期刊
ANNALEN DER PHYSIK
卷 527, 期 9-10, 页码 713-722出版社
WILEY-V C H VERLAG GMBH
DOI: 10.1002/andp.201500110
关键词
Markov chains; Anderson localization; Google matrix; PageRank
资金
- EC FET Open project New tools and algorithms for directed network analysis (NADINE) [288956]
- Ministry of Education and Science of Russian Federation
We introduce a number of random matrix models describing the Google matrix G of directed networks. The properties of their spectra and eigenstates are analyzed by numerical matrix diagonalization. We show that for certain models it is possible to have an algebraic decay of PageRank vector with the exponent similar to real directed networks. At the same time the spectrum has no spectral gap and a broad distribution of eigenvalues in the complex plain. The eigenstates of G are characterized by the Anderson transition from localized to delocalized states and a mobility edge curve in the complex plane of eigenvalues.
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