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An index to quantify an individual’s scientific research output
J. E. Hirsch
Department of Physics, University of California, San Diego La Jolla, CA 92093-0319 I propose the index h, defined as the number of papers with citation number higher or equal to h, as a useful index to characterize the scientific output of a researcher.

arXiv:physics/0508025v5 [physics.soc-ph] 29 Sep 2005


For the few scientists that earn a Nobel prize, the impact and relevance of their research work is unquestionable. Among the rest of us, how does one quantify the cumulative impact and relevance of an individual’s scientific research output? In a world of not unlimited resources such quantification (even if potentially distasteful) is often needed for evaluation and comparison purposes, egfor university faculty recruitment and advancement, award of grants, etc. The publication record of an individual and the citation record are clearly data that contain useful information. That information includes the number (Np ) of papers published over n years, the number of citations j (Nc ) for each paper (j), the journals where the papers were published and their impact parameter, etc. This isa large amount of information that will be evaluated with different criteria by different people. Here I would like to propose a single number, the ”h-index”, as a particularly simple and useful way to characterize the scientific output of a researcher. A scientist has index h if h of his/her Np papers have at least h citations each, and the other (Np − h) papers have no more than h citations each.The research reported here concentrated on physicists, however I suggest that the h−index should be useful for other scientific disciplines as well. (At the end of the paper I discuss some observations for the h−index in biological sciences.) The highest h among physicists appears to be E. Witten’s, h = 110. That is, Witten has written 110 papers with at least 110 citations each. That gives a lowerbound on the total number of citations to Witten’s papers at h2 = 12, 100. Of course the total number of citations (Nc,tot ) will usually be much larger than h2 , since h2 both underestimates the total number of citations of the h most cited papers and ignores the papers with fewer than h citations. The relation between Nc,tot and h will depend on the detailed form of the particulardistribution[1, 2], and it is useful to define the proportionality constant a as Nc,tot = ah2 . (1)

I find empirically that a ranges between 3 and 5. Other prominent physicists with high h’s are A.J. Heeger (h = 107), M.L. Cohen (h = 94), A.C. Gossard (h = 94), P.W. Anderson (h = 91), S. Weinberg (h = 88), M.E. Fisher (h = 88), M. Cardona (h = 86), P.G. deGennes (h = 79), J.N. Bahcall (h = 77), Z. Fisk

(h= 75), D.J. Scalapino (h = 75), G. Parisi (h = 73), S.G. Louie (h = 70), R. Jackiw (h = 69), F. Wilczek (h = 68), C. Vafa (h = 66), M.B. Maple (h = 66), D.J. Gross (h = 66), M.S. Dresselhaus (h = 62), S.W. Hawking (h = 62). I argue that h is preferable to other single-number criteria commonly used to evaluate scientific output of a researcher, as follows: (0) Total number of papers (Np ):Advantage: measures productivity. Disadvantage: does not measure importance nor impact of papers. (1) Total number of citations (Nc,tot ): Advantage: measures total impact. Disadvantage: hard to find; may be inflated by a small number of ’big hits’, which may not be representative of the individual if he/she is coauthor with many others on those papers. In such cases the relation Eq. (1) will imply a veryatypical value of a, larger than 5. Another disadvantage is that Nc,tot gives undue weight to highly cited review articles versus original research contributions. (2) Citations per paper, i.e. ratio of Nc,tot to Np : Advantage: allows comparison of scientists of different ages. Disadvantage: hard to find; rewards low productivity, penalizes high productivity. (3) Number of ’significant papers’,...