The mathematical relation between the impact factor and the uncitedness factor

Leo Egghe

doi:10.1007/s11192-007-1902-x

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Scientometrics

Volume/Issue:: Volume 76: Issue 1

The mathematical relation between the impact factor and the uncitedness factor

Author:

Leo Egghe

Leo Egghe

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Pages:: 117–123

Online Publication Date:: 23 May 2008

Publication Date:: 01 Jul 2008

Article Category:: Research Article

DOI:: https://doi.org/10.1007/s11192-007-1902-x

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Abstract

In a general framework, given a set of articles and their received citations (time periods of publication or citation are not important here) one can define the impact factor (IF) as the total number of received citations divided by the total number of publications (articles). The uncitedness factor (UF) is defined as the fraction of the articles that received no citations. It is intuitively clear that IF should be a decreasing function of UF. This is confirmed by the results in [van Leeuwen & Moed, 2005] but all the given examples show a typical shape, seldom seen in informetrics: a horizontal S-shape (first convex then concave). Adopting a simple model for the publication-citation relation, we prove this horizontal S-shape in this paper, showing that such a general functional relationship can be generally explained.

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Scientometrics

Print ISSN:: 0138-9130

Online ISSN:: 1588-2861

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Scientometrics
Language	English
Size	B5
Year of Foundation	1978
Volumes per Year	1
Issues per Year	12
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ISSN	0138-9130 (Print)
ISSN	1588-2861 (Online)