Characterisation of the x-index and the rec-index

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 x-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 x-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 in uential researchers who have relatively few, but highly-cited, publications and prolific researchers who have many, but less-cited, publications

Journal ranking should depend on the level of aggregation

Journal ranking is becoming more important in assessing the quality of academic research. Several indices have been suggested for this purpose, typically on the basis of a citation graph between the journals. We follow an axiomatic approach and find an impossibility theorem: any self-consistent ranking method, which satisfies a natural monotonicity property, should depend on the level of aggregation. Our result presents a trade-off between two axiomatic properties and reveals a dilemma of aggregation.Comment: 10 pages, 2 figure

How to count citations if you must

Citation indices are regularly used to inform critical decisions about promotion, tenure, and the allocation of billions of research dollars. Nevertheless, most indices (e.g., the h-index) are motivated by intuition and rules of thumb, resulting in undesirable conclusions. In contrast, five natural properties lead us to a unique new index, the Euclidean index, that avoids several shortcomings of the h-index and its successors. The Euclidean index is simply the Euclidean length of an individual's citation list. Two empirical tests suggest that the Euclidean index outperforms the h-index in practice

Ranking authors using fractional counting of citations : an axiomatic approach

This paper analyzes from an axiomatic point of view a recent proposal for counting citations: the value of a citation given by a paper is inversely proportional to the total number of papers it cites. This way of fractionally counting citations was suggested as a possible way to normalize citation counts between fields of research having different citation cultures. It belongs to the “citing-side” approach to normalization. We focus on the properties characterizing this way of counting citations when it comes to ranking authors. Our analysis is conducted within a formal framework that is more complex but also more realistic than the one usually adopted in most axiomatic analyses of this kind

An axiomatic approach to bibliometric rankings and indices

This paper analyzes several well-known bibliometric indices using an axiomatic approach. We concentrate on indices aiming at capturing the global impact of a scientific output and do not investigate indices aiming at capturing an average impact. Hence, the indices that we study are designed to evaluate authors or groups of authors but not journals. The bibliometric indices that are studied include classic ones such as the number of highly cited papers as well as more recent ones such as the h-index and the g-index. We give conditions that characterize these indices, up to the multiplication by a positive constant. We also study the bibliometric rankings that are induced by these indices. Hence, we provide a general framework for the comparison of bibliometric rankings and indices