Partenaires

CNRS
UPS



Rechercher

Sur ce site

Sur le Web du CNRS


Accueil du site > Publications > Publications 2010 > Spectral properties of the Google matrix of the World Wide Web and other directed networks

Spectral properties of the Google matrix of the World Wide Web and other directed networks

B. Georgeot, O. Giraud, D.L. Shepelyansky

par Bertrand Georgeot - 18 février 2010

We study numerically the spectrum and eigenstate properties of the Google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university World Wide Web networks. The spectra have gapless structure in the vicinity of the maximal eigenvalue for Google damping parameter alpha equal to unity. The vocabulary networks have relatively homogeneous spectral density, while university networks have pronounced spectral structures which change from one university to another, reflecting specific properties of the networks. We also determine specific properties of eigenstates of the Google matrix, including the PageRank. The fidelity of the PageRank is proposed as a new characterization of its stability.