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An entropy-based measure for the evolution of h index research

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Abstract

The h index has been comprehensively developed and diffusely applied following its initial proposal in 2005 by Jorge Hirsch. However, while the numbers of papers and authors measured continue to grow, it is not known whether such increases in quantity mean that the research itself is advancing. Accordingly, the present study sets out to establish an analysis method, based on the concept of entropy, with which to elucidate the evolution of the h index. The results suggest that there are four stages, as follows: the emerging stage, the preliminary growth stage, the real growth stage, and the maturity stage. Meanwhile, the research of the h index is found to be in flux, and it is concluded that further development of the metric will require profound theoretical achievements as well as embedded innovation, or else the evolution of the h index will decline following a shortened maturity stage.

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References

  • Abbasi, A., Altmann, J., & Hossain, L. (2011). Identifying the effects of co-authorship networks on the performance of scholars: a correlation and regression analysis of performance measures and social network analysis measures. Journal of Informetrics, 5(4), 594–607.

    Google Scholar 

  • Abdellatif, W., Shao, M., Jalal, S., Ding, J., Vijayasarathi, A., et al. (2019). Novel geographic thematic study of the largest radiology societies globally: how is gender structure biased within editorial boards. American Journal of Roentgenology, 213(1), 2–7.

    Google Scholar 

  • Abramo, G., Costa, C., & D’Angelo, C. A. (2015). A multivariate stochastic model to assess research performance. Scientometrics, 102(2), 1755–1772.

    Google Scholar 

  • Aguillo, I. F. (2012). Is Google Scholar useful for bibliometrics? A webometric analysis. Scientometrics, 91(2), 343–351.

    Google Scholar 

  • 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 

  • Ameer, M., & Afzal, M. T. (2019). Evaluation of h index and its qualitative and quantitative variants in neuroscience. Scientometrics, 121(2), 653–673.

    Google Scholar 

  • Arnold, D. (2009). Integrity under attack: The state of scholarly publishing. SIAM News, 42(10), 2–3.

    Google Scholar 

  • Ayaz, S., Masood, N., & Islam, M. A. (2018). Predicting scientific impact based on h index. Scientometrics, 114(3), 993–1010.

    Google Scholar 

  • Bar-Ilan, J. (2008). Which h index?: A comparison of WOS, Scopus and Google Scholar. Scientometrics, 74(2), 257–271.

    Google Scholar 

  • Bar-Ilan, J., Haustein, S., Milojević, S., Peters, I., & Wolfram, D. (2018). Peer review, bibliometrics and altmetrics: Do we need them all? Proceedings of the Association for Information Science and Technology, 55(1), 653–656.

    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 

  • Ben-Naim, A. (2011). Entropy: Order or information. Journal of Chemical Education, 88(5), 594–596.

    Google Scholar 

  • Bertoli-Barsotti, L., & Lando, T. (2017). A theoretical model of the relationship between the h index and other simple citation indicators. Scientometrics, 111(3), 1415–1448.

    Google Scholar 

  • Bornmann, L. (2014). Do altmetrics point to the broader impact of research? An overview of benefits and disadvantages of altmetrics. Journal of Informetrics, 8(4), 895–903.

    Google Scholar 

  • Bornmann, L., & Daniel, H. (2005). Does the h index for ranking of scientists really work? Scientometrics, 65(3), 391–392.

    Google Scholar 

  • Bornmann, L., & Marx, W. (2011). The h index as a research performance indicator. European Science Editing, 37(3), 77–80.

    Google Scholar 

  • Bornmann, L., Rüdiger, M., & 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(5), 830–837.

    Google Scholar 

  • Boyack, K. W., Borner, K., & Klavans, R. (2009). Mapping the structure and evolution of chemistry research. Scientometrics, 79(1), 45–60.

    Google Scholar 

  • Braun, T., Glänzel, W., & Schubert, A. (2006). A Hirsch-type index for journals. Scientometrics, 69(1), 169–173.

    Google Scholar 

  • Burmaoglu, S., Saritas, O., Kidak, L. B., & Berber, I. C. (2017). Evolution of connected health: A network perspective. Scientometrics, 112, 1419–1438.

