Hirsch指数与总引文分布的标度及类动力学交换行为：Scopus-CiteScore数据分析
Scaling and Kinetic Exchange Like Behavior of Hirsch Index and Total Citation Distributions: Scopus-CiteScore Data Analysis
AI总结：
本文分析Scopus中12万名高被引作者的h指数、总引文和论文数分布，用Gamma型动力学交换财富模型拟合，并借助平方根标度揭示各组篇均引文与类Dunbar协调数差异。
摘要：
我们分析了来自Stanford cite-score（或c-score）2022榜单中得分最高的120,000位作者（科学家）的Hirsch指数（h）、总引文数（N_c）和论文总数（N_p）的数据分布f(h)、f(N_c)和f(N_p)，以及来自Scopus数据的相应h（3 ≤ h ≤ 284）、N_c（1009 ≤ N_c ≤ 428620）和N_p（3 ≤ N_p ≤ 3791）统计量。出于正文中说明的原因，我们将这些最高得分者（c-score在5.6125至3.3461范围内）的数据划分为六个连续且规模相等的组，每组包含20,000位作者或科学家。我们尝试在每个组中用Gamma分布拟合f(h)、f(Nc)和f(Np)，将其视为固定储蓄倾向动力学交换模型中的“财富分布”，并发现f(h) ~ h^{γ_h} exp(-h/T_h)，其中拟合噪声水平或温度水平（T_h）以及h的平均值、指数γ_h由每个组中的“引文储蓄倾向”决定。我们进一步表明，利用先前提出的类幂律标度h = D_c N_c^{α_c}（或h = D_p N_p^{α_p}），其中α_c = 1/2 = α_p，我们可以从观测到的f(N_c)或f(N_p)导出观测到的f(h)，其中D_c = 0.5，而D_p取决于所考虑的组。这一观察表明，每组中的篇均引文数（N_c/N_p）（= (D_p/D_c)^2 = 4D_p^2）随此处考虑的六个组的c-score范围而变化（从58到29），这意味着属于不同组或网络的科学家具有不同的有效类Dunbar协调数。
英文摘要：
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 $f(h) \sim h^{γ_h} \mathrm{exp} (-h/T_h)$ with fitting noise level or temperature level ($T_h$) and average value of $h$, and the power $γ_h$ determined by the ``citation saving propensity'' in each Group. We further showed that using some earlier proposed power law scaling like $h = D_c N_c^{α_c}$ (or $h = D_p N_p^{α_p}$) with $α_c = 1/2 = α_p$, 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.
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