View source for G-index

{{Short description|Citation metric}}
{{DISPLAYTITLE:''g''-index}}
{{Citation metrics}}
{{For|the G-index in photometry|Spectral G-index}}
The '''''g''-index''' is an [[author-level metric]] suggested in 2006 by Leo Egghe.<ref name="Egghe">{{cite journal
 |last1=Egghe |first1=Leo
 |year=2006
 |title=Theory and practise of the ''g''-index
 |journal=Scientometrics
 |volume=69 |issue=1 |pages=131–152
 |doi=10.1007/s11192-006-0144-7
|hdl=1942/981
 |s2cid=207236267
 |hdl-access=free
 }}</ref> The index is calculated based on the distribution of [[citation]]s received by a given researcher's publications, such that 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. Hence, a ''g''-index of 10 indicates that the top 10 publications of an author have been cited at least 100 times (10<sup>2</sup>), a ''g''-index of 20 indicates that the top 20 publications of an author have been cited 400 times (20<sup>2</sup>).  

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
[[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).]]
: <math>g^2 \le \sum_{i \le g } c_i</math> 
as
: <math>g \le \frac1g \sum_{i \le g} c_i.</math>
The ''g''-index is an alternative for the older [[h-index|''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.<ref name="Egghe"/> 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. 
{| class="wikitable"
|+ An example of two authors who both have 10 publications, both authors have a ''h''-index of 6. However, Author&nbsp;1 has a g-index of 10, while Author&nbsp;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).<ref>
{{cite journal
 |last1=Woeginger |first1=Gerhard J. |author-link=Gerhard J. Woeginger
 |year=2008
 |title=An axiomatic analysis of Egghe's ''g''-index
 |journal=Journal of Informetrics
 |volume=2 |issue=4 |pages=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>
{{cite journal
 |last1=Tol |first1=Richard S. J.
 |year=2008
 |title=A rational, successive g-index applied to economics departments in Ireland
 |journal=Journal of Informetrics
 |volume=2 |issue=2 |pages=149–155
 |doi=10.1016/j.joi.2008.01.001
}} [http://ideas.repec.org/p/sgc/wpaper/147.html 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''<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>.

==References==
<references/>

[[Category:Author-level metrics]]

{{Academic publishing}}