, Volume 118, Issue 2, pp 673–686 | Cite as

hα: An index to quantify an individual’s scientific leadership

  • J. E. HirschEmail author


The \(\alpha\) person is the dominant person in a group. We define the \(\alpha\)-author of a paper as the author of the paper with the highest h-index among all the coauthors, and an \(\alpha\)-paper of a scientist as a paper authored or coauthored by the scientist where he/she is the \(\alpha\)-author. For most but not all papers in the literature there is only one \(\alpha\)-author. We define the \(h_\alpha\) index of a scientist as the number of papers in the h-core of the scientist (i.e. the set of papers that contribute to the h-index of the scientist) where this scientist is the \(\alpha\)-author. We also define the \(h'_\alpha\) index of a scientist as the number of \(\alpha\)-papers of this scientist that have \(\ge\)\(h'_\alpha\) citations. \(h_\alpha\) and \(h'_\alpha\) contain similar information, while \(h'_\alpha\) is conceptually more appealing it is harder to obtain from existing databases, hence of less current practical interest. We propose that the \(h_\alpha\) and/or \(h'_\alpha\) indices, or other variants discussed in the paper, are useful complements to the h-index of a scientist to quantify his/her scientific achievement, that rectify an inherent drawback of the h-index, its inability to distinguish between authors with different coauthorships patterns. A high h index in conjunction with a high \(h_\alpha /h\) ratio is a hallmark of scientific leadership.


h-Index Coauthorship Scientific leadership 



The author is grateful to a colleague for thoughtful comments.


