TL;DR
This paper examines the h-index, a popular metric for scientific impact, and explores its relationship with total citations, revealing that sqrt{c} generally scales with h and analyzing the distribution of their ratio.
Contribution
It provides an empirical analysis confirming the relationship between the h-index and total citations, and investigates the distribution of their ratio among physicists.
Findings
sqrt{c} scales as h in physicists
The ratio sqrt{c}/2h is sharply peaked around 1
Outliers indicate different publication record types
Abstract
The h-index -- the value for which an individual has published at least h papers with at least h citations -- has become a popular metric to assess the citation impact of scientists. As already noted in the original work of Hirsch and as evidenced from data of a representative sample of physicists, sqrt{c} scales as h, where c is the total number citations to an individual. Thus sqrt{c} appears to be equivalent to the h index. As a further check of this equivalence, the distribution of the ratio s=sqrt{c}/2h for this sample is sharply peaked about 1. The outliers in this distribution reveal fundamentally different types of individual publication records.
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