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Citation network centrality: a scientific awards predictor?

by   Osame Kinouchi, et al.

K index is an easily computable centrality index in complex networks, such as a scientific citations network. A researcher has a K index equal to K if he or she is cited by K articles that have at least K citations. The K index has several advantages over Hirsh's h index and, in previous studies, has shown better correlation with Nobel prizes than any other index given by the Web of Science, including the h index. However, correlation is not causation. Here we perform an experiment using the K index, producing a shortlist to predict future Physics Nobel candidates. Our list has been built before the 2019 Nobel Prizes announcements and should be compared to the actual results of the current and following years.


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  • We propose that the -index could be a good network centrality index for the physics community and relevant to predict the likelihood of scientific prizes;

  • We propose an experiment where a list of highly cited candidates is refined to predict Physics Nobel Prizes in the near future;

  • We present a list with twelve candidates with highest -index from an initial list of physicists from Clarivate Highly Cited Researchers 2019 (HCR).

  • We present and discuss the versus plane for the candidates.

1 Introduction

Statistical physicists have made important contributions to the interdisciplinary area of complex networks Newman (2010); Barabási (2016). In particular, physicists have intensively studied scientometric networks thanks to the availability of large and reliable data banks Newman (2001); Barabâsi et al. (2002); Wang et al. (2008); Ren et al. (2012); Clough and Evans (2016); Xie et al. (2016). Indeed, an important advancement for the area came with the introduction of the -index by physicist Jorge E. Hirsch Hirsch (2005). A researcher has -index if he/she has published papers each one with at least citations. Centrality indexes proposals for citation networks experienced a boom after the introduction of the -index Batista et al. (2006); Egghe (2006); Hirsch (2007); Schreiber (2010); Todeschini and Baccini (2016).

A decisive advantage of the -index over its competitors is its ease of calculation. However, it also is known that the -index has several drawbacks. For example, if a researcher has published a small or moderate number of papers, then necessarily , even if every paper is of very high quality and has received thousands of citations.

Recently, we have proposed the -index, centrality index that is complementary to -index and also easy to calculate in the Web of Science (WoSKinouchi et al. (2018); Kinouchi and Cardoso (2018). In these publications, we verified that Physics and Physiology Nobel Prizes laureates have very high -index (often above ) but sometimes moderate -index. However, this is only a correlation, and the growth of the -index could have occurred after the acceptance of the prize.

Here we propose to test -index’s predictive power by using it to refine the Clarivate Highly Cited Researchers 2019 (HCR) list of candidates to the 2019 Physics Nobel Prizes. Our task is a hard one since it depends only on a brute correlation between a scientometric index and the awards, and does not take into account nuanced and sociological guesses about the actual candidates.

2 Materials and Methods

2.1 The Highly Cited Researchers list of Clarivate Analytics

As a primary source, we used Clarivate Highly Cited Researchers 2019 (HCR) list to furnish an initial sample of candidates that have Research ID or Orcid. The methodology used by HCR to achieve this sample list is not of our concern now, and can be found in Our data and automated ranking script is available for public use at

Our task is to refine the HCR list by using the -index. We will produce a shortlist of candidates which is the maximum number of Nobel laureates for a period of four years and about of the original HCR 2019 list.

For comparison, the and -indexes for the physicists from the HCR list are presented in Fig. 1. The -index is furnished directly by the WoS.

2.2 Calculation of the -index

The -index has been devised to measure the impact of the papers that cite a researcher, not just to measure the quantity or distribution of citations. If a maximum number of papers cite a given author, each one with at least citations, then the researcher has -index equal to  Kinouchi et al. (2018); Kinouchi and Cardoso (2018).

Centrality indexes that tried to improve the -index, in general, involve impractical calculations Todeschini and Baccini (2016). The decisive advantage of the -index is that it is easily determined by simple inspection of the WoS platform. We presume that other platforms like Google Scholar Citations could also be easily adapted to provide automatically.

On the WoS, currently, one can obtain the -index of a researcher from the following simple steps:

  • Search the production of a given author;

  • Click on the link Create Citation Report;

  • Click on the link Citing Articles () (or Citing Articles without self-citations, if desired);

  • Have the list of citing articles ranked from the most cited (defined as rank ) to the least cited (that is the default ranking presented by WoS);

  • Compare the article rank (on the left) with its citation count on the right. When but , stop: the -index is .

