The h -index formalism
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The h‑index formalism Leo Egghe1 · Ronald Rousseau2,3 Received: 22 July 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract This article provides an overview of the development of the h-index formalism. We begin with the original formulation as provided by Hirsch and move on to the latest versions. In this we show how the h-index formalism has evolved over time. Lesser known versions, in particular the continuous version of the h-index is brought to the front. We also discuss the Prathap–Kosmulski–Schubert successive h-indices. As announced in the title we focus on the h-index formalism, omitting generalizations, such as the g-index, and applications in research assessment. Keywords h-Index · Generalized h-index · Discrete and continuous case · Successive h-indices · Higher-order h-indices
Introduction Traditionally serious doubt has been raised about the reliability of bibliometrics as applied to individuals or small groups (King 1987). Narin (1976, p.160) already pointed out several pitfalls when applying citation analysis to individual scientists. This point has recently been stressed again by Moed (2020), who referred to calculating indicators at the level of an individual and stated that claiming that such indicators by themselves measure an individual’s performance, is a case of false precision. Yet, in 2005 this idea has been challenged by Hirsch (2005) who introduced a new indicator based on publications and citations, and aiming particularly at the evaluation of individuals. Although this indicator, known as the h-index, has several disadvantages when applied in a research evaluation setting, it took bibliometrics by storm and became one of the most popular indicators. As Hirsch’ original publication inspired hundreds of scientists, soon several reviews were published, see e.g., Rousseau (2008), Alonso et al. (2009), Egghe (2010) and Schubert and Schubert (2019). * Ronald Rousseau [email protected]; [email protected] Leo Egghe [email protected] 1
University of Hasselt, Hasselt, Belgium
2
Faculty of Social Sciences, University of Antwerp, 2020 Antwerp, Belgium
3
Centre for R&D Monitoring (ECOOM) and Department of MSI, KU Leuven, 3000 Leuven, Belgium
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Vol.:(0123456789)
Scientometrics
Recent books too devoted considerable attention to the h-index and its generalizations (Todeschini and Baccini 2016; Vitanov 2016; Rousseau et al. 2018). It should be observed that the h-index is not obtained as a simple mathematical operation on the data, such as adding, multiplying or dividing, applied to numbers of publications or received citations, but is obtained as the result of a process. Indeed data must be ranked and then a comparison must be made to obtain the h-index (see further for the complete definition). In the next sections we will ignore the h-index as an indicator for research evaluation but instead study the mathematical formalism.
Formalizing: discrete version In this section, we show how the same discrete formalism has been defined in different situations a
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