  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.
