000077229 001__ 77229
000077229 005__ 20200716101515.0
000077229 0247_ $$2doi$$a10.1103/PhysRevE.99.012311
000077229 0248_ $$2sideral$$a110396
000077229 037__ $$aART-2019-110396
000077229 041__ $$aeng
000077229 100__ $$aWang, X.
000077229 245__ $$aStructural transition in interdependent networks with regular interconnections
000077229 260__ $$c2019
000077229 5060_ $$aAccess copy available to the general public$$fUnrestricted
000077229 5203_ $$aNetworks 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.
000077229 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E36-17R$$9info:eu-repo/grantAgreement/ES/MINECO/FIS2017-87519-P
000077229 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000077229 590__ $$a2.296$$b2019
000077229 591__ $$aPHYSICS, MATHEMATICAL$$b9 / 55 = 0.164$$c2019$$dQ1$$eT1
000077229 591__ $$aPHYSICS, FLUIDS & PLASMAS$$b13 / 34 = 0.382$$c2019$$dQ2$$eT2
000077229 592__ $$a0.958$$b2019
000077229 593__ $$aCondensed Matter Physics$$c2019$$dQ1
000077229 593__ $$aStatistical and Nonlinear Physics$$c2019$$dQ1
000077229 593__ $$aStatistics and Probability$$c2019$$dQ2
000077229 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000077229 700__ $$aKooij, R.E.
000077229 700__ $$0(orcid)0000-0002-0895-1893$$aMoreno, Y.$$uUniversidad de Zaragoza
000077229 700__ $$aVan Mieghem, P.
000077229 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica
000077229 773__ $$g99, 1 (2019), 012311$$pPhys. rev., E$$tPHYSICAL REVIEW E$$x2470-0045
000077229 8564_ $$s475978$$uhttps://zaguan.unizar.es/record/77229/files/texto_completo.pdf$$yVersión publicada
000077229 8564_ $$s24527$$uhttps://zaguan.unizar.es/record/77229/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000077229 909CO $$ooai:zaguan.unizar.es:77229$$particulos$$pdriver
000077229 951__ $$a2020-07-16-09:21:57
000077229 980__ $$aARTICLE