Scaling and Kinetic Exchange Like Behavior of Hirsch Index and Total Citation Distributions: Scopus-CiteScore Data Analysis

Abstract

We analyze the data distributions $f(h)$, $f(N_c$) and $f(N_p)$ of the Hirsch index $(h)$, total citations ($N_c$) and total number of papers ($N_p$) of the top scoring 120,000 authors (scientists) from the Stanford cite-score (or c-score) 2022 list and their corresponding $h$ ($3\le h\le 284$), $N_c(1009\le N_c\le 428620$) and $N_p$ ($3\le N_p\le 3791$) 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 $f(h)\sim h^{{\gamma }_h}\exp (-h/T_h)$ with fitting noise level or temperature level ($T_h$) and average value of $h$, and the power ${\gamma }_h$ determined by the ``citation saving propensity'' in each Group. We further showed that using some earlier proposed power law scaling like $h=D_c{N}_c^{{\alpha }_c}$ (or $h=D_p{N}_p^{{\alpha }_p}$) with ${\alpha }_c=1/2={\alpha }_p$, we can derive the observed $f(h)$ from the observed $f(N_c)$ or $f(N_p)$, with $D_c=0.5$, but $D_p$ depending on the Group considered. This observation suggests that the average citations per paper ($N_c/N_p$) in each group ($=(D_p/D_c{)}^2=4D_p^2$) 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.

Accepted for publication in Physica A

References in corpus (3)

• Limiting Value of the Kolkata Index for Social Inequality and a Possible Social Constant
• On the meaning of the h-index
• Gintropic Scaling of Scientometric Indexes

Cited by in corpus (1)

• Q-factor: A measure of competition between the topper and the average in percolation and in SOC