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

Asim Ghosh and Bikas K. Chakrabarti

Physica A: Statistical Mechanics and its Applications, 2023, vol. 626, issue C

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.

Keywords: Citations distribution; h-index; c-Score; Kinetic exchange model; Scaling relation; Dunbar number; Citation network (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:626:y:2023:i:c:s0378437123006167

DOI: 10.1016/j.physa.2023.129061

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