**6. Conclusions**

We investigated papers published from 1981 to 2015 and contained in SCI-E. The total number of papers is 34,666,719 and that of citations is 591,321,826. We extracted the largest connected component from this dataset. The obtained citation network consists of 34,428,322 nodes (articles) and 591,177,607 links (citations).

The right-tail part of the rank size distribution of citations follows the power law distribution with exponent *μ* = 2, that is, *R*(*k*) ∝ *k*<sup>−</sup><sup>2</sup> . Furthermore, we introduced the generalized beta distribution of the second kind (GB2) as the best-fit function to the whole range of citation distribution. We introduced the stochastic model with growth, preferential attachment, and aging effect. Through the numerical analysis, we obtained the value of the parameter set.

Although the number of citations represent the popularity of papers, Google's PageRank reflects the prestige of papers. We evaluated Google's PageRank for the largest connected component which consists of 34,428,322 articles and 591,177,607 link citations. We found that the citations and Google numbers have a positive linear relation. We consider this positive linear relation as a benchmark and selected extremely prestigious and extremely popular papers. We found that the subject of extremely prestigious papers is almost information science. Furthermore, we found that extremely popular papers are divided into popular papers and rising papers.

We conclude this chapter by describing two remaining issues. One concerns the stochastic model. Though we introduce GB2 as the best-fit function to the whole range of citation distribution, there is no stochastic model that explains GB2. The other concerns the weight of links in the citation network. Almost all studies have investigated citation networks as unweighted networks. However, it is possible to define weight of links, for example, similarity between papers.
