**1. Introduction**

Citation analysis has a long history. Recently, Hou [1] applied the new method called the reference publication year spectroscopy (RPYS) to 2543 papers including 56,392 references regarding citation analysis in Science Citation Index Expand (SCI-E) and Social Science Citation Index (SSCI) data from 1970 to July 2016. This investigation clarified that the development of citation analysis is divided into five periods: before 1990, 1901–1950, 1951–1970, 1971–2000, and 2001–2016. In this chapter, we focused on the distribution of citations which were introduced by Price [2] and extensively investigated in the third period, that is, 1950s–1970s. In this chapter, we consider that the number of citations expresses the popularity of papers.

The fifth period, that is, 2001–2016, is characterized by a period of rapid expansion and diversified directions. In this period, many conceptions have been introduced, for example, scientific

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

evaluation indices, citation networks, information visualization, and citing behaviors. A variety of new impact measures has been proposed based on social network analysis in sociology and of network science originated from physics, mathematics, and information science. Bollen [3] summarized 39 impact measures and investigated the correlation between them by using the principal component analysis. Then, Bollen [3] indicated that the notion of scientific impact is a multidimensional construct that cannot be adequately measured by any single indicator, although some measures are more suitable than others.

In this chapter, we focus on the Google's PageRank which is first proposed by Brin and Page [4] to obtain the list of useful web pages for queries by users. Thus, if we define the usefulness of web page as the number of links cited by the other web pages, the search engine should propose the list of portal sites, that is, popular web pages. Hence, this list is useless for web users. To overcome this problem, based on the concept of vote, Brin and Page [4] defined the usefulness of web pages as the number of votes from the linking web pages. In the algorithm of Google's PageRank, the number of ballets is proportional to the usefulness of the web page, that is, the useful web page has many ballets. As a result, the useful web page collects votes from the useful web pages. Thus, the Google's PageRank expresses the prestige of web pages. We consider that this characteristic of Google's PageRank is valid for the case of citation network.

This chapter is organized as follows. In Section 2, we explain characteristics of dataset used in this chapter. The distribution of citation and the stochastic model of citation network are elucidated in Section 3. In Section 4, we introduce Google's PageRank and calculate it. We consider the correlation between citation and PageRank in Section 5. Section 6 is devoted to conclusions.
