Do we need the g-index?

Using a very small sample of 8 datasets it was recently shown by De Visscher (2011) that the g-index is very close to the square root of the total number of citations. It was argued that there is no bibliometrically meaningful difference. Using another somewhat larger empirical sample of 26 datasets I show that the difference may be larger and I argue in favor of the g-index. 1. Introduction The h-index is given by the largest number h of papers of a researcher which have received at least h citations. One criticism is that the excess citations, i.e., all citations which exceed h for a given publication do not have an effect. Therefore Egghe (2006) proposed the g-index which is given by the largest number g of papers which have received at least g citations on average (Schreiber, 2010). Recently De Visscher (2011) utilized a rather small sample of the citation records of 8 famous physicists which had previously been analyzed by Schreiber (2008a, 2010). De Visscher showed that g is very close to the square root √S of the total number S of citations which would mean that the index is essentially a metric of this total number. De Visscher concluded that the g-index is not necessary and he also argued that the h-index is more meaningful, because it rewards a so-called " consistent " citation record in which the highly cited papers show a rather homogeneous citation distribution. Egghe (2012) took a different view and argued in favor of the g-index, just because it awards non-consistent impact. De Visscher already pointed out that it is premature to generalize his results because of the small sample size and he proposed further studies. It is the aim of the present investigation to provide such an analysis for a different and larger sample, comprising the citation datasets of 26 more average physicists. In this case the difference between g and √S is more pronounced as already suspected by De Visscher (2011). This can be traced back to the fact that a larger share of the papers does not contribute to the g-core, i.e., the g-defining set of publications. Although these papers have rather small citation frequencies, their cumulative effect is not so small that the deviations between g and √S can be neglected. Additionally the observation that certain datasets yield especially large deviations corroborates my assumption that there is a bibliometrically …