IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2021-10-24T16:15:02ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2014-12-03T13:43:24Z2014-12-18T13:54:35Zhttp://eprints.imtlucca.it/id/eprint/2391This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/23912014-12-03T13:43:24ZGoogle matrix of the citation network of Physical ReviewWe study the statistical properties of spectrum and eigenstates of the Google matrix of the citation network of Physical Review for the period 1893–2009. The main fraction of complex eigenvalues with largest modulus is determined numerically by different methods based on high-precision computations with up to p=16384 binary digits that allow us to resolve hard numerical problems for small eigenvalues. The nearly nilpotent matrix structure allows us to obtain a semianalytical computation of eigenvalues. We find that the spectrum is characterized by the fractal Weyl law with a fractal dimension df≈1. It is found that the majority of eigenvectors are located in a localized phase. The statistical distribution of articles in the PageRank-CheiRank plane is established providing a better understanding of information flows on the network. The concept of ImpactRank is proposed to determine an influence domain of a given article. We also discuss the properties of random matrix models of Perron-Frobenius operators.Klaus M. FrahmYoung-Ho Eomyoungho.eom@imtlucca.itDima L. Shepelyansky2014-12-03T11:36:48Z2014-12-18T13:55:22Zhttp://eprints.imtlucca.it/id/eprint/2389This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/23892014-12-03T11:36:48ZTime evolution of Wikipedia network rankingWe study the time evolution of ranking and spectral properties of the Google matrix of English Wikipedia hyperlink network during years 2003–2011. The statistical properties of ranking of Wikipedia articles via PageRank and CheiRank probabilities, as well as the matrix spectrum, are shown to be stabilized for 2007–2011. A special emphasis is done on ranking of Wikipedia personalities and universities. We show that PageRank selection is dominated by politicians while 2DRank, which combines PageRank and CheiRank, gives more accent on personalities of arts. The Wikipedia PageRank of universities recovers 80% of top universities of Shanghai ranking during the considered time period. Young-Ho Eomyoungho.eom@imtlucca.itKlaus M. FrahmAndrás BenczúrDima L. Shepelyansky