{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T22:22:52Z","timestamp":1782166972175,"version":"3.54.5"},"reference-count":28,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2019,6,5]],"date-time":"2019-06-05T00:00:00Z","timestamp":1559692800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["TIN2017-84821-P"],"award-info":[{"award-number":["TIN2017-84821-P"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Networks are useful to describe the structure of many complex systems. Often, understanding these systems implies the analysis of multiple interconnected networks simultaneously, since the system may be modelled by more than one type of interaction. Multiplex networks are structures capable of describing networks in which the same nodes have different links. Characterizing the centrality of nodes in multiplex networks is a fundamental task in network theory. In this paper, we design and discuss a centrality measure for multiplex networks with data, extending the concept of eigenvector centrality. The essential feature that distinguishes this measure is that it calculates the centrality in multiplex networks where the layers show different relationships between nodes and where each layer has a dataset associated with the nodes. The proposed model is based on an eigenvector centrality for networks with data, which is adapted according to the idea behind the two-layer approach PageRank. The core of the centrality proposed is the construction of an irreducible, non-negative and primitive matrix, whose dominant eigenpair provides a node classification. Several examples show the characteristics and possibilities of the new centrality illustrating some applications.<\/jats:p>","DOI":"10.3390\/sym11060763","type":"journal-article","created":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T03:38:01Z","timestamp":1559792281000},"page":"763","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["An Eigenvector Centrality for Multiplex Networks with Data"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6521-4331","authenticated-orcid":false,"given":"Francisco","family":"Pedroche","sequence":"first","affiliation":[{"name":"Institut de Matem\u00e0tica Multidisciplin\u00e0ria, Universitat Polit\u00e8cnica de Val\u00e8ncia, E-46022 Val\u00e8ncia, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2562-8123","authenticated-orcid":false,"given":"Leandro","family":"Tortosa","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Artificial Intelligence, University of Alicante, Campus de San Vicente, Ap. Correos 99, E-03080 Alicante, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2990-1879","authenticated-orcid":false,"given":"Jos\u00e9 F.","family":"Vicent","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Artificial Intelligence, University of Alicante, Campus de San Vicente, Ap. Correos 99, E-03080 Alicante, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,5]]},"reference":[{"key":"ref_1","unstructured":"Estrada, E. (2012). The Structura of Complex Networks. Theory and Applications, Oxford University Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1038\/nphys3865","article-title":"The physics of spreading processes in multilayer networks","volume":"12","author":"Granell","year":"2016","journal-title":"Nat. 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