title: Google matrix of the citation network of Physical Review.
abstract: We 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 d(f) ≈ 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.
authors.affiliation: Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, 31062 Toulouse, France.
authors.forename: Klaus M
authors.initials: KM
authors.lastname: Frahm
authors.affiliation: Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, 31062 Toulouse, France.
authors.forename: Young-Ho
authors.initials: YH
authors.lastname: Eom
authors.affiliation: Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, 31062 Toulouse, France.
authors.forename: Dima L
authors.initials: DL
authors.lastname: Shepelyansky