000056192 001__ 56192 000056192 005__ 20190529115149.0 000056192 0247_ $$2doi$$a10.1103/PhysRevX.3.041022 000056192 0248_ $$2sideral$$a85241 000056192 037__ $$aART-2014-85241 000056192 041__ $$aeng 000056192 100__ $$aDe Domenico, M. 000056192 245__ $$aMathematical formulation of multilayer networks 000056192 260__ $$c2014 000056192 5060_ $$aAccess copy available to the general public$$fUnrestricted 000056192 5203_ $$aA network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates generalizing “traditional” network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper, we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of several important network descriptors and dynamical processes—including degree centrality, clustering coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion—for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems. 000056192 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/FIS2012-38266$$9info:eu-repo/grantAgreement/ES/MINECO/FIS2011-25167$$9info:eu-repo/grantAgreement/EC/FP7/317614/EU/Mathematical framework for multiplex networks/PLEXMATH 000056192 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000056192 590__ $$a9.043$$b2014 000056192 591__ $$aPHYSICS, MULTIDISCIPLINARY$$b5 / 78 = 0.064$$c2014$$dQ1$$eT1 000056192 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000056192 700__ $$aSolé-Ribalta, A. 000056192 700__ $$0(orcid)0000-0002-5655-1587$$aCozzo, E.$$uUniversidad de Zaragoza 000056192 700__ $$aKivelä, M. 000056192 700__ $$0(orcid)0000-0002-0895-1893$$aMoreno, Y.$$uUniversidad de Zaragoza 000056192 700__ $$aPorter, M.A. 000056192 700__ $$aGómez, S. 000056192 700__ $$aArenas, A. 000056192 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000056192 773__ $$g3, 4 (2014), 041022 [15 pp]$$pPhysical review. X$$tPhysical review. X$$x2160-3308 000056192 8564_ $$s1482292$$uhttps://zaguan.unizar.es/record/56192/files/texto_completo.pdf$$yVersión publicada 000056192 8564_ $$s122744$$uhttps://zaguan.unizar.es/record/56192/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000056192 909CO $$ooai:zaguan.unizar.es:56192$$particulos$$pdriver 000056192 951__ $$a2019-05-29-11:33:24 000056192 980__ $$aARTICLE