# Citation metrics

Information about the citation metrics calculated by Publish or Perish

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.

Metric | Description |
---|---|

Publication years | Earliest and latest publication year found in the currently selected results. |

Citation years | Number of years from the earliest year found in the currently selected results to the year of the search (usually the current year). |

Papers | Total number of currently selected results. |

Citations | The sum of the citation counts across all currently selected results. |

Cites/year | Average number of citations per year (i.e., Citations / Citation years) |

Cites/paper | The sum of the citation counts across all papers, divided by the total number of papers. The median and mode are also calculated and available separately. |

Cites/author [PoP6] |
Average number of citations per author, calculated as follows: For each paper, its citation count is divided by the number of authors for that paper to give the normalized per-author citation count for the paper. The normalized citation counts are then summed across all papers to give the number of citations per author over the result set. |

Papers/author [PoP6] |
Average number of papers per author, calculated as follows: For each paper, 1/ |

Authors/paper | The average number of authors per paper, calculated as the sum of the author counts across all papers, divided by the total number of papers. The median and mode are also calculated and available separately. |

h-index | Hirsch's h-index, described below. |

g-index | Egghe's g-index, described below. |

hI,norm | Normalized individual h-index, described below. |

hI,annual | Annualized individual h-index, described below. |

hA-index | Average citation h-index, described below |

*Count [PoP6] | The number of results whose cites/year metric equals or exceeds the "star" threshold set in the Preferences: Results settings. In PoP7 in the new terminology acc10 correspond to the previous *Count. |

Papers with ACC >= 1,2,5,10,20 [PoP7] |
ACC = annual citation count (= citations / years_since_publication) ACCn = number of articles with an annual citation count >= n The various ACC levels are subsets of each other; all articles in acc10 are also part of acc5, acc2, and acc1; etc. |

## 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} = ah^{2}*), 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 h^{2}, 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 g

^{2}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.

Copyright © 2021 David Adams. All rights reserved. Page last modified on Sun 31 Oct 2021 18:48

Web master of Harzing.com and developer of the Publish or Perish software, among other things. He holds BSc and MSc degrees in Electrical Engineering, a PhD in Operations Research, and likes to watch academic life from a safe distance.