  1. 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, 3, 273–289.CrossRefGoogle Scholar
  2. Ancheyta, J. (2015). A correction of h-index to account for the relative importance of authors in manuscripts. International Journal of Oil Gas and Coal Technology, 10, 221–232.CrossRefGoogle Scholar
  3. Ausloos, M. (2015). Assessing the true role of coauthors in the h-index measure of an author scientific impact. Physica A, 422, 136–142.MathSciNetCrossRefGoogle Scholar
  4. Bornmann, L. (2014). h-Index research in scientometrics: A summary. Journal of Informetrics, 8, 478–485.CrossRefGoogle Scholar
  5. Bornmann, L., & Daniel, H. D. (2007). What do we know about the h index? Journal of the American Socieyt for Information Science and Technology, 58, 1381–1385.CrossRefGoogle Scholar
  6. Bornmann, L., & Daniel, H.-D. (2010). The citation speed index: A useful bibliometric indicator to add to the h index. Journal of Informetrics, 4, 444–446.CrossRefGoogle Scholar
  7. Bornmann, L., Mutz, R., & Daniel, H. D. (2008). Are there better indices for evaluation purposes than the h index? A comparison of nine different variants of the h index using data from biomedicine. Journal of the American Society for Information Science and Technology, 59, 830–837.CrossRefGoogle Scholar
  8. Crispo, E. (2015). A new index to use in conjunction with the h-index to account for an author’s relative contribution to publications with high impact. Journal of the Association for Information Science and Technology, 66, 2381–2383.CrossRefGoogle Scholar
  9. Dorta-Gonzalez, P., & Dorta-Gonzalez, M. I. (2011). Central indexes to the citation distribution: A complement to the h-index. Scientometrics, 88, 729–745.CrossRefGoogle Scholar
  10. Egghe, L. (2008). Mathematical theory of the h- and \(g\)-index in case of fractional counting of authorship. Journal of the American Society for Information Science and Technology, 59, 1608–1616.CrossRefGoogle Scholar
  11. Egghe, L., & Rousseau, R. (2008). An h-index weighted by citation impact. Information Processing and Management, 44, 770–780.CrossRefGoogle Scholar
  12. Galam, S. (2011). Tailor based allocations for multiple authorship: A fractional \(gh\)-index. Scientometrics, 89, 365–379.CrossRefGoogle Scholar
  13. Gibb, B. C. (2012). Lies, damned lies and h-indices. Nature Chemistry, 4, 513–514.CrossRefGoogle Scholar
  14. Guns, R., & Rousseau, R. (2009). Real and rational variants of the h-index and the \(g\)-index. Journal of Informetrics, 3, 64–71.CrossRefGoogle Scholar
  15. Hirsch, J. E. (2005). An index to quantify an individual’s scientific research output. Proceedings of the National Academy of Science, 102, 16569–16572.CrossRefzbMATHGoogle Scholar
  16. Hirsch, J. E. (2010). An index to quantify an individuals scientific research output that takes into account the effect of multiple coauthorship. Scientometrics, 85, 741–754.CrossRefGoogle Scholar
  17. Hu, X., Rosseau, R., & Chen, J. (2010). In those fields where multiple authorship is the rule, the h-index should be supplemented by role-based h-indices. Journal of Information Science, 36, 73–85.CrossRefGoogle Scholar
  18. Jin, B., Liang, L. M., Rousseau, R., & Egghe, L. (2007). The R- and AR-indices: Complementing the h-index. Chinese Science Bulletin, 52, 863–863.Google Scholar
  19. Lando, T., & Bertoli-Barsotti, L. (2014). New tools for complementing the h-index: An empirical study. Mathematical Methods in Economics, 2014, 566–571.Google Scholar
  20. Liu, X. Z., & Fang, H. (2012). Modifying h-index by allocating credit of multi-authored papers whose author names rank based on contribution. Journal of Informetrics, 6, 557–565.CrossRefGoogle Scholar
  21. Mazurek, J. (2018). A modification to Hirsch index allowing comparisons across different scientific fields. Current Science, 114, 2238–2239.Google Scholar
  22. Perry, M., & Reny, P. J. (2016). How to count citations if you must. American Economic Review, 106, 2722–2741.CrossRefGoogle Scholar
  23. Prathap, G. (2012). The Inconsistency of the h-index. Journal of the American Society for Information Science and Technology, 63, 1480–1481.CrossRefGoogle Scholar
  24. Rousseau, R., & Ye, F. (2008). A proposal for a dynamic h-type index. Journal of the American Society for Information Science and Technology, 59, 1853–1855.CrossRefGoogle Scholar
  25. Schreiber, M. (2008). To share the fame in a fair way, \(h_m\) modifies h for multi-authored manuscripts. New Journal of Physics, 10, 040201.CrossRefGoogle Scholar
  26. Schreiber, M. (2008). A modification of the h-index: The \(h_m\)-index accounts for multi-authored manuscripts. Journal of Informetrics, 2, 211–216.CrossRefGoogle Scholar
  27. Schreiber, M. (2009). A case study of the modified Hirsch index \(h_m\) accounting for multiple coauthors. Journal of the American Society for Information Science and Technology, 60, 1274–1282.CrossRefGoogle Scholar
  28. Schreiber, M. (2018). A skeptical view on the Hirsch index and its predictive power. Physica Scripta, 93, 10201.CrossRefGoogle Scholar
  29. Tscharntke, T., et al. (2007). Author sequence and credit for contributions in multiauthored publications. PLoS Biology, 5(1), e18.CrossRefGoogle Scholar
  30. Van Eck, N. J., & Waltman, L. (2008). Generalizing the h- and \(g\)-indices. Journal of Informetrics, 2, 263–271.CrossRefGoogle Scholar
  31. Van Raan, A. F. J. (2006). Comparison of the Hirsch-index with standard bibliometric indicators and with peer judgment for 147 chemistry research groups. Scientometrics, 67, 491–502.CrossRefGoogle Scholar
  32. Vavrycuk, V. (2018). Fair ranking of researchers and research teams. PLoS ONE, 13(4), e0195509.CrossRefGoogle Scholar
  33. Waltman, L., & Nees, J. (2012). The inconsistency of the h-index. Journal of the American Society for Information Science and Technology, 63, 406–415.CrossRefGoogle Scholar
  34. Yaminfirooz, M., & Gholinia, H. (2015). Multiple h-index: A new scientometric indicator. Electronic Library, 33(547), 556.Google Scholar
  35. Zhang, C.-T. (2009). The e-index, complementing the h-index for excess citations. PLoS ONE, 4, e5429.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of California, San DiegoLa JollaUSA

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