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One of the pillars of the geometric approach to networks has been thedevelopment of model-based mapping tools that embed real networks in its latentgeometry. In particular, the tool Mercator embeds networks into the hyperbolicplane. However, some real networks are better described by the multidimensionalformulation of the underlying geometric model. Here, we introduce $D$-Mercator,a model-based embedding method that produces multidimensional maps of realnetworks into the $(D+1)$-hyperbolic space, where the similarity subspace isrepresented as a $D$-sphere. We used $D$-Mercator to produce multidimensionalhyperbolic maps of real networks and estimated their intrinsic dimensionalityin terms of navigability and community structure. Multidimensionalrepresentations of real networks are instrumental in the identification offactors that determine connectivity and in elucidating fundamental issues thathinge on dimensionality, such as the presence of universality in criticalbehavior.

The D-Mercator method for the multidimensional hyperbolic embedding of real networks