Spectral properties of the Google matrix of the World Wide Web and other directed networks - Université Toulouse 3 Accéder directement au contenu
Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2010

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

Bertrand Georgeot
Olivier Giraud
Dima Shepelyansky

Résumé

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.

Dates et versions

hal-00457759 , version 1 (18-02-2010)

Identifiants

Citer

Bertrand Georgeot, Olivier Giraud, Dima Shepelyansky. Spectral properties of the Google matrix of the World Wide Web and other directed networks. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2010, 81, pp.056109. ⟨10.1103/PhysRevE.81.056109⟩. ⟨hal-00457759⟩
50 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More