Citation metrics

Information about the citation metrics calculated by Publish or Perish

David Adams - Tue 20 Dec 2016 16:26 (updated Sat 15 Apr 2023 07:30)

Publish or Perish calculates a large number of citation metrics. Please note that these metrics are only as good as their input. We recommend that you consult the following topics for information about the limitations of the citation metrics and the underlying sources that Publish or Perish uses:

• Metrics tutorial page
• Accuracy of the results
• Reflections on the h-index
• Reflections on Google Scholar

The table below lists the metrics that are directly visible in the Publish or Perish main window, in its Results panel (Publish or Perish version 7 and earlier) or Citation metrics panel (Publish or Perish version 8 and later).

Additional metrics are available when you use one of the Save Metrics As... or Copy Metrics As... commands from the Publish or Perish main menu, one of the pop-up menus (available by right-clicking on a search or result), or the Copy Results or Save Results button.

h-index

The h-index was proposed by J.E. Hirsch in his paper An index to quantify an individual's scientific research output, arXiv:physics/0508025 v5 29 Sep 2005. It is defined as follows:

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

It aims to measure the cumulative impact of a researcher's output by looking at the amount of citation his/her work has received. Publish or Perish calculates and displays the h index proper, its associated proportionality constant a (from N_c,tot = ah²), and the rate parameter m (from h ~ mn, where n is the number of years since the first publication).

The properties of the h-index have been analyzed in various papers; see for example Leo Egghe and Ronald Rousseau: An informetric model for the Hirsch-index, Scientometrics, Vol. 69, No. 1 (2006), pp. 121-129.

Publish or Perish also calculates the e-index as proposed by Chun-Ting Zhang in his paper The e-index, complementing the h-index for excess citations, PLoS ONE, Vol 5, Issue 5 (May 2009), e5429. The e-index is the (square root) of the surplus of citations in the h-set beyond h², i.e., beyond the theoretical minimum required to obtain a h-index of 'h'. The aim of the e-index is to differentiate between scientists with similar h-indices but different citation patterns.

These metrics are shown as h-index, Hirsch a=y.yy, m=z.zz, and e-index in the output.

For applications of the h-index, see the h-index and g-index tutorial page.

g-index

The g-index was proposed by Leo Egghe in his paper Theory and practice of the g-index, Scientometrics, Vol. 69, No 1 (2006), pp. 131-152. It is defined as follows:

[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.

It aims to improve on the h-index by giving more weight to highly-cited articles.

This metric is shown as g-index in the output.

For applications of the g-index, see the h-index and g-index tutorial page.

Contemporary h-index

The Contemporary h-index was proposed by Antonis Sidiropoulos, Dimitrios Katsaros, and Yannis Manolopoulos in their paper Generalized h-index for disclosing latent facts in citation networks, arXiv:cs.DL/0607066 v1 13 Jul 2006.

It adds an age-related weighting to each cited article, giving (by default; this depends on the parametrization) less weight to older articles. The weighting is parametrized; the Publish or Perish implementation uses gamma=4 and delta=1, like the authors did for their experiments. This means that for an article published during the current year, its citations count four times. For an article published 4 years ago, its citations count only once (4/4). For an article published 6 years ago, its citations count 4/6 times, and so on.

This metric is shown as hc-index and ac=y.yy in the output.

For application of this index and some related ones, see the tutorial page about various h-indices.

Individual h-index (3 variations)

The Individual h-index was proposed by Pablo D. Batista, Monica G. Campiteli, Osame Kinouchi, and Alexandre S. Martinez in their paper Is it possible to compare researchers with different scientific interests?, Scientometrics, Vol 68, No. 1 (2006), pp. 179-189.

It divides the standard h-index by the average number of authors in the articles that contribute to the h-index, in order to reduce the effects of co-authorship; the resulting index is called h_I.

Publish or Perish also implements an alternative individual h-index, h_I,norm, that takes a different approach: instead of dividing the total h-index, it first normalizes the number of citations for each paper by dividing the number of citations by the number of authors for that paper, then calculates h_I,norm as the h-index of the normalized citation counts. This approach is much more fine-grained than Batista et al.'s; we believe that it more accurately accounts for any co-authorship effects that might be present and that it is a better approximation of the per-author impact, which is what the original h-index set out to provide.

The third variation is due to Michael Schreiber and first described in his paper To share the fame in a fair way, h_m modifies h for multi-authored manuscripts, New Journal of Physics, Vol 10 (2008), 040201-1-8. Schreiber's method uses fractional paper counts instead of reduced citation counts to account for shared authorship of papers, and then determines the multi-authored h_m index based on the resulting effective rank of the papers using undiluted citation counts.

These metrics are shown as hI-index (Batista et al.'s), hI,norm (PoP's), and hm-index (Schreiber's) in the output.

For applications, see the tutorial page about the hI,norm index.

Average annual increase in individual h-index

The individual, average annual increase of the h-index called hI,annual was proposed by Anne-Wil Harzing, Satu Alakangas and David Adams in their paper hIa: An individual annual h-index to accommodate disciplinary and career length differences, Scientometrics, vol. 99, no. 3, pp. 811-821, which is available online on the Harzing.com web site.

As of release 4.3 Publish or Perish calculates and displays this new index. The average annual increase in the individual h-index is useful for the following reasons:

• In common with the hI,norm index, it removes to a considerable extent any discipline-specific publication and citation patterns that otherwise distort the h-index.
• It also reduces the effect of career length and provides a fairer comparison between junior and senior researchers.

The hI,annual is meant as an indicator of an individual's average annual research impact, as opposed to the lifetime score that is given by the h-index or hI,norm.

This metric is shown as hI,annual in the output.

For applications, see the tutorial page about the hIa index.

Age-weighted citation rate (AWCR, AWCRpA) and AW-index

The age-weighted citation rate was inspired by Bihui Jin's note The AR-index: complementing the h-index, ISSI Newsletter, 2007, 3(1), p. 6.

The AWCR measures the number of citations to an entire body of work, adjusted for the age of each individual paper. It is an age-weighted citation rate, where the number of citations to a given paper is divided by the age of that paper. Jin defines the AR-index as the square root of the sum of all age-weighted citation counts over all papers that contribute to the h-index.

However, in the Publish or Perish implementation we sum over all papers instead, because we feel that this represents the impact of the total body of work more accurately. (In particular, it allows younger and as yet less cited papers to contribute to the AWCR, even though they may not yet contribute to the h-index.)

The AW-index is defined as the square root of the AWCR to allow comparison with the h-index; it approximates the h-index if the (average) citation rate remains more or less constant over the years.

The per-author age-weighted citation rate is similar to the plain AWCR, but is normalized to the number of authors for each paper.

These metrics are shown as AWCR, AWCRpA and AW-index in the output.

hA-index

The h_a-index was proposed by Yves Fassin in The average citation h_a-index, ISSI Newsletter, 2020, 16(4), pp. 64-67, available online.

The calculation of the h_a-index follows a similar pattern as the h-index, but divides the citation count of each paper by the age of the paper before ranking them and calculating the index as follows: the h_a-index of a given dataset is the largest number of papers in the dataset that have obtained at least h_a citations per year on average. In doing so, the h_a-index gives a measure of the sustained citation rate of the data set, rather than only the total number of citations.

Note: As a practical matter and at the request of Yves Fassin, Publish or Perish, during the calculation of the h_a-index ranking, rounds average citation counts up to the next whole number if their fraction ≥ 0.5.

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