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Soft Communities in Similarity Space

  • Guillermo García-Pérez
  • M. Ángeles Serrano
  • Marián Boguñá
Article
  • 17 Downloads

Abstract

The \(\mathbb {S}^1\) model has been central in the development of the field of network geometry. It places nodes in a similarity space and connects them with a likelihood depending on an effective distance which combines similarity and popularity dimensions, with popularity directly related to the degrees of the nodes. The \(\mathbb {S}^1\) model has been mainly studied in its homogeneous regime, in which angular coordinates are independently and uniformly scattered on the circle. We now investigate if the model can generate networks with targeted topological features and soft communities, that is, inhomogeneous angular distributions. To that end, hidden degrees must depend on angular coordinates, and we propose a method to estimate them. We conclude that the model can be topologically invariant with respect to the soft-community structure. Our results expand the scope of the model beyond the independent hidden variables limit and can have an important impact in the embedding of real-world networks.

Keywords

Complex networks Hidden metric spaces Similarity space Communities 

Notes

Acknowledgements

We acknowledge support from a James S. McDonnell Foundation Scholar Award in Complex Systems; the ICREA Academia prize, funded by the Generalitat de Catalunya; Ministerio de Economía y Competitividad of Spain Projects No. FIS2013-47282-C2-1-P and no. FIS2016-76830-C2-2-P (AEI/FEDER, UE).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departament de Física de la Matèria CondensadaUniversitat de BarcelonaBarcelonaSpain
  2. 2.Universitat de Barcelona Institute of Complex Systems (UBICS)Universitat de BarcelonaBarcelonaSpain
  3. 3.ICREABarcelonaSpain

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