I propose the index h, defined as the number of papers with citation number ≥h, as a useful index to characterize the scientific output of a researcher.

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An index to quantify an individual's scientific research output

We study the distributions of citations received by a single publication within several disciplines, spanning broad areas of science. We show that the probability that an article is cited c times has large variations between different disciplines, but all distributions are rescaled on a universal curve when the relative indicator cf = c/c0 is considered, where c0 is the average number of citations per article for the discipline. In addition we show that the same universal behavior occurs when citation distributions of articles published in the same field, but in different years, are compared. These findings provide a strong validation of cf as an unbiased indicator for citation performance across disciplines and years. Based on this indicator, we introduce a generalization of the h index suitable for comparing scientists working in different fields.

https://www.pnas.org/content/pnas/105/45/17268.full.pdf

Universality of citation distributions: Toward an objective measure of scientific impact

To account for strong ageing characteristics of citation networks, we modify the PageRank algorithm by initially distributing random surfers exponentially with age, in favour of more recent publications. The output of this algorithm, which we call CiteRank, is interpreted as approximate traffic to individual publications in a simple model of how researchers find new information. We optimize parameters of our algorithm to achieve the best performance. The results are compared for two rather different citation networks: all American Physical Society publications between 1893 and 2003 and the set of high-energy physics theory (hep-th) preprints. Despite major differences between these two networks, we find that their optimal parameters for the CiteRank algorithm are remarkably similar. The advantages and performance of CiteRank over more conventional methods of ranking publications are discussed.

https://iopscience.iop.org/article/10.1088/1742-5468/2007/06/P06010/pdf

Ranking scientific publications using a model of network traffic

I propose to sharpen the index h, suggested by Hirsch as a useful index to characterize the scientific output of a researcher, by excluding the self-citations. Performing a self-experiment and also discussing in detail two anonymous data sets, it is shown that self-citations can significantly reduce the h index in contrast to Hirsch's expectations. This result is confirmed by an analysis of 13 further data sets.

https://iopscience.iop.org/article/10.1209/0295-5075/78/30002/pdf

Self-citation corrections for the Hirsch index

We develop a model for the distribution of scientific citations. The model involves a dual mechanism: in the direct mechanism, the author of a new paper finds an old paper A and cites it. In the indirect mechanism, the author of a new paper finds an old paper A only via the reference list of a newer intermediary paper B, which has previously cited A. By comparison to citation databases, we find that papers having few citations are cited mainly by the direct mechanism. Papers already having many citations (“classics”) are cited mainly by the indirect mechanism. The indirect mechanism gives a power-law tail. The “tipping point” at which a paper becomes a classic is about 25 citations for papers published in the Institute for Scientific Information (ISI) Web of Science database in 1981, 31 for Physical Review D papers published from 1975–1994, and 37 for all publications from a list of high h-index chemists assembled in 2007. The power-law exponent is not universal. Individuals who are highly cited have a systematically smaller exponent than individuals who are less cited.

https://www.pnas.org/content/pnas/107/37/16023.full.pdf

Nonuniversal power law scaling in the probability distribution of scientific citations

https://physicstoday.scitation.org/doi/pdf/10.1063/1.1955479

Matthew Sands

Papers

Capturing the Wisdom of Feynman