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

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