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arXiv · 0903.5172

Delocalization transition for the Google matrix

Olivier Giraud·Bertrand Georgeot·Dima L. Shepelyansky
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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.

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BibTeXRIS

Olivier Giraud, Bertrand Georgeot, Dima L. Shepelyansky. 2009-03-30. Delocalization transition for the Google matrix. https://doi.org/10.1103/physreve.80.026107

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