim Kitsak (TU Delft - Network Architectures and Services)
Rodrigo Aldecoa (Northeastern University)
Konstantin Zuev (California Institute of Technology Division of Engineering and Applied Science)
Dmitri Krioukov (Northeastern University)
More Info
expand_more
Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.
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.
help_outline