Random hyperbolic graphs in $d+1$ dimensions

Abstract

We consider random hyperbolic graphs in hyperbolic spaces of any dimension $d+1\ge 2$. 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 $d\to \infty$. 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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Cited by in corpus (6)

• Detecting the ultra low dimensionality of real networks
• Growing hyperbolic networks beyond two dimensions: the generalised popularity-similarity optimisation model
• Greedy routing optimisation in hyperbolic networks
• Community detection robustness of graph neural networks
• The Shortest-Path distance on graphons
• $({\omega }_1,{\omega }_2)$-temporal random hyperbolic graphs