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Gintropic scaling of scientometric indexes

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  • Biró, Tamás S.
  • Telcs, András
  • Józsa, Máté
  • Néda, Zoltán

Abstract

The most frequently used indicators for the productivity and impact of scientists are the total number of publication (Npub), total number of citations (Ncit) and the Hirsch (h) index. Since the seminal paper of Hirsch, in 2005, it is largely debated whether the h index can be considered as an indicator independent of Npub and Ncit. Exploiting the Paretian form for the distribution of citations for the papers authored by a researcher, here we discuss scaling relations between h, Npub and Ncit. The analysis incorporates the Gini index as an inequality measure of citation distributions and a recently proposed inequality kernel, gintropy (resembling to the entropy kernel). We find a new upper bound for the h value as a function of the total number of citations, confirmed on massive data collected from Google Scholar. Our analyses reveals also that the individualized Gini index calculated for the citations received by the publications of an author peaks around 0.8, a value much higher than the one usually reported for socio-economic inequalities.

Suggested Citation

  • Biró, Tamás S. & Telcs, András & Józsa, Máté & Néda, Zoltán, 2023. "Gintropic scaling of scientometric indexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    • Handle: RePEc:eee:phsmap:v:618:y:2023:i:c:s0378437123002728
    DOI: 10.1016/j.physa.2023.128717
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    1. Tietze, Anna & Galam, Serge & Hofmann, Philip, 2020. "Crediting multi-authored papers to single authors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    2. Lutz Bornmann & Rüdiger Mutz & Hans‐Dieter Daniel, 2008. "Are there better indices for evaluation purposes than the h index? A comparison of nine different variants of the h index using data from biomedicine," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 59(5), pages 830-837, March.
    3. Krisztina Barcza & András Telcs, 2009. "Paretian publication patterns imply Paretian Hirsch index," Scientometrics, Springer;Akadémiai Kiadó, vol. 81(2), pages 513-519, November.
    4. Lucio Bertoli-Barsotti & Tommaso Lando, 2017. "The h-index as an almost-exact function of some basic statistics," Scientometrics, Springer;Akadémiai Kiadó, vol. 113(2), pages 1209-1228, November.
    5. Leo Egghe & Ronald Rousseau, 2021. "The h-index formalism," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(7), pages 6137-6145, July.
    6. Suchismita Banerjee & Soumyajyoti Biswas & Bikas K. Chakrabarti & Sai Krishna Challagundla & Asim Ghosh & Suhaas Reddy Guntaka & Hanesh Koganti & Anvesh Reddy Kondapalli & Raju Maiti & Manipushpak Mit, 2023. "Evolutionary dynamics of social inequality and coincidence of Gini and Kolkata indices under unrestricted competition," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 34(04), pages 1-29, April.
    7. Zoltán Néda & Levente Varga & Tamás S Biró, 2017. "Science and Facebook: The same popularity law!," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-11, July.
    8. Gangan Prathap, 2022. "Letter to the editor: comments on the paper of Gagolewski et al.: Ockham’s index of citation impact," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(10), pages 6051-6054, October.
    9. Ghosh, Asim & Chakrabarti, Bikas K., 2021. "Limiting value of the Kolkata index for social inequality and a possible social constant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    10. Manna, S.S. & Biswas, Soumyajyoti & Chakrabarti, Bikas K., 2022. "Near universal values of social inequality indices in self-organized critical models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    11. Bertoli-Barsotti, Lucio & Lando, Tommaso, 2019. "How mean rank and mean size may determine the generalised Lorenz curve: With application to citation analysis," Journal of Informetrics, Elsevier, vol. 13(1), pages 387-396.
    12. Bertoli-Barsotti, Lucio & Lando, Tommaso, 2015. "On a formula for the h-index," Journal of Informetrics, Elsevier, vol. 9(4), pages 762-776.
    13. Grzegorz Siudem & Barbara Żogała-Siudem & Anna Cena & Marek Gagolewski, 2020. "Three dimensions of scientific impact," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 117(25), pages 13896-13900, June.
    14. Serge Galam, 2011. "Tailor based allocations for multiple authorship: a fractional gh-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 89(1), pages 365-379, October.
    15. Marek Gagolewski & Barbara Żogała-Siudem & Grzegorz Siudem & Anna Cena, 2022. "Ockham’s index of citation impact," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(5), pages 2829-2845, May.
    16. Mingers, John & Leydesdorff, Loet, 2015. "A review of theory and practice in scientometrics," European Journal of Operational Research, Elsevier, vol. 246(1), pages 1-19.
    17. Asim Ghosh & Bikas K Chakrabarti, 2021. "Limiting Value of the Kolkata Index for Social Inequality and a Possible Social Constant," Papers 2102.01527, arXiv.org, revised Apr 2021.
    18. Lucio Bertoli-Barsotti & Tommaso Lando, 2017. "A theoretical model of the relationship between the h-index and other simple citation indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 111(3), pages 1415-1448, June.
    19. Tam'as S. Bir'o & Zolt'an N'eda, 2020. "Gintropy: Gini index based generalization of Entropy," Papers 2007.04829, arXiv.org.
    20. Alonso, S. & Cabrerizo, F.J. & Herrera-Viedma, E. & Herrera, F., 2009. "h-Index: A review focused in its variants, computation and standardization for different scientific fields," Journal of Informetrics, Elsevier, vol. 3(4), pages 273-289.
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    1. Ghosh, Asim & Chakrabarti, Bikas K., 2023. "Scaling and kinetic exchange like behavior of Hirsch index and total citation distributions: Scopus-CiteScore data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).

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