Delocalization transition for the Google matrix
Condensed Matter journal club
Delocalization transition for the Google matrix
- Event time: 11:30am
- Event date: 5th February 2010
- Speaker: Arno Proeme (Formerly School of Physics & Astronomy, University of Edinburgh)
- Location: Room 2511, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB
Event details
Abstract
We study the localization properties of eigenvectors of the Google matrix, generated both from the world wide web and from the Albert-Barabási model of networks. We establish the emergence of a delocalization phase for the PageRank vector when network parameters are changed. For networks with localized PageRank, eigenvalues of the matrix in the complex plane with a modulus above a certain threshold correspond to localized eigenfunctions while eigenvalues below this threshold are associated with delocalized relaxation modes. We argue that, for networks with delocalized PageRank, the efficiency of information retrieval by Google-type search is strongly affected since the PageRank values have no clear hierarchical structure in this case.Phys. Rev. E 80 026107 (2009)
Authors
O. Giraud, B. Georgeot, and D.L. Shepelyansky
About Condensed Matter journal club
Given the diversity of research in the CM group, chosen topics vary widely. We tend to stick to high-impact journals - Nature, Science, PNAS and PRL have been popular - but this is not prescriptive..