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

TL;DR

This study analyzes the distributions of Hirsch index, total citations, and total papers among top scientists, revealing scaling behaviors and proposing models that connect these metrics through kinetic exchange and power-law relations.

Contribution

It introduces a kinetic exchange model to describe citation and publication distributions and derives their relationships using power-law scaling, revealing variations across different scientist groups.

Findings

Distributions fit Gamma models with specific parameters.

Power-law relations connect Hirsch index with citations and papers.

Variations in citation per paper indicate different network coordination numbers.

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 $f(h) \sim h^{\gamma_h} \mathrm{exp} (-h/T_h)$ 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.