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The D-Mercator method for the multidimensional hyperbolic embedding of real networks
Robert Jankowski1,2, Antoine Allard3,4, Marián Boguñá1,2
1Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, 08028, Barcelona, Spain.
Nature Communications
|November 22, 2023
Summary
We introduce D-Mercator, a new tool for mapping networks into multidimensional hyperbolic spaces. This method reveals network dimensionality, improving understanding of connectivity and community structures.
Area of Science:
- Network science
- Complex systems
- Geometric data analysis
Background:
- Model-based mapping tools embed real networks in latent geometry.
- Mercator embeds networks into the hyperbolic plane.
- Some networks require multidimensional geometric models.
Purpose of the Study:
- Introduce D-Mercator, a novel embedding method.
- Map real networks into (D+1)-hyperbolic space.
- Represent similarity subspace as a D-sphere.
Main Methods:
- D-Mercator model-based embedding.
- Multidimensional hyperbolic mapping of real networks.
- Estimation of intrinsic dimensionality via navigability and community structure.
Main Results:
- Generated multidimensional hyperbolic maps of real networks.
- Quantified network dimensionality.
- Identified factors influencing connectivity and community structure.
Conclusions:
- Multidimensional network representations are crucial for understanding connectivity determinants.
- D-Mercator aids in elucidating dimensionality-dependent phenomena like universality in critical behavior.
- This approach advances the geometric analysis of complex networks.
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