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The ''g''-index is an author-level metric suggested in 2006 by Leo Egghe. The index is calculated based on the distribution of 
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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 papers. Roughly, the effect is that ''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. 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 papers. Therefore, in all cases ''g'' is at least ''h'', and is in most cases higher. 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 published papers exceeds the total number of published papers; 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 papers, their ''g''-index will increase.
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
preprint
/ref>{{Clarify, reason=What rational generalization did he propose?, date=April 2010 Tol also proposed a collective ''g''-index. :Given a set of researchers ranked in decreasing order of their ''g''-index, the ''g''1-index is the (unique) largest number such that the top ''g''1 researchers have on average at least a ''g''-index of ''g''1.
citation
A citation is a reference to a source. More precisely, a citation is an abbreviated alphanumeric expression embedded in the body of an intellectual work that denotes an entry in the bibliographic references section of the work for the purpose of ...
s received by a given researcher's publications, such that given a set of articles rank
Rank is the relative position, value, worth, complexity, power, importance, authority, level, etc. of a person or object within a ranking, such as:
Level or position in a hierarchical organization
* Academic rank
* Diplomatic rank
* Hierarchy
* H ...
ed 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 ''g''2 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
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as
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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 papers. Roughly, the effect is that ''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. 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 papers. Therefore, in all cases ''g'' is at least ''h'', and is in most cases higher. 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 published papers exceeds the total number of published papers; 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 papers, their ''g''-index will increase.
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
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called '' cardinal ...
and thus lacks in discriminatory power. Therefore, Tol (2008) proposed a rational
Rationality is the quality of being guided by or based on reasons. In this regard, a person acts rationally if they have a good reason for what they do or a belief is rational if it is based on strong evidence. This quality can apply to an abil ...
generalisation.preprint
/ref>{{Clarify, reason=What rational generalization did he propose?, date=April 2010 Tol also proposed a collective ''g''-index. :Given a set of researchers ranked in decreasing order of their ''g''-index, the ''g''1-index is the (unique) largest number such that the top ''g''1 researchers have on average at least a ''g''-index of ''g''1.
References