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The '''''g''-index''' is an index for quantifying [[scientific]] [[productivity]] based on [[scientific publication|publication]] record. It was suggested in 2006 by Leo Egghe.<ref name="Egghe">Egghe, Leo (2006) Theory and practise of the g-index, Scientometrics, vol. 69, No 1, pp.&nbsp;131–152. {{DOI|10.1007/s11192-006-0144-7}}</ref><br />
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The index is calculated based on the distribution of [[citation]]s received by a given researcher's publications:<br />
:''Given a set of articles [[ranking|rank]]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<sup>2</sup> citations.''<br />
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Just as with the [[h-index]], the g-index is a number which is the same for two different quantities:<br />
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g is (1) the number of highly cited articles, such that each of them has brought (2) on average g citations.<br />
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This is in fact a rewriting of the definition<br />
:<math>g^2 \le \sum_{{i \le g }}c_{i} </math> <br />
as<br />
:<math>g \le \frac1g \sum_{{i\le g}}c_{i}</math><br />
[[File:Gindex1.jpg|thumb|275px|right| An example of a g-index (the raw citation data, plotted with stars, allows the h-index to also be extracted for comparison).]]<br />
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. 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.<ref name="Egghe"/> 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.<br />
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The g-index has been characterized in terms of three natural axioms by Woeginger (2008).<ref>Woeginger, G.J. (2008) An axiomatic analysis of Egghe’s g-index, Journal of Informetrics, vol. 2, pp.&nbsp;364–368. {{DOI|10.1016/j.joi.2008.05.002}}</ref> 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 number|rational]] generalisation.<ref>Tol, R.S.J. (2008) A rational, successive g-index applied to economics departments in Ireland, Journal of Informetrics, vol. 2, pp.&nbsp;149–155. [http://ideas.repec.org/p/sgc/wpaper/147.html preprint]</ref> {{Clarify|reason=What rational generalization did he propose?|date=April 2010}}<br />
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Tol also proposed a collective g-index.<br />
:''Given a set of researchers ranked in decreasing order of their g-index, the g<sub>1</sub>-index is the (unique) largest number such that the top g<sub>1</sub> researchers have on average at least a g-index of g<sub>1</sub>.''<br />
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==See also==<br />
* [[h-index]]<br />
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==References==<br />
<references/><br />
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[[Category:Bibliometrics]]<br />
[[Category:Academic publishing]]<br />
[[Category:Index numbers]]</div>84.226.181.252