Delocalization transition for the Google matrix

Details Delocalization transition for the Google matrix Delocalization transition for the Google matrix

2009-03-30

arxiv.org/abs/0903.5172v1

Phys. Rev. E 80, 026107 (2009)

Computer Science

Information Retrieval

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

Scientific paper

10.1103/PhysRevE.80.026107

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.

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