G-index

The '''g-index''' is an author-level metric suggested in 2006 by Leo Egghe. 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 g2 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 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). g^2 \le \sum_{i \le g } c_i as g \le \frac1g \sum_{i \le g} c_i. 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 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. 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 1 has a g-index of 10, while Author 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 |}