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)
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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.
| Item Type: | Article |
|---|---|
| Identification Number: | 10.1103/PhysRevE.89.052814 |
| Additional Information: | © 2014 American Physical Society |
| Uncontrolled Keywords: | PACS number(s): 89.75.Hc, 89.20.Hh, 89.75.Fb |
| Subjects: | H Social Sciences > HA Statistics Q Science > QC Physics Z Bibliography. Library Science. Information Resources > Z665 Library Science. Information Science |
| Research Area: | Computer Science and Applications |
| Depositing User: | Ms T. Iannizzi |
| Date Deposited: | 03 Dec 2014 13:43 |
| Last Modified: | 18 Dec 2014 13:54 |
| URI: | http://eprints.imtlucca.it/id/eprint/2391 |
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