A number of citations have been used to measure the value of paper. However, recently, Google’s PageRank is also extensively applied to quantify the worth of papers. In this chapter, we summarize the recent progress of studies on citations and PageRank. We also show our latest investigations of the citation network consisting of 34,666,719 articles and 591,321,826 citations. We propose the generalized beta distribution of the second kind to explain the distribution of citation and introduce the stochastic model with aging effect and super preferential attachment. Furthermore, we clarify the positive linear relation between citations and Google’s PageRank. By using this relationship as the benchmark to classify papers, we extract extremely prestigious papers, popular papers, and rising papers.
Part of the book: Scientometrics