g-index

The g-index is an index for quantifying scientific productivity based on publication record. It was suggested in 2006 by Leo Egghe.^[1]

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

g^{2}\leq \sum _{i\leq g}c_{i}

as

g\leq {\frac {1}{g}}\sum _{i\leq g}c_{i}

An example of a g-index (the raw citation data, plotted with stars, allows the h-index to also be extracted for comparison).

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. In a way, this is similar to the h-index, with the difference that the number of citations for a single article is not critical. The g-index attempts to address shortcomings of the h-index. Roughly, g is expected to be in a good correlation with the total number of citations an author has received, while h correlates with the highest number of citations which the most quoted paper brings to his author.^[2] Accordingly g is found to be greater than h.^[1]

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.

References

^ ^a ^b 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
^ If the total sum of citations is T and the maximal among them is C, then T=C+(T-C) and g~√T while h~√C.

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
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

[Egghe-1] 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

[2] If the total sum of citations is T and the maximal among them is C, then T=C+(T-C) and g~√T while h~√C.

[1]

[2]

See also

References