eprintid: 2391
rev_number: 11
eprint_status: archive
userid: 6
dir: disk0/00/00/23/91
datestamp: 2014-12-03 13:43:24
lastmod: 2014-12-18 13:54:35
status_changed: 2014-12-03 13:43:24
type: article
metadata_visibility: show
creators_name: Frahm, Klaus M.
creators_name: Eom, Young-Ho
creators_name: Shepelyansky, Dima L.
creators_id: 
creators_id: youngho.eom@imtlucca.it
creators_id: 
title: Google matrix of the citation network of Physical Review
ispublished: pub
subjects: HA
subjects: QC
subjects: Z665
divisions: CSA
full_text_status: public
keywords: PACS number(s): 89.75.Hc, 89.20.Hh, 89.75.Fb
note: © 2014 American Physical Society
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 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.
date: 2014-05
date_type: published
publication: Physical Review E
volume: 89
publisher: American Physical Society
pagerange: 052814
id_number: 10.1103/PhysRevE.89.052814
refereed: TRUE
issn: 1539-3755
official_url: http://link.aps.org/doi/10.1103/PhysRevE.89.052814
citation:   Frahm, Klaus M. and Eom, Young-Ho and Shepelyansky, Dima L.  Google matrix of the citation network of Physical Review.  Physical Review E, 89.  052814.  ISSN 1539-3755      (2014)  
document_url: http://eprints.imtlucca.it/2391/1/PhysRevE_Eom_2014.pdf