# Comprehensive evaluation of *h*-index and its extensions in the domain of mathematics

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## Abstract

Until the late 90’s, conventional bibliometric indices such as, publication count, citation count, and number of co-authors have extensively been employed by the scientific community to rank the researchers. In 2005, inception of a renowned ranking measure *h*-*index* has grabbed the substantial importance; the community considered *h*-index as a quintessential ranking measure. Subsequently, different variants and extensions of *h*-index have also been proposed. To date, plethora of the studies exists that harnesses *h*-index, its variants and extensions for researchers’ ranking. Nonetheless, the community does not agree upon a single measure that can be deemed as an optimal ranking measure. This is due to the fact that most of the contemporary studies have evaluated them either by employing a small amount of data or presumed their significance on the basis of hypothetical or imaginary case scenarios. We argue that comprehensive empirical investigation of these measures must be performed in order to tackle their real behavior. This study evaluates the *h*-*index* and its extensions by employing a comprehensive data set of authors from Mathematics discipline. The first experimental step involves the computation of correlation among the obtained values of the extensions to determine the similarity and divergence among them. Afterwards, we considered the data of international award winners from four prestigious Mathematics societies as benchmark to validate the potential of these measures by analyzing the dependence of societies on them. The outcomes revealed that overall 45% of the authors have appeared at the top occurrences of the ranked list. Out of all extensions, *fraction count on paper* has outperformed by bringing 55% of the awardees at top 10% of its ranked list.

## Keywords

NASL LMS*h*-index Variants of

*h*-index Mathematics Author ranking

## References

- 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*(4), 273–289.Google Scholar - Ayaz, S., & Afzal, M. T. (2016). Identification of conversion factor for completing-h index for the field of mathematics.
*Scientometrics,**109*(3), 1511–1524.Google Scholar - Balog, K., Azzopardi, L., & De Rijke, M. (2006). Formal models for expert finding in enterprise corpora. In
*Proceedings of the 29th annual international ACM SIGIR conference on research and development in information retrieval*. ACM.Google Scholar - Batista, P. D., Campiteli, M. G., & Kinouchi, O. (2006). Is it possible to compare researchers with different scientific interests?
*Scientometrics,**68*(1), 179–189.Google Scholar - Bogers, T., & Van den Bosch, A. (2008). Recommending scientific articles using citeulike. In
*Proceedings of the 2008 ACM conference on recommender systems*. ACM.Google Scholar - Bornmann, L., Mutz, R., Hug, S. E., & Daniel, H. D. (2011). A multilevel meta-analysis of studies reporting correlations between the h index and 37 different h index variants.
*Journal of Informetrics,**5*(3), 346–359.Google Scholar - Burrell, Q. (2007). Hirsch index or Hirsch rate? Some thoughts arising from Liang’s data.
*Scientometrics,**73*(1), 19–28.Google Scholar - Cabrerizo, F. J., Alonso, S., Herrera-Viedma, E., & Herrera, F. (2010). q2-Index: Quantitative and qualitative evaluation based on the number and impact of papers in the Hirsch core.
*Journal of Informetrics,**4*(1), 23–28.Google Scholar - Cameron, D. H. L., Aleman-Meza, B., Decker, S., & Arpinar, I. B. (2007). SEMEF: A taxonomy-based discovery of experts, expertise and collaboration networks. Doctoral dissertation, University of Georgia.Google Scholar
- Corder, G. W., & Foreman, D. I. (2009). Comparing variables of ordinal or dichotomous scales: spearman rank-order, point-biserial, and biserial correlations. In
*Nonparametric statistics for non*-*statisticians: A step*-*by*-*step approach*(pp. 122–154). Hoboken: Wiley.Google Scholar - Deng, H., Han, J., Lyu, M. R., & King, I. (2012). Modeling and exploiting heterogeneous bibliographic networks for expertise ranking. In
*Proceedings of the 12th ACM/IEEE*-*CS joint conference on digital libraries*(pp. 71–80). ACM.Google Scholar - 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*(10), 1608–1616.Google Scholar - Egghe, L., & Rousseau, R. (2008). An H-index weighted by citation impact.
*Information Processing and Management,**44*(2), 770–780.Google Scholar - Fang, H., & Zhai, C. (2007). Probabilistic models for expert finding. In
*European conference on information retrieval*(pp. 418–430). Berlin: Springer.Google Scholar - Harzing, A. W. (2014). A longitudinal study of Google Scholar coverage between 2012 and 2013.
*Scientometrics,**98*(1), 565–575.Google Scholar - Hirsch, J. E. (2005). An index to quantify an individual’s scientific research output.
*Proceedings of the National Academy of Sciences of the United States of America,**102*(46), 16569–16572.zbMATHGoogle Scholar - Jin, B. (2006). h-index: An evaluation indicator proposed by scientist.
*Science Focus,**1*(1), 8–9.**(in Chinese)**.Google Scholar - Kosmulski, M. (2006). A new Hirsch-type index saves time and works equally well as the original h-index.
*ISSI Newsletter,**2*(3), 4–6.Google Scholar - Kosmulski, M. (2007). MAXPROD—A new index for assessment of the scientific output of an individual, and a comparison.
*Cybermetrics,**11,*1–5.Google Scholar - Liu, N. C., & Cheng, Y. (2005). The academic ranking of world universities.
*Higher Education in Europe,**30*(2), 127–136.Google Scholar - Liu P, Dew P. (2004). Using semantic web technologies to improve expertise matching within academia. In
*International conference on knowledge management*(pp. 370–378).Google Scholar - Raheel, M., Ayaz, S., & Afzal, M. T. (2018). Evaluation of h-index, its variants and extensions based on publication age & citation intensity in civil engineering.
*Scientometrics*,*114*(3), 1107–1127.Google Scholar - Schreiber, M. (2008a). An empirical investigation of the g-index for 26 physicists in comparison with the h-index, the A-index, and the R-index.
*Journal of the American Society for Information Science and Technology,**59*(9), 1513–1522.Google Scholar - Schreiber, M. (2008b). To share the fame in a fair way, hm modifies h for multi-authored manuscripts.
*New Journal of Physics,**10*(4), 040201.MathSciNetGoogle Scholar - Schreiber, M. (2010). Twenty Hirsch index variants and other indicators giving more or less preference to highly cited papers.
*Annalen der Physik,**522*(8), 536–554.Google Scholar - Sidiropoulos, A., Katsaros, D., & Manolopoulos, Y. (2007). Generalized Hirsch h-index for disclosing latent facts in citation networks.
*Scientometrics,**72*(2), 253–280.Google Scholar - Sun, J., Ma, J., Cheng, X., Liu, Z., & Cao, X. (2013). Finding an expert: A model recommendation system. In:
*Thirty fourth international conference on information systems*, Milan.Google Scholar - Tho, Q. T., Hui, S. C., & Fong, A. C. M. (2007). A citation-based document retrieval system for finding research expertise.
*Information Processing & Management,**43*(1), 248–264.Google Scholar - Tol, R. (2009). The h-index and its alternatives: An application to the 100 most prolific economists.
*Scientometrics,**80*(2), 317–324.Google Scholar - Wu, Q. (2010). The w-index: A measure to assess scientific impact by focusing on widely cited papers.
*Journal of the American Society for Information Science and Technology,**61*(3), 609–614.Google Scholar - Yiman-Seid, D., & Kobsa, A. (2003). Expert finding systems for organizations.
*Journal of Organizational Computing and Electronic Commerce,**13,*1–14.Google Scholar