  Over the last decade, random hyperbolic graphs have proved successful in
providing geometric explanations for many key properties of real-world
networks, including strong clustering, high navigability, and heterogeneous
degree distributions. These properties are ubiquitous in systems as varied as
the internet, transportation, brain or epidemic networks, which are thus
unified under the hyperbolic network interpretation on a surface of constant
negative curvature. Although a few studies have shown that hyperbolic models
can generate community structures, another salient feature observed in real
networks, we argue that the current models are overlooking the choice of the
latent space dimensionality that is required to adequately represent clustered
networked data. We show that there is an important qualitative difference
between the lowest-dimensional model and its higher-dimensional counterparts
with respect to how similarity between nodes restricts connection
probabilities. Since more dimensions also increase the number of nearest
neighbors for angular clusters representing communities, considering only one
more dimension allows us to generate more realistic and diverse community
structures.
