000099305 001__ 99305 000099305 005__ 20231006143303.0 000099305 0247_ $$2doi$$a10.1016/j.csfx.2020.100021 000099305 0248_ $$2sideral$$a122820 000099305 037__ $$aART-2019-122820 000099305 041__ $$aeng 000099305 100__ $$aMartínez-Martínez, C.T. 000099305 245__ $$aSpectral and localization properties of random bipartite graphs 000099305 260__ $$c2019 000099305 5060_ $$aAccess copy available to the general public$$fUnrestricted 000099305 5203_ $$aBipartite 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. 000099305 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E36-17R-FENOL$$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/FIS2017-87519-P 000099305 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000099305 592__ $$a0.0$$b2019 000099305 593__ $$aMathematics (miscellaneous)$$c2019 000099305 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000099305 700__ $$aMéndez-Bermúdez, J.A. 000099305 700__ $$0(orcid)0000-0002-0895-1893$$aMoreno, Y.$$uUniversidad de Zaragoza 000099305 700__ $$aPineda-Pineda, J.J. 000099305 700__ $$aSigarreta, J.M. 000099305 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000099305 773__ $$g3, 100021 (2019), [7 pp]$$tChaos, Solitons and Fractals: X$$x2590-0544 000099305 8564_ $$s1226517$$uhttps://zaguan.unizar.es/record/99305/files/texto_completo.pdf$$yVersión publicada 000099305 8564_ $$s2648014$$uhttps://zaguan.unizar.es/record/99305/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000099305 909CO $$ooai:zaguan.unizar.es:99305$$particulos$$pdriver 000099305 951__ $$a2023-10-06-14:07:16 000099305 980__ $$aARTICLE