Random hyperbolic graphs in 𝑑+1 dimensions

Gabriel Budel, Maksim Kitsak, Rodrigo Aldecoa, Konstantin Zuev, Dmitri Krioukov
Physical Review
E 109, 054131 (2024)
May 30, 2024


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.

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