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

Abstract

We analyse 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 (2022) list and their corresponding h (3 ≤ h ≤ 284), Nc(1009 ≤ N c ≤ 428620) and Np (3 ≤ Np ≤ 3791) statistics from the Scopus data, dividing the data into six equal Groups, each containing 20,000 authors or scientists. We find, in each Group, f (h), f (Nc) and f (Np) fit well with the kinetic exchange (model with fixed "wealth saving propensity") wealth distribution: For example like Gamma function distributions f (h) ∼ h γ h exp(−h/T h ), having similar relations between the fitting noise level or temperature level (T h ) and average value of h, where the power γ h is determined by the "citation saving propensity" in each group. The observation that h = DcN αc c = DpN αp p , with αc = 1/2 = αp, suggesting the average coordination (Dunbar-like) number of the citation network, given by the average citations per paper (in each group) equal to Nc/Np = (Dp/Dc) 2 ranges from 58 to 29.