https://doi.org/10.1140/epjb/s10051-024-00722-3
Regular Article - Statistical and Nonlinear Physics
Super-diffusion in multiplex networks with long-range interactions
1
Departamento de Ingeniería Eléctrica, Electrónica, Automática y Física Aplicada, ETSIDI, Universidad Politécnica de Madrid, 28040, Madrid, Spain
2
Instituto de Física, Universidade Federal da Bahia, 40210-210, Salvador, Brazil
3
Departamento de Física, Universidad de Pamplona, Campus Universitario, 543050, Pamplona, Colombia
4
Centre for Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Muniz, Fundação Oswaldo Cruz (FIOCRUZ), Salvador, Brazil
Received:
13
March
2024
Accepted:
5
June
2024
Published online:
25
June
2024
This work investigates the emergence of structural super-diffusion in finite multiplex networks, focusing on situations where long-range interactions (LRIs) are present in at least one of the layers. Employing the Lévy random walk model, we explore how the likelihood of observing LRIs and the strength of the coupling among layers, specifically through the inter-layer diffusion coefficient, affect the relaxation time of the entire multiplex network. Our aim is to determine if this collective relaxation time is shorter compared to that in isolated layer configurations. We quantify the relaxation times through algebraic connectivity, the second-smallest eigenvalue of the network’s (Supra-)Laplacian matrix. The formalism is adapted to scenarios where long-range jumps may exist by considering Mellin or Laplace transforms. We study samples of multiplexes whose layers are obtained from the models by Erdös-Rény, Watts-Strogatz and Barabási-Albert, and discuss in great detail the results for multiplexes with two layers. Besides the rather common enhancement of multiplex diffusion in comparison to the diffusion observed in their isolated layers, our results show that the timescale of layers with LRIs may be still faster than that due only to the usual multiplex network, speeding-up the whole system’s diffusion. In addition, we also provide enough evidences that a novel linear diffusion regime emerges with strong inter-layer coupling and the presence of LRIs in one or more layers.
Alfonso Allen-Perkins, Alfredo Blanco Serrano and Roberto F. S. Andrade have contributed equally to this work.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
