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/