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arXiv · 1105.1062

Universal Emergence of PageRank

K. M. Frahm·B. Georgeot·D. L. Shepelyansky
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Abstract

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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K. M. Frahm, B. Georgeot, D. L. Shepelyansky. 2011-05-05. Universal Emergence of PageRank. https://doi.org/10.1088/1751-8113/44/46/465101

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