Universal Emergence of PageRank

K. M. Frahm; B. Georgeot; D. L. Shepelyansky

doi:10.1088/1751-8113/44/46/465101

paper

Universal Emergence of PageRank

arXiv:1105.1062 · doi:10.1088/1751-8113/44/46/465101

Abstract

The PageRank algorithm enables to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter $α \in] 0, 1 [$ . Using extensive numerical simulations of large web networks, with a special accent on British University networks, we determine numerically and analytically the universal features of PageRank vector at its emergence when $α \to 1$ . The whole network can be divided into a core part and a group of invariant subspaces. For $α \to 1$ 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 $α \to 1$ is controlled by eigenvalues of the core part of the Google matrix which are extremely close to unity leading to large relaxation times as for example in spin glasses.

research at http://www.quantware.ups-tlse.fr/ 18 pages, 7 figures discussion updates

Universal Emergence of PageRank

Abstract

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