    Google Scholar 

  • Burrows, R. (2012). Living with the h index? Metric assemblages in the contemporary academy. The Sociological Review, 60(2), 355–372.

    Google Scholar 

  • Chakrabarti, C. G., & Ghosh, K. (2010). Maximum-entropy principle: Ecological organization and evolution. Journal of Biological Physics, 36(2), 175–183.

    Google Scholar 

  • Chang, Y. W., Huang, M. H., & Lin, C. W. (2015). Evolution of research subjects in library and information science based on keyword, bibliographical coupling, and co-citation analyses. Scientometrics, 105(3), 2071–2087.

    Google Scholar 

  • Chen, C., Zhang, J., & Vogeley, M. S. (2010). Making sense of the evolution of a scientific domain: A visual analytic study of the sloan digital sky survey research. Scientometrics, 83(3), 669–688.

    Google Scholar 

  • Cobo, M. J., López-Herrera, A. G., Herrera-Viedma, E., & Herrera, F. (2011). An approach for detecting, quantifying, and visualizing the evolution of a research field: A practical application to the fuzzy sets theory field. Journal of Informetrics, 5(1), 146–166.

    Google Scholar 

  • Cronin, B., & Meho, L. (2006). Using the h index to rank influential information scientists. Journal of the American Society for Information Science and Technology, 57, 1275–1278.

    Google Scholar 

  • Csajbók, E., Berhidi, A., Vasas, L., & Schubert, A. (2007). Hirsch index for countries based on Essential Science Indicators data. Scientometrics, 73(1), 91–117.

    Google Scholar 

  • Da Silva, J. A. T. (2018). The Google Scholar h index: Useful but burdensome metric. Scientometrics, 117(1), 631–635.

    Google Scholar 

  • Durieux, V., & Gevenois, P. A. (2010). Bibliometric indicators: Quality measurements of scientific publication. Radiology, 255(2), 342–351.

    Google Scholar 

  • Egghe, L. (2006). Theory and practise of the g-index. Scientometrics, 69(1), 131–152.

    MathSciNet  Google Scholar 

  • Egghe, L. (2013). A rationale for the relation between the citer h index and the classical h index of a researcher. Berlin: Springer.

    Google Scholar 

  • Egghe, L., & Rousseau, R. (2007). An h index weighted by citation impact. Information Processing and Management, 44, 770–780.

    Google Scholar 

  • Eloy, J. A., Bobian, M., Svider, P. F., Culver, A., Siegel, B., Gray, S. T., et al. (2017). Association of gender with financial relationships between industry and academic otolaryngologists. JAMA Otolaryngology-Head and Neck Surgery, 143, 796–802.

    Google Scholar 

  • Geraci, L., Balsis, S., & Busch, A. J. B. (2015). Gender and the h index in psychology. Scientometrics, 105(3), 2023–2034.

    Google Scholar 

  • Ghani, R., Qayyum, F., Afzal, M. T., & Maurer, H. (2019). Comprehensive evaluation of h index and its extensions in the domain of mathematics. Scientometrics, 118(3), 809–822.

    Google Scholar 

  • Glanzel, W. (2006). On the h index: A mathematical approach to a new measure of publication activity and citation impact. Scientometrics, 67, 315–321.

    Google Scholar 

  • Hanna, T. N., Duszak, R., Jr., Chahine, A., Zygmont, M. E., Herr, K. D., & Horný, M. (2019). The introduction and development of the h index for imaging utilizers: A novel metric for quantifying utilization of emergency department imaging. Academic Emergency Medicine, 26(10), 1125–1134.

    Google Scholar 

  • Hicks, D., Wouters, P., Waltman, L., & Rijckes, S. (2015). The Leiden manifesto for research metrics: Use these ten principles to guide research evaluations. Nature, 520, 429–431.

    Google Scholar 

  • Hirsch, J. E. (2005). An index to quantify an individual's scientific research output. PNAS, 102(46), 16569–16572.

    MATH  Google Scholar 

  • Hirsch, J. E. (2010). An index to quantify an individual’s scientific research output that takes into account the effect of multiple coauthorship. Scientometrics, 85(3), 741–754.

    Google Scholar 

  • Hong, Y. M., & Lee, T. H. (2003). Inference on via generalized spectrum and nonlinear time series models. Review of Economics and Statistics, 85(4), 1048–1062.

