Spectral properties of Google matrix of Wikipedia and other networks |
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Authors: | Leonardo Ermann Klaus M. Frahm Dima L. Shepelyansky |
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Affiliation: | 1942. Departamento de Física Teórica, GIyA, Comisión Nacional de Energía Atómica, 1429, Buenos Aires, Argentina 2942. Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, 31062, Toulouse, France
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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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