Eur. Phys. J. B (2013) 86: 193
https://doi.org/10.1140/epjb/e2013-31090-8

Regular Article

Spectral properties of Google matrix of Wikipedia and other networks

¹ Departamento de Física Teórica, GIyA, Comisión Nacional de Energía Atómica, 1429 Buenos Aires, Argentina
² Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, 31062 Toulouse, France

^a e-mail: dima@irsamc.ups-tlse.fr

Received: 5 December 2012
Published online: 29 April 2013

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.