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

@article{Georgeot2010SpectralPO,
  title={Spectral properties of the Google matrix of the World Wide Web and other directed networks},
  author={Bertrand Georgeot and Olivier Giraud and Dima L. Shepelyansky},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2010},
  volume={81 5 Pt 2},
  pages={
          056109
        }
}
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 α equal to unity. The vocabulary networks have relatively homogeneous spectral density, while university networks have pronounced spectral structures which change from one university to… 
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