On the meaning of the h-index

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.