000075801 001__ 75801 000075801 005__ 20191212102140.0 000075801 0247_ $$2doi$$a10.1088/1367-2630/aadf9f 000075801 0248_ $$2sideral$$a108480 000075801 037__ $$aART-2018-108480 000075801 041__ $$aeng 000075801 100__ $$ade Arruda, G.F. 000075801 245__ $$aA polynomial eigenvalue approach for multiplex networks 000075801 260__ $$c2018 000075801 5060_ $$aAccess copy available to the general public$$fUnrestricted 000075801 5203_ $$aWe explore the block nature of the matrix representation of multiplex networks, introducing a new formalism to deal with its spectral properties as a function of the inter-layer coupling parameter. This approach allows us to derive interesting results based on an interpretation of the traditional eigenvalue problem. Specifically, our formalism is based on the reduction of the dimensionality of a matrix of interest but increasing the power of the characteristic polynomial, i.e, a polynomial eigenvalue problem. This approach may sound counterintuitive at first, but it enable us to relate the quadratic eigenvalue problem for a 2-Layer multiplex network with the spectra of its respective aggregated network. Additionally, it also allows us to derive bounds for the spectra, among many other interesting analytical insights. Furthermore, it also permits us to directly obtain analytical and numerical insights on the eigenvalue behavior as a function of the coupling between layers. Our study includes the supra-adjacency, supra-Laplacian and the probability transition matrices, which enables us to put our results under the perspective of structural phases in multiplex networks. We believe that this formalism and the results reported will make it possible to derive new results for multiplex networks in the future. 000075801 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E36-17R$$9info:eu-repo/grantAgreement/ES/MINECO/FIS2017-87519-P 000075801 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000075801 590__ $$a3.773$$b2018 000075801 591__ $$aPHYSICS, MULTIDISCIPLINARY$$b12 / 81 = 0.148$$c2018$$dQ1$$eT1 000075801 592__ $$a1.664$$b2018 000075801 593__ $$aPhysics and Astronomy (miscellaneous)$$c2018$$dQ1 000075801 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000075801 700__ $$0(orcid)0000-0002-5655-1587$$aCozzo, E. 000075801 700__ $$aRodrigues, F.A. 000075801 700__ $$0(orcid)0000-0002-0895-1893$$aMoreno, Y.$$uUniversidad de Zaragoza 000075801 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000075801 773__ $$g20 (2018), 095004 [19 pp]$$pNew j. phys.$$tNEW JOURNAL OF PHYSICS$$x1367-2630 000075801 8564_ $$s2316858$$uhttps://zaguan.unizar.es/record/75801/files/texto_completo.pdf$$yVersión publicada 000075801 8564_ $$s12027$$uhttps://zaguan.unizar.es/record/75801/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000075801 909CO $$ooai:zaguan.unizar.es:75801$$particulos$$pdriver 000075801 951__ $$a2019-12-12-10:11:50 000075801 980__ $$aARTICLE