PageRank is one of the principle criteria according to which Google ranks Web pages. PageRank can be interpreted as a frequency of visiting a Web page by a random surfer, and thus it reflects the popularity of a Web page. Google computes the PageRank using the power iteration method, which requires about one week of intensive computations. In the present work we propose and analyze Monte Carlo-type methods for the PageRank computation. There are several advantages of the probabilistic Monte Carlo methods over the deterministic power iteration method: Monte Carlo methods already provide good estimation of the PageRank for relatively important pages after one iteration; Monte Carlo methods have natural parallel implementation; and finally, Monte Carlo methods allow one to perform continuous update of the PageRank as the structure of the Web changes.
Avrachenkov, K., Litvak, N., Nemirovsky, D., & Osipova, N. (2007). Monte Carlo methods in PageRank computation: When one iteration is sufficient. SIAM journal on numerical analysis, 45(LNCS4549/2), 890-904. [10.1137/050643799]. https://doi.org/10.1137/050643799