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Published on: March 18, 2019
Random hyperbolic graphs in d+1 dimensions
Gabriel Budel1, Maksim Kitsak1, Rodrigo Aldecoa2,3
1Faculty of Electrical Engineering, Mathematics and Computer Science, <a href="https://ror.org/02e2c7k09">Delft University of Technology</a>, 2628 CD, Delft, the Netherlands.
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.
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