3 Results and Discussion

In table I, we present twelve candidates from the Clarivate HCR list ranked by the -index. In Fig. 1, we present the versus plane for all researchers from the HCR, where the top highest -indexes are represented as red triangles. A filtered group, where graphene researchers have been removed, is represented by green inverted triangles. This has been done because graphene has already been the theme of a Nobel Prize in 2010.

Our objective with Fig. 1 is to show that scientists with high do not necessarily have high and vice-versa. and have complementary information. Fig. 1 should be compared to the vs. plots in Kinouchi et al. (2018); Kinouchi and Cardoso (2018), where Nobel laureates show values well above other scientists’ of similar . However, it is not clear how much their indexes have grown after receiving their prizes. A considerable inertial growth is a plausible hypothesis and correlation effects are difficult to separate.

Rank Name K h
1 Michael Graetzel 611 206
2 Paul Alivisatos 605 145
3 Sergey V Morozov 559 37
4 Younan Xia 542 189
5 Pulickel Ajayan 541 147
6 Philip Kim 519 83
7 Zhong Lin (Z.L.) Wang 515 195
8 John P. Perdew 502 86
9 Yi Cui 495 124
10 Mikhail I. Katsnelson 489 89
11 Yang Yang 471 120
12 Alex K. Zettl 460 105
Table 1: List of our twelve Nobel Prize candidates as ranked by the -index
Figure 1: -index vs -index for the candidates of Table 1 (triangles), of Table 2 (inverted triangles) and other highly cited researchers (circles).

Fig. 1 intends not to be correlational but predictive. All candidates have high citation rates and comparable -index. However, we have chosen the top twelve as our (crude) test of the predictive power of the -index.

A limitation of our study is that our original sample is from Clarivate HCR; if possible nominee candidates are not initially on the list, then our present ranking cannot detect and choose them.

Another limitation of our study is that the chosen names are, in principle, uncorrelated, that is, do not refer to a common discovery or a similar research topic. By contrast, the Nobel Prize for a given year is typically awarded to researchers who have made progress on similar topics or discoveries. Also, it is possible that researchers with very high or will not be laureated because they work on a topic that has already been awarded in the past.

Our methodology can be adjusted to incorporate the information discussed above. For example, we have noticed a very high proportion of authors with large in the area of materials science, especially graphene research – which has already been an awarded topic in 2010. To correct for this bias, we have produced a second list where graphene researchers are removed. The new list with candidates and with graphene scientists filtered out is given in Table 2 and has five new names as a replacement.

Rank Name K h
1 Michael Graetzel 611 206
2 Paul Alivisatos 605 145
3 Younan Xia 542 189
4 Zhong Lin (Z.L.) Wang 515 195
5 John P. Perdew 502 86
6 Yi Cui 495 124
7 Yang Yang 471 120
8 Mohammad K Nazeeruddin 436 126
9 Naomi Halas 427 123
10 John Rogers 405 126
11 Arthur J. Nozik 386 77
12 Peter Zoller 379 116
Table 2: List of twelve Nobel Prize candidates as ranked by the -index with graphene scientists filtered out.

4 Conclusion

It is an open question whether bibliometric information can have predictive power for scientific prizes. Prizes denote qualitative scientific recognition at the sociological level, where human factors are very important. Nobody would think that a prize should be decided by ranking the production of scientists by some automatic metric. At the same time, prizes intend to recognize original contributions whose impact is reflected in the bibliometric indexes, so it is plausible that predictive information is hidden in these indexes.

From a list of highly cited researchers, we proposed candidates for the 2019 or following years’ Physics Nobel Prizes. We have presented a naive ranking and also an improved ranking where a citation bias for materials scientists studying graphene was filtered out. Our list of candidates can be updated and also used in future years.

The predictive study of this paper could be extended to other scientific prizes such as the Wolf Prize, the Boltzmann Medal, the Fundamental Physics Prize, and prizes in other scientific disciplines. The only difference is that the sample of initial candidates should be selected in accord with the specific scientific area. These predictive tests, perhaps in the form of annual contests, could be useful benchmarks for evaluation of centrality indexes that can then be used in other, less monitored and less well-studied, complex networks.


O. K. acknowledges financial support from the National Council for Scientific and Technological Development (CNPq) and CNAIPS – Center for Natural and Artificial Information Processing Systems (University of Sao Paulo). This paper results from research activity performed at The São Paulo Research Foundation (FAPESP) Center for Neuromathematics (FAPESP grant 2013/07699-0).



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