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  • Letter
  • Open Access

Multiplexity amplifies geometry in networks

Jasper van der Kolk1,2,*, Dmitri Krioukov3, Marián Boguñá1,2,†, and M. Ángeles Serrano1,2,4,‡

  • *Contact author: vanderkolkj@ceu.edu
  • †Contact author: marian.boguna@ub.edu
  • ‡Contact author: marian.serrano@ub.edu
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Phys. Rev. Research 7, L042046 – Published 1 December, 2025

DOI: https://doi.org/10.1103/cm34-kjd4

Abstract

Many real-world networks are multilayer, with nontrivial correlations across layers. Here, we show that these correlations amplify geometry in networks. We focus on mutual clustering—a measure of the number of triangles that are present in all layers among the same triplets of nodes—and find that this clustering is abnormally high in many real-world networks, even when clustering in each individual layer is weak. We explain this unexpected phenomenon using a simple multiplex network model with latent geometry: Links that are most congruent with this geometry are the ones that persist across layers, amplifying the cross-layer triangle overlap. This result reveals a different dimension in which multilayer networks are radically distinct from their constituent layers.

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Outline

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Phys. Rev. Research 7, L042046– Published 1 December, 2025
  • Received 23 May 2025
  • Accepted 31 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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