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Spectral properties of Google matrix of Wikipedia and other networks

Author

Listed:
  • Leonardo Ermann
  • Klaus Frahm
  • Dima Shepelyansky

Abstract

We study the properties of eigenvalues and eigenvectors of the Google matrix of the Wikipedia articles hyperlink network and other real networks. With the help of the Arnoldi method, we analyze the distribution of eigenvalues in the complex plane and show that eigenstates with significant eigenvalue modulus are located on well defined network communities. We also show that the correlator between PageRank and CheiRank vectors distinguishes different organizations of information flow on BBC and Le Monde web sites. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Leonardo Ermann & Klaus Frahm & Dima Shepelyansky, 2013. "Spectral properties of Google matrix of Wikipedia and other networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(5), pages 1-10, May.
    • Handle: RePEc:spr:eurphb:v:86:y:2013:i:5:p:1-10:10.1140/epjb/e2013-31090-8
    DOI: 10.1140/epjb/e2013-31090-8
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    Citations

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    Cited by:

    1. Vivek Kandiah & Hubert Escaith & Dima L. Shepelyansky, 2015. "Google matrix of the world network of economic activities," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(7), pages 1-20, July.
    2. Young-Ho Eom & Pablo Aragón & David Laniado & Andreas Kaltenbrunner & Sebastiano Vigna & Dima L Shepelyansky, 2015. "Interactions of Cultures and Top People of Wikipedia from Ranking of 24 Language Editions," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-27, March.
    3. Young-Ho Eom & Dima L Shepelyansky, 2013. "Highlighting Entanglement of Cultures via Ranking of Multilingual Wikipedia Articles," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-10, October.
    4. Leonardo Ermann & Dima L. Shepelyansky, 2015. "Google matrix analysis of the multiproduct world trade network," Papers 1501.03371, arXiv.org.

    More about this item

    Keywords

    Statistical and Nonlinear Physics;

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