**Author details**

On the other hand, there are also outliers which have low prestige comparing to popularity. These articles are located below the solid gray line in **Figure 8** and are regarded as extremely popular papers. These articles are extracted by the order of citation rank with the constraint

which are published in Nature, Science, and the Proceedings of the National Academy of Science of the United State of America (PNAS). Besides, publication year of these papers

papers are low. The other group includes papers which are mainly published in Cell and are

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 (arti-

The right-tail part of the rank size distribution of citations follows the power law distribu-

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

are approximately over 10 years ago. Furthermore, the growth rate of citations, *k*'

published relatively recently. What is more, the growth rate of citations, *k*'

4096 0.1262 5.45 M. Corbetta Control of goal-

4446 0.1213 5.91 A. Brunet Akt promotes

3972 0.1280 5.06 J.D. Fontenot Foxp3 programs the

are extremely high. Thus, we can regard these papers as rising papers.

. **Table 4** depicts the top 20 extremely popular papers selected by using

. Furthermore, we introduced the generalized beta

/*k*, of those

Neurosciences & Neurology

& Molecular Biology; Cell Biology

Immunology

/*k*, of those papers

*<sup>k</sup>* <sup>&</sup>gt; 5. These articles are divided into two groups. One group contains papers

**)** *rG***/***rk* **First author Title Journal, Year Subject**

Nature Reviews Neuroscience, 2002

Nature Immunology, 2003

Cell, 1999 Biochemistry

directed and stimulus-driven…

cell survival by phosphorylating

development and…

and…

given by the ratio *r*

**6. Conclusions**

the constraint *r*

*rk k***(***k***'**

228 Scientometrics

751 3806 (5109)

752 3805 (4313)

785 3739 (4363)

> *G*/*r k*

cles) and 591,177,607 links (citations).

tion with exponent *μ* = 2, that is, *R*(*k*) ∝ *k*<sup>−</sup><sup>2</sup>

*G*/*r*

**Table 4.** Top 20 extremely popular papers.

**)** *rG G***(10−<sup>5</sup>**

Wataru Souma1 \* and Mari Jibu2

