99305 20231006143303.0 doi 10.1016/j.csfx.2020.100021 sideral 122820 ART-2019-122820 eng Martínez-Martínez, C.T. Spectral and localization properties of random bipartite graphs 2019 Access copy available to the general public Unrestricted Bipartite graphs are often found to represent the connectivity between the components of many systems such as ecosystems. A bipartite graph is a set of n nodes that is decomposed into two disjoint subsets, having m and n-m vertices each, such that there are no adjacent vertices within the same set. The connectivity between both sets, which is the relevant quantity in terms of connections, can be quantified by a parameter a ¿ [0, 1] that equals the ratio of existent adjacent pairs over the total number of possible adjacent pairs. Here, we study the spectral and localization properties of such random bipartite graphs. Specifically, within a Random Matrix Theory (RMT) approach, we identify a scaling parameter ¿ = ¿(n, m, a) that fixes the localization properties of the eigenvectors of the adjacency matrices of random bipartite graphs. We also show that, when ¿ < 1/10 (¿ > 10) the eigenvectors are localized (extended), whereas the localization–to–delocalization transition occurs in the interval 1/10 < ¿ < 10. Finally, given the potential applications of our findings, we round off the study by demonstrating that for fixed ¿, the spectral properties of our graph model are also universal. info:eu-repo/grantAgreement/ES/DGA/E36-17R-FENOL info:eu-repo/grantAgreement/ES/MINECO-FEDER/FIS2017-87519-P info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 0.0 2019 Mathematics (miscellaneous) 2019 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Méndez-Bermúdez, J.A. Moreno, Y. Universidad de Zaragoza (orcid)0000-0002-0895-1893 Pineda-Pineda, J.J. Sigarreta, J.M. 2004 405 Universidad de Zaragoza Dpto. Física Teórica Área Física Teórica 3, 100021 (2019), [7 pp] Chaos, Solitons and Fractals: X 2590-0544 1226517 http://zaguan.unizar.es/record/99305/files/texto_completo.pdf Versión publicada 2648014 http://zaguan.unizar.es/record/99305/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:99305 articulos driver 2023-10-06-14:07:16 ARTICLE