  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.
