Paper Info
Title
Characterisation of the $$\chi$$ χ -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 $$\chi$$-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 $$\chi$$-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.
Year
DOI
Venue
2019
10.1007/s11192-019-03151-7
Scientometrics
Keywords
Field
DocType
h-index, -index, rec-index, Bibliometric index, Core publications, Quantity versus quality, Axiomatic characterisation
Monotonic function,Discrete mathematics,Data mining,Scale invariance,Ranking,Computer science,Axiom,Generalization,Citation,Rectangle,Equivalence (measure theory)
Journal
Volume
Issue
ISSN
120
2
0138-9130
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Mark Levene11272252.84
Trevor I. Fenner213536.89
Judit Bar-Ilan31638124.05