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Axiomatics for the Hirsch index and the Egghe index

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  • Quesada, Antonio

Abstract

The Hirsch index and the Egghe index are both numbers that synthesize a researcher's output. The h-index associated with researcher r is the maximum number h such that r has h papers with at least h citations each. The g-index is the maximum number g of papers by r such that the average number of citations of the g papers is at least g. Both indices are characterized in terms of four axioms. One identifies outputs deserving index at most one. A second one establishes a strong monotonicity condition. A third one requires the index to satisfy a property of subadditivity. The last one consists of a monotonicity condition, for the h-index, and an aggregate monotonicity condition, for the g-index.

Suggested Citation

  • Quesada, Antonio, 2011. "Axiomatics for the Hirsch index and the Egghe index," Journal of Informetrics, Elsevier, vol. 5(3), pages 476-480.
    • Handle: RePEc:eee:infome:v:5:y:2011:i:3:p:476-480
    DOI: 10.1016/j.joi.2011.01.009
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    References listed on IDEAS

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    1. Woeginger, Gerhard J., 2008. "An axiomatic analysis of Egghe’s g-index," Journal of Informetrics, Elsevier, vol. 2(4), pages 364-368.
    2. Quesada, Antonio, 2009. "Monotonicity and the Hirsch index," Journal of Informetrics, Elsevier, vol. 3(2), pages 158-160.
    3. Woeginger, Gerhard J., 2008. "An axiomatic characterization of the Hirsch-index," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 224-232, September.
    4. Burgos, Albert, 2010. "Ranking Scientists," UMUFAE Economics Working Papers 10609, DIGITUM. Universidad de Murcia.
    5. Antonio Quesada, 2010. "More axiomatics for the Hirsch index," Scientometrics, Springer;Akadémiai Kiadó, vol. 82(2), pages 413-418, February.
    6. 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.
    7. 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. 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.
    3. Adachi, Tsuyoshi & Kongo, Takumi, 2015. "Further axiomatizations of Egghe's g-index," Journal of Informetrics, Elsevier, vol. 9(4), pages 839-844.
    4. Osório, António (António Miguel), 2019. "The value and credits of n-authors publications," Working Papers 2072/376026, Universitat Rovira i Virgili, Department of Economics.
    5. Bouyssou, Denis & Marchant, Thierry, 2014. "An axiomatic approach to bibliometric rankings and indices," Journal of Informetrics, Elsevier, vol. 8(3), pages 449-477.
    6. Woeginger, Gerhard J., 2014. "Investigations on the step-based research indices of Chambers and Miller," Journal of Informetrics, Elsevier, vol. 8(3), pages 659-666.
    7. Motty Perry & Philip J. Reny, 2016. "How to Count Citations If You Must," American Economic Review, American Economic Association, vol. 106(9), pages 2722-2741, September.
    8. Haley, M. Ryan & McGee, M. Kevin, 2020. "Jointly valuing journal visibility and author citation count: An axiomatic approach," Journal of Informetrics, Elsevier, vol. 14(1).
    9. 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.
    10. L'aszl'o Csat'o, 2019. "Journal ranking should depend on the level of aggregation," Papers 1904.06300, arXiv.org, revised Sep 2019.
    11. Mukherjee, Conan & Alam, Aftab, 2016. "On Evaluating Author's Performance by Publications: An Axiomatic Study," Working Papers 2016:14, Lund University, Department of Economics, revised 12 May 2017.
    12. Kongo, Takumi, 2014. "An alternative axiomatization of the Hirsch index," Journal of Informetrics, Elsevier, vol. 8(1), pages 252-258.
    13. David I. Stern & Richard S.J. Tol, 2018. "How to Count Citations If You Must: Comment," Working Paper Series 0118, Department of Economics, University of Sussex Business School.
    14. 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.
    15. Chambers, Christopher P. & Miller, Alan D., 2014. "Scholarly influence," Journal of Economic Theory, Elsevier, vol. 151(C), pages 571-583.
    16. David I. Stern & Richard S. J. Tol, 2021. "Depth and breadth relevance in citation metrics," Economic Inquiry, Western Economic Association International, vol. 59(3), pages 961-977, July.
    17. Csató, László, 2019. "Journal ranking should depend on the level of aggregation," Journal of Informetrics, Elsevier, vol. 13(4).
    18. Lasso de la Vega, Casilda & Volij, Oscar, 2018. "Ranking scholars: A measure representation," Journal of Informetrics, Elsevier, vol. 12(2), pages 510-517.
    19. 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.
    20. Conan Mukherjee & Ranojoy Basu & Aftab Alam, 2020. "A measure of authorship by publications," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 41(3), pages 354-361, April.

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