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

Robert Jankowski, Antoine Allard, Marián Boguñá and M. Ángeles Serrano ()
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Robert Jankowski: Universitat de Barcelona
Antoine Allard: Université Laval
Marián Boguñá: Universitat de Barcelona
M. Ángeles Serrano: Universitat de Barcelona

Nature Communications, 2023, vol. 14, issue 1, 1-11

Abstract: Abstract 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.

Date: 2023
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DOI: 10.1038/s41467-023-43337-5

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