77229 20200716101515.0 doi 10.1103/PhysRevE.99.012311 sideral 110396 ART-2019-110396 eng Wang, X. Structural transition in interdependent networks with regular interconnections 2019 Access copy available to the general public Unrestricted Networks are often made up of several layers that exhibit diverse degrees of interdependencies. An interdependent network consists of a set of graphs G that are interconnected through a weighted interconnection matrix B, where the weight of each intergraph link is a non-negative real number p. Various dynamical processes, such as synchronization, cascading failures in power grids, and diffusion processes, are described by the Laplacian matrix Q characterizing the whole system. For the case in which the multilayer graph is a multiplex, where the number of nodes in each layer is the same and the interconnection matrix B=pI, I being the identity matrix, it has been shown that there exists a structural transition at some critical coupling p*. This transition is such that dynamical processes are separated into two regimes: if p>p*, the network acts as a whole; whereas when p<p*, the network operates as if the graphs encoding the layers were isolated. In this paper, we extend and generalize the structural transition threshold p* to a regular interconnection matrix B (constant row and column sum). Specifically, we provide upper and lower bounds for the transition threshold p* in interdependent networks with a regular interconnection matrix B and derive the exact transition threshold for special scenarios using the formalism of quotient graphs. Additionally, we discuss the physical meaning of the transition threshold p* in terms of the minimum cut and show, through a counterexample, that the structural transition does not always exist. Our results are one step forward on the characterization of more realistic multilayer networks and might be relevant for systems that deviate from the topological constraints imposed by multiplex networks. info:eu-repo/grantAgreement/ES/DGA/E36-17R info:eu-repo/grantAgreement/ES/MINECO/FIS2017-87519-P info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 2.296 2019 PHYSICS, MATHEMATICAL 9 / 55 = 0.164 2019 Q1 T1 PHYSICS, FLUIDS & PLASMAS 13 / 34 = 0.382 2019 Q2 T2 0.958 2019 Condensed Matter Physics 2019 Q1 Statistical and Nonlinear Physics 2019 Q1 Statistics and Probability 2019 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Kooij, R.E. (orcid)0000-0002-0895-1893 Moreno, Y. Universidad de Zaragoza Van Mieghem, P. 2004 405 Universidad de Zaragoza Dpto. Física Teórica Área Física Teórica 99, 1 (2019), 012311 Phys. rev., E PHYSICAL REVIEW E 2470-0045 475978 http://zaguan.unizar.es/record/77229/files/texto_completo.pdf Versión publicada 24527 http://zaguan.unizar.es/record/77229/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:77229 articulos driver 2020-07-16-09:21:57 ARTICLE