Characterisation of the $$\chi$$-index and the rec-index

Abstract

Axiomatic characterisation of a bibliometric index provides insight into the properties that the index satisfies and facilitates the comparison of different indices. A geometric generalisation of the h-index, called the χ-index, has recently been proposed to address some of the problems with the h-index, in particular, the fact that it is not scale invariant, i.e., multiplying the number of citations of each publication by a positive constant may change the relative ranking of two researchers. While the square of the h-index is the area of the largest square under the citation curve of a researcher, the square of the χ-index, which we call the rec-index (or rectangle-index), is the area of the largest rectangle under the citation curve. Our main contribution here is to provide a characterisation of the rec-index via three properties: monotonicity, uniform citation and uniform equivalence. Monotonicity is a natural property that we would expect any bibliometric index to satisfy, while the other two properties constrain the value of the rec-index to be the area of the largest rectangle under the citation curve. The rec-index also allows us to distinguish between influential researchers who have relatively few, but highly-cited, publications and prolific researchers who have many, but less-cited, publications.

Bibliometric indices as a measure of long-term competitive balance in knockout tournaments

“…However, this is not necessarily an appropriate approach in a knockout tournament. We consider two other bibliometric indices, in particular, the Euclidean index (Perry and Reny, 2016) and the rectangle index (Fenner et al, 2018;Levene et al, 2019).…”

“…The current paper offers a solution to these issues by using bibliometric indices. In particular, the Euclidean index (Perry and Reny, 2016) and the rectangle index (Fenner et al, 2018;Levene et al, 2019) will be considered for this purpose with various weights assigned for the achievements of the teams, analogously to the number of times a paper has been referred to. An axiomatic comparison will be provided to highlight the differences between the two measures.…”

A two-dimensional bibliometric index reflecting both quality and quantity

“…We now formally define the two-dimensional index (rec I , rec P ) introduced in [LFB19]. We first define the publication vector p = p 1 , p 2 , .…”

“…A vertical rectangle (with height greater than or equal to width) represents the influence of a researcher, and a horizontal one (with width greater than or equal to height) the prolificity of the researcher. In fact, as suggested in [LFB19], we can represent a researcher by the pair of indices (rec I (x), rec P (x)), where, rec I (x) is the area of the largest vertical rectangle under the citation curve of the citation vector x, and rec P (x) is the area of the largest horizonal rectangle under the citation curve of x (the formal definitions are given in Section 2). For simplicity of notation, we abbreviate these to rec I and rec P when x is apparent from context.…”

Modeling a successful citation trajectory structure for scholar's impact evaluation in Israeli academia

“…Ref. [ 7 ]). As has been shown in previous research, there is a wide diversity in publication, citation and h-index scores even among prominent scientists, such as tenured professors [ 8 ].…”