# g-index

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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

*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 (10

^{2}), a

*g*-index of 20 indicates that the top 20 publications of an author have been cited 400 times (20

^{2}).

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

as

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.^{[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 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.

Author 1 | Author 2 | |
---|---|---|

Paper 1 | 30 | 10 |

Paper 2 | 17 | 9 |

Paper 3 | 15 | 9 |

Paper 4 | 13 | 9 |

Paper 5 | 8 | 8 |

Paper 6 | 6 | 6 |

Paper 7 | 5 | 5 |

Paper 8 | 4 | 4 |

Paper 9 | 3 | 2 |

Paper 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*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

[edit]- ^
^{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