    Google Scholar 

  • Jin, B., Liang, L., Rousseau, R., & Egghe, L. (2007). The R- and AR-indices: Complementing the h index. Chinese science bulletin, 52(6), 855–863.

    Google Scholar 

  • Khan, N. R., Hassan, S., Oravec, C. S., Norrdahl, S. P., Brittany, F., et al. (2019). An analysis of publication productivity during residency for 1506 neurosurgical residents and 117 residency departments in North America. Neurosurgery, 84(4), 857–867.

    Google Scholar 

  • Khan, N., Thompson, C. J., Choudhri, A. F., Boop, F. A., & Klimo, P., Jr. (2013). Part I: The application of the h index to groups of individuals and departments in academic neurosurgery. World Neurosurgery, 80(6), 759–765.

    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 

  • Kuhn, T. S. (1962). The structure of scientific revolutions. Chicago: The University of Chicago Press.

    Google Scholar 

  • Lesne, A. (2014). Shannon entropy: a rigorous notion at the crossroads between probability, information theory, dynamical systems and statistical physics. Mathematical Structures in Computer Science, 24(3), e240311.1–e240311.63.

    MathSciNet  MATH  Google Scholar 

  • Liao, H. C., Tang, M., Luo, L., & Li, C. Y. (2018). A bibliometric analysis and visualization of medical big data research. Sustainability, 10(1), 166.

    Google Scholar 

  • Lü, L., Zhou, T., Zhang, Q. M., & Stanley, H. E. (2016). The h index of a network node and its relation to degree and coreness. Nature Communications, 7, 10168.

    Google Scholar 

  • Majima, H., & Suzuki, A. (2015). Identities for entropy change associated with the time-evolution of an open system. Foundations of Physics, 45(8), 914–922.

    MathSciNet  MATH  Google Scholar 

  • Mao, G., Zou, H., Chen, G., Du, H., & Zuo, J. (2015). Past, current and future of biomass energy research: A bibliometric analysis. Renewable and Sustainable Energy Reviews, 52, 1823–1833.

    Google Scholar 

  • Meho, L. I., & Rogers, Y. (2008). Citation counting, citation ranking, and h index of human–computer interaction researchers: A comparison between Scopus and web of science. Journal of the Association for Information Science and Technology, 59(11), 1711–1726.

    Google Scholar 

  • Mingers, J., & Leydesdorff, L. (2015). A review of theory and practice in Scientometrics. European Journal of Operational Research, 246(1), 1–19.

    MATH  Google Scholar 

  • Mingers, J., & Xu, F. (2010). The drivers of citations in management science journals. European Journal of Operational Research, 205, 422–430.

    MATH  Google Scholar 

  • Mueller, C., Wright, R., & Girod, S. (2017). The publication gender gap in us academic surgery. BMC Surgery, 17(1), 16.

    Google Scholar 

  • Neylon, C., & Wu, S. (2009). Article level metrics and the evolution of scientific impact. PLoS Biology, 7(11), e1000242.

    Google Scholar 

  • Nie, Y., Lu, T., & Gao, J. (2017). Co-evolution entropy as a new index to explore power system transition: A case study of China's electricity domain. Journal of Cleaner Production, 165, 951–967.

    Google Scholar 

  • Panaretos, J., & Malesios, C. (2009). Assessing scientific research performance and impact with single indices. Scientometrics, 81(3), 635.

    Google Scholar 

  • Pastor-Satorras, R., & Castellano, C. (2017). Index in complex networks. Physical Review E, 95(2), 022301.

    MathSciNet  Google Scholar 

  • Prathap, G. (2010a). Is there a place for a mock h-index? Scientometrics, 84(1), 153–165.

    Google Scholar 

  • Prathap, G. (2010b). The 100 most prolific economists using the p-index. Scientometrics, 84(1), 167–172.

    Google Scholar 

  • Prathap, G. (2011a). The Energy–Exergy–Entropy (or EEE) sequences in bibliometric assessment. Scientometrics, 87(3), 515–524.

    Google Scholar 

  • Prathap, G. (2011b). Energy indicators and percentile ranking normalization. Scientometrics, 91(3), 997–1003.

