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The h-index formalism

Author

Listed:
  • Leo Egghe

    (University of Hasselt)

  • Ronald Rousseau

    (University of Antwerp
    KU Leuven)

Abstract

This article provides an overview of the development of the h-index formalism. We begin with the original formulation as provided by Hirsch and move on to the latest versions. In this we show how the h-index formalism has evolved over time. Lesser known versions, in particular the continuous version of the h-index is brought to the front. We also discuss the Prathap–Kosmulski–Schubert successive h-indices. As announced in the title we focus on the h-index formalism, omitting generalizations, such as the g-index, and applications in research assessment.

Suggested Citation

  • Leo Egghe & Ronald Rousseau, 2021. "The h-index formalism," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(7), pages 6137-6145, July.
    • Handle: RePEc:spr:scient:v:126:y:2021:i:7:d:10.1007_s11192-020-03699-9
    DOI: 10.1007/s11192-020-03699-9
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    References listed on IDEAS

    as
    1. Dilruba Mahbuba & Ronald Rousseau, 2013. "Year-based h-type indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 96(3), pages 785-797, September.
    2. Leo Egghe & Ronald Rousseau, 2019. "A geometric relation between the h-index and the Lorenz curve," Scientometrics, Springer;Akadémiai Kiadó, vol. 119(2), pages 1281-1284, May.
    3. Denis Bouyssou & Thierry Marchant, 2011. "Ranking scientists and departments in a consistent manner," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 62(9), pages 1761-1769, September.
    4. van Eck, Nees Jan & Waltman, Ludo, 2008. "Generalizing the h- and g-indices," Journal of Informetrics, Elsevier, vol. 2(4), pages 263-271.
    5. Leo Egghe & Ronald Rousseau, 2006. "An informetric model for the Hirsch-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 121-129, October.
    6. Ludo Waltman & Nees Jan van Eck, 2012. "The inconsistency of the h‐index," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 63(2), pages 406-415, February.
    7. Ronald Rousseau, 2016. "Citation data as a proxy for quality or scientific influence are at best PAC (probably approximately correct)," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 67(12), pages 3092-3094, December.
    8. Anthony F. J. Raan, 2006. "Comparison of the Hirsch-index with standard bibliometric indicators and with peer judgment for 147 chemistry research groups," Scientometrics, Springer;Akadémiai Kiadó, vol. 67(3), pages 491-502, June.
    9. Leo Egghe, 2008. "Modelling successive h-indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 77(3), pages 377-387, December.
    10. András Schubert, 2007. "Successive h-indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 70(1), pages 201-205, January.
    11. E. Garfield & I. H. Sher, 1963. "New factors in the evaluation of scientific literature through citation indexing," American Documentation, Wiley Blackwell, vol. 14(3), pages 195-201, July.
    12. Yuxian Liu & Ronald Rousseau, 2009. "Properties of Hirsch-type indices: the case of library classification categories," Scientometrics, Springer;Akadémiai Kiadó, vol. 79(2), pages 235-248, May.
    13. Egghe, Leo & Rousseau, Ronald, 2019. "Solution by step functions of a minimum problem in L2[0,T], using generalized h- and g-indices," Journal of Informetrics, Elsevier, vol. 13(3), pages 785-792.
    14. Michael G. Banks, 2006. "An extension of the Hirsch index: Indexing scientific topics and compounds," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 161-168, October.
    15. Egghe, Leo & Rousseau, Ronald, 2020. "Polar coordinates and generalized h-type indices," Journal of Informetrics, Elsevier, vol. 14(2).
    16. Egghe, Leo & Rousseau, Ronald, 2019. "Infinite sequences and their h-type indices," Journal of Informetrics, Elsevier, vol. 13(1), pages 291-298.
    17. Ludo Waltman & Nees Jan van Eck, 2012. "The inconsistency of the h-index," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 63(2), pages 406-415, February.
    18. van Eck, N.J.P. & Waltman, L., 2008. "Generalizing the h- and g-indices," ERIM Report Series Research in Management ERS-2008-049-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    19. Tibor Braun & Wolfgang Glänzel & András Schubert, 2006. "A Hirsch-type index for journals," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 169-173, October.
    20. Edit Csajbók & Anna Berhidi & Lívia Vasas & András Schubert, 2007. "Hirsch-index for countries based on Essential Science Indicators data," Scientometrics, Springer;Akadémiai Kiadó, vol. 73(1), pages 91-117, October.
    21. Alonso, S. & Cabrerizo, F.J. & Herrera-Viedma, E. & Herrera, F., 2009. "h-Index: A review focused in its variants, computation and standardization for different scientific fields," Journal of Informetrics, Elsevier, vol. 3(4), pages 273-289.
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    Cited by:

    1. Egghe, Leo, 2021. "A theory of pointwise defined impact measures," Journal of Informetrics, Elsevier, vol. 15(3).
    2. Marek Gagolewski & Barbara Żogała-Siudem & Grzegorz Siudem & Anna Cena, 2022. "Ockham’s index of citation impact," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(5), pages 2829-2845, May.
    3. Chen, Meiqian & Guo, Zhaoxia & Dong, Yucheng & Chiclana, Francisco & Herrera-Viedma, Enrique, 2021. "Citations optimal growth path: A tool to analyze sensitivity to citations of h-like indexes," Journal of Informetrics, Elsevier, vol. 15(4).
    4. Biró, Tamás S. & Telcs, András & Józsa, Máté & Néda, Zoltán, 2023. "Gintropic scaling of scientometric indexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    5. Cena, Anna & Gagolewski, Marek & Siudem, Grzegorz & Żogała-Siudem, Barbara, 2022. "Validating citation models by proxy indices," Journal of Informetrics, Elsevier, vol. 16(2).

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