Dimension matters when modeling network communities in hyperbolic spaces

Abstract

Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations to many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree distributions. 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 data with communities. 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 increases 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.