Gintropic Scaling of Scientometric Indexes

TL;DR

This paper investigates the scaling relations between scientometric indicators like h-index, total publications, and citations, using inequality measures and large data analysis to establish new bounds and insights into citation distributions.

Contribution

It introduces a new upper bound for the h-index based on total citations and applies inequality measures like Gini and gintropy to analyze citation distributions.

Findings

Established a new upper bound for h-index as a function of total citations.

Found the Gini index for citations peaks around 0.8, indicating high inequality.

Confirmed the scaling relations using large Google Scholar datasets.

Abstract

The most frequently used indicators for the productivity and impact of scientists are the total number of publication ($N_{pub}$), total number of citations ($N_{cit}$) and the Hirsch (h) index. Since the seminal paper of Hirsch, in 2005, it is largely debated whether the h index can be considered as an indicator independent of $N_{pub}$ and $N_{cit}$. Exploiting the Paretian form for the distribution of citations for the papers authored by a researcher, here we discuss scaling relations between h, $N_{pub}$ and $N_{cit}$. The analysis incorporates the Gini index as an inequality measure of citation distributions and a recently proposed inequality kernel, gintropy (resembling to the entropy kernel). We find a new upper bound for the h value as a function of the total number of citations, confimed on massive data collected from Google Scholar. Our analyses reveals also that the individualized Gini index calculated for the citations received by the publications of an author peaks around 0.8, a value much higher than the one characteristic for the usual socio-economic inequalities.