The index is calculated based on the distribution of citations received by a given researcher's publications:
- 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.
Just as with the h-index, the g-index is a number which is the same for two different quantities:
g is (1) the number of highly cited articles, such that each of them has brought (2) on average g citations.
This is in fact a rewriting of the definition
In other words, this means that in order to have a g-index of n an author that produces n articles should have, on average, n citations for each of them. Unlike the h-index, the g-index depends on the full citation count of very highly cited papers. Roughly, h is the number of papers of a quality threshold that rises as h rises; g allows citations from higher-cited papers to be used to bolster lower-cited papers in meeting this threshold. Therefore, in all cases g is at least h, and is in most cases higher. However, unlike the h-index, the g-index saturates whenever the average number of citations for all published papers exceeds the total number of published papers; the way it is defined, the g-index is not adapted to this situation.
The g-index has been characterized in terms of three natural axioms by Woeginger (2008). The simplest of these three axioms states that by moving citations from weaker articles to stronger articles, one's research index should not decrease. Like the h-index, the g-index is a natural number and thus lacks in discriminatory power. Therefore, Tol (2008) proposed a rational generalisation. [clarification needed]
Tol also proposed a collective g-index.
- Given a set of researchers ranked in decreasing order of their g-index, the g1-index is the (unique) largest number such that the top g1 researchers have on average at least a g-index of g1.
- Egghe, Leo (2006) Theory and practise of the g-index, Scientometrics, vol. 69, No 1, pp. 131–152. doi:10.1007/s11192-006-0144-7
- Woeginger, G.J. (2008) An axiomatic analysis of Egghe’s g-index, Journal of Informetrics, vol. 2, pp. 364–368. doi:10.1016/j.joi.2008.05.002
- Tol, R.S.J. (2008) A rational, successive g-index applied to economics departments in Ireland, Journal of Informetrics, vol. 2, pp. 149–155. preprint