A Bibliometric Index Based on Collaboration Distances

The h-index by Hirsch[1] has recently earned a lot of popularity in bibliometrics, being echoed in Nature and implemented in the Web of Science bibliometric database. Previous indicators were the total number of papers or the total number of citations. Following the widely accepted idea that not all papers should count equally, the h-index counts only those papers that are significant enough according to their number of citations. However, as for qualifying the significance of citations, beyond excluding self-citations by recent proposals[2,3,4,5,6], the fact that not all citations should count equally has remained unaddressed, with the exception of [7]. The h-index can be described in terms of a pool of evaluated objects (papers), a quality function on the evaluated object (citations received by each paper) and a sentencing line crossing the origin (y = x). When the evaluated objects are ordered by descreasing quality, then the intersection of the sentencing line with the graph of the quality function yields the index value. Based on this abstraction, we present a new index, the c-index, in which the evaluated objects are the citations received (by a paper, an author, a research group, a journal, etc.), the quality of a citation is the collaboration distance between the authors of the cited and the citing papers when the citation appears, and the sentencing line takes a slope α between 0 and ∞. To mitigate the small world effect we suggest taking α ≈ 1/4. As a result, the new index counts only those citations which are significant enough, where significance is proportional to the collaboration distance between the cited and the citing authors. While an h-index x means that there are x papers with at least x citations each and the rest of papers with at most x citations, a c-index x means that there are x citations (regardless of the papers to which these citations refer) at collaboration distance at least α x and the rest of citations at collaboration distance at most α x. If we want to differentiate between recurrent collaborations and occasional collaborations, a refined version of the classical distance can be defined, where the distance between two coauthors is inversely proportional to the number of joint papers between them.