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Google's PageRank algorithm was firstly proposed by Brin and Page.Many researchers carried on it, in both computational and theoretical research regions. Especially, the sensitivity analysis has been studied intensively. Thanks to the well-behaved characteristics of Google matrix,it is well known that the principal eigenvalue is always equal to unity.In this paper, we apply Kato's perturbation theory to the sensitivity analysis of Google matrix. We obtain the explicit form of PageRank vector under small perturbation, without assuming that the perturbation is imposed only on a single factor.
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