The Egghe number is considered to be an improved alternative to the Hirsch number, at least to solve some problems the later has. The h-index ignores the number of citations to each individual article beyond what is needed to achieve a certain h-index. Hence an academic with an h-index of 5 could theoretically have a total of 25 citations (5 for each paper), but could also have more than a 1000 citations (4 papers with 250 citations each and one paper with 5 citations). In reality these extremes will be unlikely. However, once a paper belongs to the top h papers, its subsequent citations no longer "count". Such a paper can double or triple its citations without influencing the h-index (Egghe, 2006). Hence, in order to give more weight to highly-cited articles Leo Egghe (2006) proposed the g-index. The g-index is defined as follows:
Given a set of articles ranked in decreasing order of the number of citations that they received, the g-index is the (unique) largest number such that the top g articles received (together) at least g2 citations.
Although the g-index has not yet attracted much attention or empirical verification, it would seem to be a very useful complement to the h-index. Here are the references (h* was proposed in 2005 and g** in 2006) - both are online:
* J. E. Hirsch, PNAS, Vol. 102, no. 46, 2005.
** L. Egghe, Scientometrics, Vol. 69, no. 1, 2006.
Finally this free software automatically computes both indexes: http://www.harzing.com/resources.htm#/pop.htm