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Theg-index is anauthor-level metric suggested in 2006 by Leo Egghe.^[1] The index is calculated based on the distribution ofcitations received by a given researcher's publications, such that given a set of articlesranked in decreasing order of the number of citations that they received, theg-index is the unique largest number such that the topg articles received together at leastg² citations. Hence, ag-index of 10 indicates that the top 10 publications of an author have been cited at least 100 times (10²), ag-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 numbern of highly cited articles for which the average number of citations is at leastn. This is in fact a rewriting of the definition

${\displaystyle g^2\le \sum _{i\le g}{c}_i}$

as

${\displaystyle g\le \frac{1}{g}\sum _{i\le g}{c}_i.}$

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

Theg-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 theh-index, theg-index is anatural number and thus lacks indiscriminatory power. Therefore, Tol (2008) proposed arational generalisation.^{[3][clarification needed]}

Tol also proposed a collectiveg-index.

Given a set of researchers ranked in decreasing order of theirg-index, theg₁-index is the (unique) largest number such that the topg₁ researchers have on average at least ag-index ofg₁.

• Author-level metrics

• Articles with short description
• Short description matches Wikidata
• Wikipedia articles needing clarification from April 2010