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Relations among the h-, g-, ψ-, and p-index and offset-ability

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  • Wei, Shelia X.
  • Tong, Tong
  • Rousseau, Ronald
  • Wang, Wanru
  • Ye, Fred Y.

Abstract

We show that the h-index, g-index, ψ-index, and p-index, are related through the inequalities: h ≤ p ≤ g ≤ ψ. Moreover, this relation is proved theoretically in the mathematical framework of Lotkaian informetrics and is verified empirically by using two datasets from the Web of Science in the fields of electrochemistry and gerontology. For quantifying their relations, we estimate the g-index, ψ-index, and their cores and ratios of cores via a second-order Taylor series when the e-index, h-index, and C1 (the maximum number of citations received by a paper) are known. Then we find for the two empirical cases, that ratios of cores and average citations are approximately stable. Compared with the g-index, the offset-ability of the h-index decreases by 20% but the average citations increase by 20%. A similar observation holds for the comparison of the g-index and ψ-index. To explore the possible applications of cores of different indices, we apply them to extract the core structure of a network. The h-core is the most efficient, while the ψ-core includes more nodes with high betweenness.

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  • Wei, Shelia X. & Tong, Tong & Rousseau, Ronald & Wang, Wanru & Ye, Fred Y., 2022. "Relations among the h-, g-, ψ-, and p-index and offset-ability," Journal of Informetrics, Elsevier, vol. 16(4).
    • Handle: RePEc:eee:infome:v:16:y:2022:i:4:s175115772200092x
    DOI: 10.1016/j.joi.2022.101340
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    as
    1. Zhao, Star X. & Rousseau, Ronald & Ye, Fred Y., 2011. "h-Degree as a basic measure in weighted networks," Journal of Informetrics, Elsevier, vol. 5(4), pages 668-677.
    2. L. Egghe, 2008. "The influence of transformations on the h‐index and the g‐index," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 59(8), pages 1304-1312, June.
    3. Eva Lillquist & Sheldon Green, 2010. "The discipline dependence of citation statistics," Scientometrics, Springer;Akadémiai Kiadó, vol. 84(3), pages 749-762, September.
    4. Gangan Prathap, 2011. "A thermodynamic explanation for the Glänzel–Schubert model for the h‐index," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 62(5), pages 992-994, May.
    5. Chun‐Ting Zhang, 2010. "Relationship of the h‐index, g‐index, and e‐index," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 61(3), pages 625-628, March.
    6. Gangan Prathap, 2014. "The zynergy-index and the formula for the h-index," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 65(2), pages 426-427, February.
    7. Juan E. Iglesias & Carlos Pecharromán, 2007. "Scaling the h-index for different scientific ISI fields," Scientometrics, Springer;Akadémiai Kiadó, vol. 73(3), pages 303-320, December.
    8. van Eck, Nees Jan & Waltman, Ludo, 2008. "Generalizing the h- and g-indices," Journal of Informetrics, Elsevier, vol. 2(4), pages 263-271.
    9. Deming Lin & Tianhui Gong & Wenbin Liu & Martin Meyer, 2020. "An entropy-based measure for the evolution of h index research," Scientometrics, Springer;Akadémiai Kiadó, vol. 125(3), pages 2283-2298, December.
    10. Filippo Radicchi & Claudio Castellano, 2013. "Analysis of bibliometric indicators for individual scholars in a large data set," Scientometrics, Springer;Akadémiai Kiadó, vol. 97(3), pages 627-637, December.
    11. Chun-Ting Zhang, 2010. "Relationship of the h-index, g-index, and e-index," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 61(3), pages 625-628, March.
    12. Gangan Prathap, 2010. "The 100 most prolific economists using the p-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 84(1), pages 167-172, July.
    13. Gangan Prathap, 2021. "Letter to the editor: Is the h-index a mock compromise between the p-index and the z-index?," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(5), pages 4537-4539, May.
