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Title
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A mathematical characterization of the Hirsch-index by means of minimal increments
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Author
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Abstract
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| The minimum configuration to have a h-index equal to h is h papers each having h citations, hence h(2) citations in total. To increase the h-index to h + 1 we minimally need (h + 1)(2) citations, an increment of I-1(h) = 2h + 1. The latter number increases with 2 per unit increase of h. This increment of the second order is denoted I-2(h) =2. If we define I-1 and I-2 for a general Hirsch configuration (say n papers each having f(n) citations) we calculate I-1(f) and I-2(f) similarly as for the h-index. We characterize all functions f for which I-2(f) = 2 and show that this can be obtained for functions f(n) different from the h-index. We show that f(n) = n (i.e. the h-index) if and only if I-2(f) = 2, f(1) = 1 and f(2) = 2. We give a similar characterization for the threshold index (where n papers have a constant number C of citations). Here we deal with second order increments I-2(f) = 0. (c) 2013 Elsevier Ltd. All rights reserved. |
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Language
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English
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Source (journal)
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Journal of informetrics. - Amsterdam
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Publication
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Amsterdam
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2013
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ISSN
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1751-1577
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DOI
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10.1016/J.JOI.2013.01.005
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Volume/pages
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7
:2
(2013)
, p. 388-393
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ISI
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000318377100016
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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