  One of the pillars of the geometric approach to networks has been the
development of model-based mapping tools that embed real networks in its latent
geometry. In particular, the tool Mercator embeds networks into the hyperbolic
plane. However, some real networks are better described by the multidimensional
formulation of the underlying geometric model. Here, we introduce $D$-Mercator,
a model-based embedding method that produces multidimensional maps of real
networks into the $(D+1)$-hyperbolic space, where the similarity subspace is
represented as a $D$-sphere. We used $D$-Mercator to produce multidimensional
hyperbolic maps of real networks and estimated their intrinsic dimensionality
in terms of navigability and community structure. Multidimensional
representations of real networks are instrumental in the identification of
factors that determine connectivity and in elucidating fundamental issues that
hinge on dimensionality, such as the presence of universality in critical
behavior.