    14. Gangan Prathap, 2010. "Is there a place for a mock h-index?," Scientometrics, Springer;Akadémiai Kiadó, vol. 84(1), pages 153-165, July.
    15. 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).
    16. Leo Egghe & Ronald Rousseau, 2006. "An informetric model for the Hirsch-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 121-129, October.
    17. Roberto Todeschini, 2011. "The j-index: a new bibliometric index and multivariate comparisons between other common indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 87(3), pages 621-639, June.
    18. Lathabai, Hiran H., 2020. "ψ-index: A new overall productivity index for actors of science and technology," Journal of Informetrics, Elsevier, vol. 14(4).
    19. Chun-Ting Zhang, 2013. "The h’-Index, Effectively Improving the h-Index Based on the Citation Distribution," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-8, April.
    20. Fred Y. Ye, 2011. "A unification of three models for the h‐index," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 62(1), pages 205-207, January.
    21. S. Alonso & F. J. Cabrerizo & E. Herrera-Viedma & F. Herrera, 2010. "hg-index: a new index to characterize the scientific output of researchers based on the h- and g-indices," Scientometrics, Springer;Akadémiai Kiadó, vol. 82(2), pages 391-400, February.
    22. Fred Y. Ye, 2011. "A unification of three models for the h-index," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 62(1), pages 205-207, January.
    23. Pascal Bador & Thierry Lafouge, 2010. "Comparative analysis between impact factor and h-index for pharmacology and psychiatry journals," Scientometrics, Springer;Akadémiai Kiadó, vol. 84(1), pages 65-79, July.
    24. Schubert, András & Glänzel, Wolfgang, 2007. "A systematic analysis of Hirsch-type indices for journals," Journal of Informetrics, Elsevier, vol. 1(3), pages 179-184.
    25. Qiang Wu, 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, Association for Information Science & Technology, vol. 61(3), pages 609-614, March.
    26. Leo Egghe, 2006. "Theory and practise of the g-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 69(1), pages 131-152, October.
    27. Jerome K. Vanclay, 2007. "On the robustness of the h‐index," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 58(10), pages 1547-1550, August.
    28. Chrisovalantis Malesios, 2015. "Some variations on the standard theoretical models for the h-index: A comparative analysis," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 66(11), pages 2384-2388, November.
    29. Gangan Prathap, 2018. "Letter to the editor: Dimensionless citation indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 115(3), pages 1433-1435, June.
    30. Jingda Ding & Chao Liu & Goodluck Asobenie Kandonga, 2020. "Exploring the limitations of the h-index and h-type indexes in measuring the research performance of authors," Scientometrics, Springer;Akadémiai Kiadó, vol. 122(3), pages 1303-1322, March.
    31. Li, Simon S. & Ye, Adam Y. & Qi, Eric P. & Stanley, H. Eugene & Ye, Fred Y., 2018. "Characterizing core–periphery structure of complex network by h-core and fingerprint curve," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1206-1215.
    32. Gangan Prathap, 2011. "A thermodynamic explanation for the Glänzel–Schubert model for the h-index," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 62(5), pages 992-994, May.
    33. Kuan, Chung-Huei & Huang, Mu-Hsuan & Chen, Dar-Zen, 2011. "Positioning research and innovation performance using shape centroids of h-core and h-tail," Journal of Informetrics, Elsevier, vol. 5(4), pages 515-528.
    34. Liu, Joan Q. & Rousseau, Ronald & Wang, Mona S. & Ye, Fred Y., 2013. "Ratios of h-cores, h-tails and uncited sources in sets of scientific papers and technical patents," Journal of Informetrics, Elsevier, vol. 7(1), pages 190-197.
    35. Egghe, L., 2008. "Examples of simple transformations of the h-index: Qualitative and quantitative conclusions and consequences for other indices," Journal of Informetrics, Elsevier, vol. 2(2), pages 136-148.