    Google Scholar 

  • Prathap, G. (2014a). Quantity, quality, and consistency as bibliometric indicators. Journal of the Association for Information Science and Technology, 65(1), 214.

    Google Scholar 

  • Prathap, G. (2014b). The Zynergy-Index and the Formula for the h-Index. Journal of the Association for Information Science and Technology, 65(2), 426–427.

    Google Scholar 

  • Prathap, G. (2019). Balance: A thermodynamic perspective. Scientometrics, 119(1), 247–255.

    Google Scholar 

  • Priem, J., Taraborelli, D., Groth, P., & Neylon, C. (2010). Altmetrics: A manifesto, 26 October 2010. https://altmetrics.org/manifesto.

  • Prigogine, I. (1978). Time, structure, and fluctuations. Science, 201(4358), 777–785.

    Google Scholar 

  • Raban, D. R., & Gordon, A. (2020). The evolution of data science and big data research: A bibliometric analysis. Scientometrics, 122, 1563–1581.

    Google Scholar 

  • Radford, D. M., Parangi, S., & Silver, J. K. (2019). h index and academic rank by sex among breast surgery fellowship faculty. Journal of the American College of Surgeons, 229(4), e49.

    Google Scholar 

  • Raheel, M., Ayaz, S., & Afzal, M. T. (2018). Evaluation of h index, its variants and extensions based on publication age and citation intensity in civil engineering. Scientometrics, 114(3), 1107–1127.

    Google Scholar 

  • Remuzgo, L., Trueba, C., & Sarabia, J. M. (2016). Evolution of the global inequality in greenhouse gases emissions using multidimensional generalized entropy measures. Physica A: Statistical Mechanics and its Applications, 444, 146–157.

    MathSciNet  MATH  Google Scholar 

  • Roldan-Valadez, E., Salazar-Ruiz, S. Y., Ibarra-Contreras, R., & Rios, C. (2019). Current concepts on bibliometrics: a brief review about impact factor, Eigenfactor score, CiteScore, SCImago Journal Rank, Source Normalized Impact per Paper, h index, and alternative metrics. Irish Journal of Medical Science (1971–), 1–13.

  • Schreiber, M. (2008). To share the fame in a fair way, hm modifies h for multi-authored manuscripts. New Journal of Physics, 10(4), 040201.

    Google Scholar 

  • Schreiber, M. (2010). A case study of the modified g index: Counting multi-author publications fractionally. Journal of Informetrics, 4(4), 636–643.

    Google Scholar 

  • Shannon, C. E. (1948). A mathematical theory of communication. The Bell System Technical Journal, 27, 379–423.

    MathSciNet  MATH  Google Scholar 

  • Shema, H., Bar-Ilan, J., & Thelwall, M. (2015). How is research blogged? A content analysis approach. Journal of the Association for Information Science and Technology, 66(6), 1136–1149.

    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 

  • Stosic, D., Stosic, D., Ludermir, T., Oliveira, W. D., & Stosic, T. (2016). Foreign exchange rate entropy evolution during financial crises. Physica A: Statistical Mechanics and its Applications, 449, 233–239.

    Google Scholar 

  • Susarla, S. M., Rada, E. M., Lopez, J., Swanson, E. W., Miller, D., Redett, R. J., et al. (2017). Does the h index correlate with academic rank among full-time academic craniofacial surgeons? Journal of Surgical Education, 74(2), 222–227.

    Google Scholar 

  • Sweileh, W. M. (2017). Global research trends of world health organization’s top eight emerging pathogens. Globalization and Health, 13(1), 9.

    Google Scholar 

  • Szwast, Z., Sieniutycz, S., & Shiner, J. S. (2002). Complexity principle of extremality in evolution of living organisms by information-theoretic entropy. Chaos, Solitons and Fractals, 13(9), 1871–1888.

    MathSciNet  MATH  Google Scholar 

  • Tananbaum, G. (2013). Article-level metrics: A SPARC primer. https://www.sparc.arl.org/sites/default/files/sparc-alm-primer.pdf, Accessed 25 Oct. 2019.

  • Therattil, P. J., Hoppe, I. C., Granick, M. S., & Lee, E. S. (2016). Application of the h index in academic plastic surgery. Annals of Plastic Surgery, 76(5), 545–549.

