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- W3044861811 abstract "Although the spectral properties of random graphs have been a long-standing focus of network theory, the properties of right eigenvectors of directed graphs have so far eluded an exact analytic treatment. We present a general theory for the statistics of the right eigenvector components in directed random graphs with a prescribed degree distribution and with randomly weighted links. We obtain exact analytic expressions for the inverse participation ratio and show that right eigenvectors of directed random graphs with a small average degree are localized. Remarkably, if the fourth moment of the degree distribution is finite, then the critical mean degree of the localization transition is independent of the degree fluctuations, which is different from localization in undirected graphs that is governed by degree fluctuations. We also show that in the high connectivity limit the distribution of the right eigenvector components is solely determined by the degree fluctuations. For delocalized eigenvectors, we recover the universal results from standard random matrix theory that are independent of the degree distribution, while for localized eigenvectors the eigenvector distribution depends on the degree distribution." @default.
- W3044861811 created "2020-07-29" @default.
- W3044861811 creator A5019990487 @default.
- W3044861811 creator A5047786826 @default.
- W3044861811 date "2021-01-29" @default.
- W3044861811 modified "2023-09-26" @default.
- W3044861811 title "Localization and Universality of Eigenvectors in Directed Random Graphs" @default.
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- W3044861811 doi "https://doi.org/10.1103/physrevlett.126.040604" @default.
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