Delocalization transition for the Google matrix
arXiv:0903.5172 · doi:10.1103/PhysRevE.80.026107
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.
4 pages, 5 figures. Research done at http://www.quantware.ups-tlse.fr/