English

Delocalization transition for the Google matrix

Information Retrieval 2009-09-04 v1 Disordered Systems and Neural Networks Adaptation and Self-Organizing Systems

Abstract

We study the localization properties of eigenvectors of the Google matrix, generated both from the World Wide Web and from the Albert-Barabasi model of networks. We establish the emergence of a delocalization phase for the PageRank vector when network parameters are changed. In the phase of localized PageRank, a delocalization takes place in the complex plane of eigenvalues of the matrix, leading to delocalized relaxation modes. We argue that the efficiency of information retrieval by Google-type search is strongly affected in the phase of delocalized PageRank.

Cite

@article{arxiv.0903.5172,
  title  = {Delocalization transition for the Google matrix},
  author = {Olivier Giraud and Bertrand Georgeot and Dima L. Shepelyansky},
  journal= {arXiv preprint arXiv:0903.5172},
  year   = {2009}
}

Comments

4 pages, 5 figures. Research done at http://www.quantware.ups-tlse.fr/

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