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Scaling and kinetic exchange like behavior of Hirsch index and total citation distributions: Scopus-CiteScore data analysis

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  • Ghosh, Asim
  • Chakrabarti, Bikas K.

Abstract

We analyze the data distributions f(h), f(Nc) and f(Np) of the Hirsch index (h), total citations (Nc) and total number of papers (Np) of the top scoring 120,000 authors (scientists) from the Stanford cite-score (or c-score) 2022 list and their corresponding h (3≤h≤284), Nc(1009≤Nc≤428620) and Np (3≤Np≤3791) statistics from the Scopus data. For reasons explained in the text, we divided the data of these top scorers (c-scores in the range 5.6125 to 3.3461) into six successive equal-sized Groups of 20,000 authors or scientists. We tried to fit, in each Group, f(h), f(Nc) and f(Np) with Gamma distributions, viewing them as the “wealth distributions” in the fixed saving-propensity kinetic exchange models and found f(h)∼hγhexp(−h/Th) with fitting noise level or temperature level (Th) and average value of h, and the power γh determined by the “citation saving propensity” in each Group. We further showed that using some earlier proposed power law scaling like h=DcNcαc (or h=DpNpαp) with αc=1/2=αp, we can derive the observed f(h) from the observed f(Nc) or f(Np), with Dc=0.5, but Dp depending on the Group considered. This observation suggests that the average citations per paper (Nc/Np) in each group (=(Dp/Dc)2=4Dp2) vary (from 58 to 29) with the c-score range of the six Groups considered here, implying different effective Dunbar-like coordination numbers of the scientists belonging to different groups or networks.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:626:y:2023:i:c:s0378437123006167
    DOI: 10.1016/j.physa.2023.129061
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    References listed on IDEAS

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    1. Anirban Chakraborti & Bikas K. Chakrabarti, 2000. "Statistical mechanics of money: How saving propensity affects its distribution," Papers cond-mat/0004256, arXiv.org, revised Jun 2000.
    2. Hajra, Kamalika Basu & Sen, Parongama, 2005. "Aging in citation networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(1), pages 44-48.
    3. 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.
    4. A. Chakraborti & B.K. Chakrabarti, 2000. "Statistical mechanics of money: how saving propensity affects its distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 17(1), pages 167-170, September.
    5. 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).
    6. 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).
    7. Filippo Radicchi & Claudio Castellano, 2013. "Analysis of bibliometric indicators for individual scholars in a large data set," Scientometrics, Springer;Akadémiai Kiadó, vol. 97(3), pages 627-637, December.
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