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Spectral properties of Google matrix of Wikipedia and other networks

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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.

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Authors and Affiliations

  1. Departamento de Física Teórica, GIyA, Comisión Nacional de Energía Atómica, 1429, Buenos Aires, Argentina

    Leonardo Ermann

  2. Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, 31062, Toulouse, France

    Leonardo Ermann, Klaus M. Frahm & Dima L. Shepelyansky

Authors
  1. Leonardo Ermann
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  2. Klaus M. Frahm
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  3. Dima L. Shepelyansky
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Correspondence to Dima L. Shepelyansky.

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Ermann, L., Frahm, K.M. & Shepelyansky, D.L. Spectral properties of Google matrix of Wikipedia and other networks. Eur. Phys. J. B 86, 193 (2013). https://doi.org/10.1140/epjb/e2013-31090-8

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  • DOI: https://doi.org/10.1140/epjb/e2013-31090-8

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