Google matrix of the citation network of Physical Review

Klaus M. Frahm, Young Ho Eom, Dima L. Shepelyansky

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 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.

Original languageEnglish
Article number052814
JournalPhysical Review E
Issue number5
StatePublished - 28 May 2014


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