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Detecting the ultra low dimensionality of real networks

Author

Listed:
  • Pedro Almagro

    (Universidad de Sevilla)

  • Marián Boguñá

    (Universitat de Barcelona
    Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona)

  • M. Ángeles Serrano

    (Universitat de Barcelona
    Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona
    Institució Catalana de Recerca i Estudis Avaçats (ICREA))

Abstract

Reducing dimension redundancy to find simplifying patterns in high-dimensional datasets and complex networks has become a major endeavor in many scientific fields. However, detecting the dimensionality of their latent space is challenging but necessary to generate efficient embeddings to be used in a multitude of downstream tasks. Here, we propose a method to infer the dimensionality of networks without the need for any a priori spatial embedding. Due to the ability of hyperbolic geometry to capture the complex connectivity of real networks, we detect ultra low dimensionality far below values reported using other approaches. We applied our method to real networks from different domains and found unexpected regularities, including: tissue-specific biomolecular networks being extremely low dimensional; brain connectomes being close to the three dimensions of their anatomical embedding; and social networks and the Internet requiring slightly higher dimensionality. Beyond paving the way towards an ultra efficient dimensional reduction, our findings help address fundamental issues that hinge on dimensionality, such as universality in critical behavior.

Suggested Citation

  • Pedro Almagro & Marián Boguñá & M. Ángeles Serrano, 2022. "Detecting the ultra low dimensionality of real networks," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
  • Handle: RePEc:nat:natcom:v:13:y:2022:i:1:d:10.1038_s41467-022-33685-z
    DOI: 10.1038/s41467-022-33685-z
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    References listed on IDEAS

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    1. Weiwei Gu & Aditya Tandon & Yong-Yeol Ahn & Filippo Radicchi, 2021. "Principled approach to the selection of the embedding dimension of networks," Nature Communications, Nature, vol. 12(1), pages 1-10, December.
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    Cited by:

    1. Robert Jankowski & Antoine Allard & Marián Boguñá & M. Ángeles Serrano, 2023. "The D-Mercator method for the multidimensional hyperbolic embedding of real networks," Nature Communications, Nature, vol. 14(1), pages 1-11, December.

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