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# Universality of citation distributions: towards an objective measure of scientific impact

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### Abstract

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 $$c_f=c/c_0$$ is considered, where $$c_0$$ 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 $$c_f$$ 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.

### Most cited references15

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### The scientific impact of nations.

(2004)
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### How Popular is Your Paper? An Empirical Study of the Citation Distribution

(1998)
Numerical data for the distribution of citations are examined for: (i) papers published in 1981 in journals which are catalogued by the Institute for Scientific Information (783,339 papers) and (ii) 20 years of publications in Physical Review D, vols. 11-50 (24,296 papers). A Zipf plot of the number of citations to a given paper versus its citation rank appears to be consistent with a power-law dependence for leading rank papers, with exponent close to -1/2. This, in turn, suggests that the number of papers with x citations, N(x), has a large-x power law decay N(x)~x^{-alpha}, with alpha approximately equal to 3.
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### The skewness of science

(1992)
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### Author and article information

###### Journal
05 June 2008
2008-10-27
###### Article
10.1073/pnas.0806977105
0806.0974