    Google Scholar 

  • Todeschini, R. (2011). The j-index: A new bibliometric index and multivariate comparisons between other common indices. Scientometrics, 87(3), 621–639.

    Google Scholar 

  • Van Eck, N. J., & Waltman, L. (2008). Generalizing the h- and g-indices. Journal of Informetrics, 2(4), 263–271.

    Google Scholar 

  • Van Raan, A. (2006). Comparison of the Hirsch index with standard bibliometric indicators and with peer judgment for 147 chemistry research groups. Scientometrics, 67(3), 491–502.

    Google Scholar 

  • Walters, G. D. (2016). Adding authorship order to the quantity and quality dimensions of scholarly productivity: evidence from group- and individual-level analyses. Scientometrics, 106(2), 769–785.

    Google Scholar 

  • Waltman, L., Costas, R., & JanvanEck, N. (2012). Some limitations of the h index: A commentary on Ruscio and colleagues’ analysis of bibliometric indices. Measurement: Interdisciplinary Research and Perspectives, 10(3), 172–175.

    Google Scholar 

  • Wan, J. K., Hua, P. H., & Rousseau, R. (2007). The pure h index: calculating an author’s h index by taking co-authors into account. COLLNET Journal of Scientometrics and Information Management, 1(2), 1–5.

    Google Scholar 

  • Werhl, A. (1978). General properties of entropy. Reviews of Modern Physics, 50, 221–261.

    MathSciNet  Google Scholar 

  • Wildgaard, L., Schneider, J. W., & Larsen, B. (2014). A review of the characteristics of 108 author-level bibliometric indicators. Scientometrics, 101(1), 125–158.

    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 

  • Wu, X., Wei, W., Tang, L., Lu, J. A., & Lü, J. (2019). Coreness and h index for weighted networks. IEEE Transactions on Circuits and Systems I: Regular Papers, 66(8), 3113–3122.

    MathSciNet  Google Scholar 

  • Xu, F., Liu, W., & Mingers, J. (2015). New journal classification methods based on the global h index. Information Processing and Management, 51(2), 50–61.

    Google Scholar 

  • Zareie, A., & Sheikhahmadi, A. (2019). EHC: Extended h-index centrality measure for identification of users’ spreading influence in complex networks. Physica A: Statistical Mechanics and its Applications, 514, 141–155.

    Google Scholar 

  • Zhai, L., Yan, X., & Zhang, G. (2018). Bi-directional h index: A new measure of node centrality in weighted and directed networks. Journal of Informetrics, 12(1), 299–314.

    Google Scholar 

  • Zhang, L., Thijs, B., & Glanzel, W. (2011). The diffusion of h-related literature. Journal of Informetrics, 5(4), 583–593.

    Google Scholar 

  • Zou, H., Du, H., Wang, Y., Zhao, L., Mao, G., Zuo, J., et al. (2017). A review of the first twenty-three years of articles published in the Journal of Cleaner Production: With a focus on trends, themes, collaboration networks, low/no-fossil carbon transformations and the future. Journal of Cleaner Production, 163, 1–14.

    Google Scholar 

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Acknowledgements

This study was supported by the Fundamental Research Funds for the Central Universities of China. The authors acknowledge with gratitude the comments and suggestions of anonymous reviewers and the editors, who provide significant contributions to this article.

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Authors and Affiliations

  1. WISE Lab, Institute of Science Studies and S&T Management, Dalian University of Technology, Dalian, 116023, China

    Deming Lin

  2. Beijing Normal University, Zhuhai, 519087, China

    Wenbin Liu

  3. DBM, BNU-HKBU United International College, Zhuhai, 519087, China

    Wenbin Liu

  4. Kent Business School, University of Kent, Canterbury, CT2 7PE, UK

    Tianhui Gong & Wenbin Liu

  5. Business School, University of Aberdeen, Aberdeen, AB24 5UA, UK

    Martin Meyer

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Lin, D., Gong, T., Liu, W. et al. An entropy-based measure for the evolution of h index research. Scientometrics 125, 2283–2298 (2020). https://doi.org/10.1007/s11192-020-03712-1

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