Universal Emergence of PageRank

Details Universal Emergence of PageRank Universal Emergence of PageRank

2011-05-05

arxiv.org/abs/1105.1062v2

J. Phys. A: Math. Theor. 44 (2011) 465101

Computer Science

Information Retrieval

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

Scientific paper

10.1088/1751-8113/44/46/465101

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, with a special accent on British University 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 extremely close to unity leading to large relaxation times as for example in spin glasses.

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