The g-index was proposed by Leo Egghe (2006). It aims to improve on the h-index by giving more weight to highly-cited articles. 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. 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.
For instance, an academic has a g-index of 30 if the top 30 most cited of his/her papers combined have at least 900 citations. It aims to improve on the h-index by giving more weight to highly-cited articles. The g-index cannot be larger than the number of articles and academic has published.
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.