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,

Event details


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)


O. Giraud, B. Georgeot, and D.L. Shepelyansky