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Further characterizations of the Hirsch index

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  • Antonio Quesada

    (Universitat Rovira i Virgili)

Abstract

The Hirsch index is a number that synthesizes a researcher’s output. It is defined as the maximum number h such that the researcher has h papers with at least h citations each. Four characterizations of the Hirsch index are suggested. The most compact one relies on the interpretation of the index as providing the number of valuable papers in an output and postulates three axioms. One, only cited papers can be valuable. Two, the index is strongly monotonic: if output x has more papers than output y and each paper in x has more citations than the most cited paper in y, then x has more valuable papers than y. And three, the minimum amount of citations under which a paper becomes valuable is different for each paper.

Suggested Citation

  • Antonio Quesada, 2011. "Further characterizations of the Hirsch index," Scientometrics, Springer;Akadémiai Kiadó, vol. 87(1), pages 107-114, April.
    • Handle: RePEc:spr:scient:v:87:y:2011:i:1:d:10.1007_s11192-010-0307-4
    DOI: 10.1007/s11192-010-0307-4
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    References listed on IDEAS

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    1. Leo Egghe, 2006. "Theory and practise of the g-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 131-152, October.
    2. Quesada, Antonio, 2009. "Monotonicity and the Hirsch index," Journal of Informetrics, Elsevier, vol. 3(2), pages 158-160.
    3. Antonio Quesada, 2010. "More axiomatics for the Hirsch index," Scientometrics, Springer;Akadémiai Kiadó, vol. 82(2), pages 413-418, February.
    4. Thierry Marchant, 2009. "An axiomatic characterization of the ranking based on the h-index and some other bibliometric rankings of authors," Scientometrics, Springer;Akadémiai Kiadó, vol. 80(2), pages 325-342, August.
    5. Woeginger, Gerhard J., 2008. "An axiomatic characterization of the Hirsch-index," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 224-232, September.
    6. Woeginger, Gerhard J., 2008. "A symmetry axiom for scientific impact indices," Journal of Informetrics, Elsevier, vol. 2(4), pages 298-303.
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    Cited by:

    1. Sylvain Béal & Sylvain Ferrières & Eric Rémila & Phillippe Solal, 2016. "An axiomatization of the iterated h-index and applications to sport rankings," Working Papers 2016-11, CRESE.
    2. Gagolewski, Marek, 2013. "Scientific impact assessment cannot be fair," Journal of Informetrics, Elsevier, vol. 7(4), pages 792-802.
    3. Ana Paula dos Santos Rubem & Ariane Lima Moura & João Carlos Correia Baptista Soares de Mello, 2015. "Comparative analysis of some individual bibliometric indices when applied to groups of researchers," Scientometrics, Springer;Akadémiai Kiadó, vol. 102(1), pages 1019-1035, January.
    4. Boczek, Michał & Hovana, Anton & Hutník, Ondrej & Kaluszka, Marek, 2021. "New monotone measure-based integrals inspired by scientific impact problem," European Journal of Operational Research, Elsevier, vol. 290(1), pages 346-357.
    5. Adachi, Tsuyoshi & Kongo, Takumi, 2015. "Further axiomatizations of Egghe's g-index," Journal of Informetrics, Elsevier, vol. 9(4), pages 839-844.
    6. Osório, António (António Miguel), 2019. "The value and credits of n-authors publications," Working Papers 2072/376026, Universitat Rovira i Virgili, Department of Economics.
    7. Bouyssou, Denis & Marchant, Thierry, 2014. "An axiomatic approach to bibliometric rankings and indices," Journal of Informetrics, Elsevier, vol. 8(3), pages 449-477.
    8. Mark Levene & Trevor Fenner & Judit Bar-Ilan, 2019. "Characterisation of the $$\chi$$χ-index and the rec-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 120(2), pages 885-896, August.
    9. L'aszl'o Csat'o, 2019. "Journal ranking should depend on the level of aggregation," Papers 1904.06300, arXiv.org, revised Sep 2019.
    10. Miroiu, Adrian, 2013. "Axiomatizing the Hirsch index: Quantity and quality disjoined," Journal of Informetrics, Elsevier, vol. 7(1), pages 10-15.
    11. Kongo, Takumi, 2014. "An alternative axiomatization of the Hirsch index," Journal of Informetrics, Elsevier, vol. 8(1), pages 252-258.
    12. Stefano Vannucci, 2017. "Hyper-H-Indices for Multi-Attribute Research Outputs: Characterizations," Department of Economics University of Siena 755, Department of Economics, University of Siena.
    13. Brandão, Luana Carneiro & Soares de Mello, João Carlos Correia Baptista, 2019. "A multi-criteria approach to the h-index," European Journal of Operational Research, Elsevier, vol. 276(1), pages 357-363.
    14. Csató, László, 2019. "Journal ranking should depend on the level of aggregation," Journal of Informetrics, Elsevier, vol. 13(4).
    15. Bouyssou, Denis & Marchant, Thierry, 2016. "Ranking authors using fractional counting of citations: An axiomatic approach," Journal of Informetrics, Elsevier, vol. 10(1), pages 183-199.

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