Metrics: h and g-index

Note: This tutorial was originally written for Publish or Perish version 4 and all screenshots come from this version. However, the information as such is also applicable for the latest Publish or Perish version 5.

Publish or Perish provides a wide range of metrics. The most important ones are listed in the most right-hand column of the results list. Here we explain the two most influential of them and then provide an illustration based on the same academics as before.

h-index

Unless you have been hiding under a stone in the last ten years, you will probably have heard about the h-index. It is defined as follows (Hirsch, 2005:16569):

A scientist has index h if h of his/her Np papers have at least h citations each, and the other (Np-h) papers have no more than h citations each.

A h-index of 20 means that an academic has published at least 20 papers that have received at least 20 citations each. The h-index thus combines an assessment of both quantity (number of papers) and an approximation of quality (impact, or citations to these papers).

h-index rewards consistent stream of high-impact publications

An academic cannot have a high h-index without publishing a substantial number of papers. However, this is not enough. These papers need to be cited in order to count for the h-index. Hence the h-index favours academics that publish a continuous stream of papers with lasting and above-average impact.

g-index

The g-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.

g-index looks at overall record

A g-index of 20 means that and academic has published at least 20 articles that combined have received at least 400 citations. However, unlike the h-index these citations could be generated by only a small number of articles. For instance an academic with 20 papers, 15 of which have no citations with the remaining five having respectively 350, 35, 10, 3 and 2 citations would have a g-index of 20, but a h-index of 3 (three papers with at least 3 citations each).

g-index allows highly-cited papers to bolster low-cited papers

Roughly, h is the number of papers of a certain “quality” [citations] threshold, a 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. 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.

What can one conclude from complex metrics?

Here I return to the publication records of Maria and myself. As indicated earlier, our total number of citations (approximately 8300 vs. 9500) and time since first publication are quite similar (17 years vs. 20 years). As a result, our number of citations per year is very similar too (489 vs 475). This time I show the more complex metrics. What can we conclude from these?

tip17a tip17

h-index

My record shows a higher h-index than that of Maria. This is not surprising, given that she has published fewer papers and hence it is more difficult for her to achieve a high h-index. In Maria’s case, only one third of her papers are not included in the h-index. In my case, this is true for nearly 60% of my papers. That said, given that her h-index is lower, it is easier for her to increase it further as her next paper only needs to acquire 27 citations to be included, whereas my next paper needs to acquire 46 citations.

g-index

My g-index is more than twice as high as that of Maria. The simple reason is that neither the g-index nor the h-index can be higher than the total number of papers published and Maria has “only” published 41 papers so far. Hence, the maximum her g-index can reach is 41. Even if she would publish another paper without any citations, her g-index would still increase. This is clearly a limitation of the g-index.

Conclusions

The h-index and g-index are both limited by the number of papers one publishes. Hence these indices – and especially the g-index – will always favour academics that publish more papers (provided they are cited at least moderately well). These indices are therefore not very suitable to assess the impact of academics that have published one or two ground-breaking contributions, but have not published any further highly cited work. For these academics, the total number of citations might be a more appropriate metric. That’s exactly why Publish or Perish provides a wide range of metrics. The variety of metrics allows you to select the metrics most appropriate to your purpose.

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