    36. Fred Y. Ye & Ronald Rousseau, 2010. "Probing the h-core: an investigation of the tail–core ratio for rank distributions," Scientometrics, Springer;Akadémiai Kiadó, vol. 84(2), pages 431-439, August.
    37. Chen, Dar-zen & Huang, Mu-hsuan & Ye, Fred Y., 2013. "A probe into dynamic measures for h-core and h-tail," Journal of Informetrics, Elsevier, vol. 7(1), pages 129-137.
    38. Hamid Bouabid & Mohamed Dalimi & Zayer ElMajid, 2011. "Impact evaluation of the voluntary early retirement policy on research and technology outputs of the faculties of science in Morocco," Scientometrics, Springer;Akadémiai Kiadó, vol. 86(1), pages 125-132, January.
    39. Prem Kumar Singh, 2022. "t-index: entropy based random document and citation analysis using average h-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(1), pages 637-660, January.
    40. Wang, Ruby W. & Wei, Shelia X. & Ye, Fred Y., 2021. "Extracting a core structure from heterogeneous information network using h-subnet and meta-path strength," Journal of Informetrics, Elsevier, vol. 15(3).
    41. Elias Sanz-Casado & Carlos García-Zorita & Ronald Rousseau, 2016. "Using h-cores to study the most-cited articles of the twenty-first century," Scientometrics, Springer;Akadémiai Kiadó, vol. 108(1), pages 243-261, July.
    42. Star X. Zhao & Paul L. Zhang & Jiang Li & Alice M. Tan & Fred Y. Ye, 2014. "Abstracting the core subnet of weighted networks based on link strengths," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 65(5), pages 984-994, May.
    43. Zhai, Li & Yan, Xiangbin & Zhang, Guojing, 2019. "The bi-directional h-index and B-core decomposition in directed networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    44. Chun-Ting Zhang, 2009. "The e-Index, Complementing the h-Index for Excess Citations," PLOS ONE, Public Library of Science, vol. 4(5), pages 1-4, May.
    45. Fred Y. Ye, 2009. "An investigation on mathematical models of the h-index," Scientometrics, Springer;Akadémiai Kiadó, vol. 81(2), pages 493-498, November.
    46. 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.
    47. Leo Egghe, 2007. "Untangling Herdan's law and Heaps' law: Mathematical and informetric arguments," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 58(5), pages 702-709, March.
    48. Gangan Prathap, 2021. "Letter to the editor: Dimensionless citation indicators for fractional counting," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(10), pages 8765-8769, October.
    49. Schreiber, M. & Malesios, C.C. & Psarakis, S., 2012. "Exploratory factor analysis for the Hirsch index, 17 h-type variants, and some traditional bibliometric indicators," Journal of Informetrics, Elsevier, vol. 6(3), pages 347-358.
    50. Gangan Prathap, 2017. "Letter to the editor: comments on the paper of Lucio Bertoli-Barsotti and Tommaso Lando: a theoretical model of the relationship between the h-index and other simple citation indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(2), pages 1133-1136, August.
    51. Qiang Wu, 2010. "The w-index: A measure to assess scientific impact by focusing on widely cited papers," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 61(3), pages 609-614, March.
    52. Anand Bihari & Sudhakar Tripathi, 2017. "EM-index: a new measure to evaluate the scientific impact of scientists," Scientometrics, Springer;Akadémiai Kiadó, vol. 112(1), pages 659-677, July.
    53. Lucio Bertoli-Barsotti & Tommaso Lando, 2017. "A theoretical model of the relationship between the h-index and other simple citation indicators," Scientometrics, Springer;Akadémiai Kiadó, vol. 111(3), pages 1415-1448, June.
    54. 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.
    55. 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.
    56. Gangan Prathap, 2012. "Evaluating journal performance metrics," Scientometrics, Springer;Akadémiai Kiadó, vol. 92(2), pages 403-408, August.
    57. András Schubert & András Korn & András Telcs, 2009. "Hirsch-type indices for characterizing networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 78(2), pages 375-382, February.
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