g-index

The g-index is an index for quantifying scientific productivity based on publication record (an author-level metric). 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, such that 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.

It can be equivalently defined as the number of highly cited articles, such that each of them has an average of 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).

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.^[1] 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).^[2] 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.^[3] ^{[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
^ 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

[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] 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

[3] 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

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See also

References