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arXiv · 2010.12303

Random hyperbolic graphs in $d+1$ dimensions

Gabriel Budel·Maksim Kitsak·Rodrigo Aldecoa·Konstantin Zuev·Dmitri Krioukov
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Abstract

We consider random hyperbolic graphs in hyperbolic spaces of any dimension $d+1\geq 2$. 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 $d \rightarrow \infty$. 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.

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Gabriel Budel, Maksim Kitsak, Rodrigo Aldecoa, Konstantin Zuev, Dmitri Krioukov. 2020-10-23. Random hyperbolic graphs in $d+1$ dimensions. https://doi.org/10.1103/physreve.109.054131

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