The G-index was developed by Leo Egghe in 2006. The original articles are available at https://doclib.uhasselt.be/dspace/bitstream/1942/983/1/an%20improvement.pdf and http://www.springerlink.com/content/4119257t25h0852w/fulltext.pdf.
The G-index is an improvement of the H-index. Egghe consideres it a drawback of the H-index that it does not take into account the citation scores of the top articles (defining h). Once articles belong to the top class it is totally unimportant whether or not they continue to be cited or not and, if cited, it is unimportant how many citations they receive. The G-index overcomes this disadvantage while keeping all advantages of the H-index and the calculation of the G-index is also as simple as the one of the H-index. The higher the number of citations in the top class that skew the citation distribution, the higher the G-score. The variance of the g-indexes of researchers will be much higher than the one of the h-indexes which makes a comparison between authors concerning their visibility in the world more apparent.
Publish or Perish calculates the G-indexes for scientists and journals based on Google Scholar's citation data at http://www.harzing.com/resources.htm.
A set of papers has a G-index g if g is the highest rank such that the top g papers have, together, at least g2 citations.
The table shows the H- and G-indexes of Price medallists. The variation of the G-indexes is greater than that of the H-indexes.
Image source: Egghe, L. 2006. Theory and practise of the g-index <http://www.akademiai.com/content/4119257t25h0852w/fulltext.pdf> 8.4.2009.