A novel bibliometric index with a simple geometric interpretation

Abstract

We propose the χ-index as a bibliometric indicator that generalises the h-index. While the h-index is determined by the maximum square that fits under the citation curve of an author when plotting the number of citations in decreasing order, the χ-index is determined by the maximum area rectangle that fits under the curve. The height of the maximum rectangle is the number of citations ck to the kth most-cited publication, where k is the width of the rectangle. The χ-index is then defined as , for convenience of comparison with the h-index and other similar indices. We present a comprehensive empirical comparison between the χ-index and other bibliometric indices, focusing on a comparison with the h-index, by analysing two datasets—a large set of Google Scholar profiles and a small set of Nobel prize winners. Our results show that, although the χ and h indices are strongly correlated, they do exhibit significant differences. In particular, we show that, for these data sets, there are a substantial number of profiles for which χ is significantly larger than h. Furthermore, restricting these profiles to the cases when ck > k or ck < k corresponds to, respectively, classifying researchers as either tending to influential, i.e. having many more than h citations, or tending to prolific, i.e. having many more than h publications.

The Most Cited Mesh Terms and Authors who Published Papers in Pubmed Central on the Topic of Medicine and Health Using Bibliometric Analyses

“…[28] due to many integer unit. Although many concepts of bibliometrics have already been proposed in the past [14,16,17,24], we have not seen any that can be effectively applied to the scientific disciplines. We suggest using the one of x-index that can effectively improve hindex with less discriminative power for evaluating authors and MeSH terms in the past.…”

“…The x-index [14] is used for improving h-index by emphasizing the citations in h-core articles. For instance, one article with 100 citations has h=1 and x=10, respectively.…”

“…i is the i-th publication in descending order of citations, and ci is the citation at the i-th publication) [14] that can effectively improve the h-index(≤citation at the i-th publication) [15] in bibliometric analyses [16,17] and investigate the four questions mentioned above. Google Maps [18.19] will be applied to the study for illustrating results on dashboards.…”

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

“…It is therefore worth noting our findings in [FHLB18], where the citations of a large number of researchers, from a Google Scholar data set made available by Radicchi and Castellano [RC13], were analysed and their rec-indices calculated. Table 11 in [FHLB18] shows that 93% of the researchers for which the χ-index was significantly larger than the h-index were more influential than prolific, i.e. for these researchers x k > k. This indicates that, in general, the rec-index satisfies the tendency to favour influence.…”

“…In this paper we focus on a (two-dimensional) geometric generalisation of the h-index, called the χ-index [FHLB18], which has recently been proposed to address some of the problems with the h-index, in particular the fact that it is not scale invariant [PR16].…”