Revisiting the sensitivity analysis of Google’s PageRank

Abstract

PageRank is widely known as a prominent method used for indexing web pages and has significantly contributed to the development of Google’s search engine. Significant contributions have been made to the analyses of PageRank, in particular, its sensitivity analyses. However, the arguments presented thus far are within in the range of the matrix perturbation theory or the analyses of Markov chains. This paper explores the application of Kato’s perturbation theory to study the sensitivity analyses of PageRank, which enables the consideration of a larger number of general situations than those in established arguments.