# Laboratoire de Physique ThéoriqueToulouse - UMR 5152

## Rechercher

Sur ce site

Sur le Web du CNRS

Accueil du site > Publications > Publications 2011 > Universal Emergence of PageRank

## Universal Emergence of PageRank

K. M. Frahm, B. Georgeot and D. L. Shepelyansky

par - 6 mai 2011

The PageRank algorithm enables to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter $\alpha \in ]0,1[$. Using extensive numerical simulations of large web networks, we determine numerically and analytically the universal features of PageRank vector at its emergence when $\alpha \rightarrow 1$. The whole network can be divided into a core part and a group of invariant subspaces. For $\alpha \rightarrow 1$ the PageRank converges to a universal power law distribution on the invariant subspaces whose size distribution also follows a universal power law. The convergence of PageRank at $\alpha \rightarrow 1$ is controlled by eigenvalues of the core part of the Google matrix which are exponentially close to unity leading to large relaxation times as for example in spin glasses.