g-index

The g-index is an author-level metric 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. Hence, a g-index of 10 indicates that the top 10 publications of an author have been cited at least 100 times (10²), a g-index of 20 indicates that the top 20 publications of an author have been cited 400 times (20²).

It can be equivalently defined as the largest number n of highly cited articles for which the average number of citations is at least n. This is in fact a rewriting of the definition

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

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

as

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

The g-index is an alternative for the older h-index. The h-index does not average the number of citations. Instead, the h-index only requires a minimum of n citations for the least-cited article in the set and thus ignores the citation count of very highly cited publications. Roughly, the effect is that h is the number of works of a quality threshold that rises as h rises; g allows citations from higher-cited works to be used to bolster lower-cited works in meeting this threshold. In effect, the g-index is the maximum reachable value of the h-index if a fixed number of citations can be distributed freely over a fixed number of publications. Therefore, in all cases g is at least h, and is in most cases higher.^[1] The g-index often separates authors based on citations to a greater extent compared to the h-index. However, unlike the h-index, the g-index saturates whenever the average number of citations for all publications exceeds the total number of publications; the way it is defined, the g-index is not adapted to this situation. However, if an author with a saturated g-index publishes more, their g-index will increase.

An example of two authors who both have 10 publications, both authors have a h-index of 6. However, Author 1 has a g-index of 10, while Author 2 has a g-index of 7.
	Author 1	Author 2
Work 1	30	10
Work 2	17	9
Work 3	15	9
Work 4	13	9
Work 5	8	8
Work 6	6	6
Work 7	5	5
Work 8	4	4
Work 9	3	2
Work 10	1	1
Total cites	102	63
Average cites	10,2	6,3

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. 69 (1): 131–152. doi:10.1007/s11192-006-0144-7. hdl:1942/981. S2CID 207236267.
^ Woeginger, Gerhard J. (2008). "An axiomatic analysis of Egghe's g-index". Journal of Informetrics. 2 (4): 364–368. doi:10.1016/j.joi.2008.05.002.
^ Tol, Richard S. J. (2008). "A rational, successive g-index applied to economics departments in Ireland". Journal of Informetrics. 2 (2): 149–155. doi:10.1016/j.joi.2008.01.001. Preprint.

[Egghe-1] Egghe, Leo (2006). "Theory and practise of the g-index". Scientometrics. 69 (1): 131–152. doi:10.1007/s11192-006-0144-7. hdl:1942/981. S2CID 207236267.

[2] Woeginger, Gerhard J. (2008). "An axiomatic analysis of Egghe's g-index". Journal of Informetrics. 2 (4): 364–368. doi:10.1016/j.joi.2008.05.002.

[3] Tol, Richard S. J. (2008). "A rational, successive g-index applied to economics departments in Ireland". Journal of Informetrics. 2 (2): 149–155. doi:10.1016/j.joi.2008.01.001. Preprint.

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