The relative significance of the H-index
  Use of the Hirsch-index ($h$) as measure of an author's visibility in the scientific literature has become popular as an alternative to a gross measure like total citations (c). I show that, at least in astrophysics, $h$ correlates tightly with overall citations. The mean relation is $h=0.5(\sqrt c+1)$. Outliers are few and not too far from the mean, especially if `normalized' ADS citations are used for $c$ and $h$. Whatever the theoretical reasoning behind it, the Hirsch index in practice does not appear to measure something significantly new. 
H. C. Spruit
astro-ph.IM cs.DL physics.soc-ph