A proposal for calculating weighted citations based on author rank.

A recent article in EMBO reports by Bornmann & Daniel (2009) commented that “the h index [...] is already regarded as the counterpart to the [impact factor]”. Indeed, the h index (Hirsch, 2005) is increasingly being used to evaluate the achievements of individual scientists, and major citation databases—such as the Scientific Citation Index (SCI; Thomson Reuters, New York, NY, USA) and Scopus (Elsevier, Amsterdam, The Netherlands)— already list by default the h index and total citations of every published scientist. However, this use confuses two distinct concepts: the citation number for a paper and that for an author, which differ because in a paper with multiple authors, To address this, I propose a quan titative scheme to calculate co-author weight coefficients. Consider a paper of five authors with the last being the corresponding author. Weight coefficients c for the first and corres ponding authors are 1 for both. Contributions of the second, third, and fourth authors are proportional to 4, 3 and 2, respectively, hence coefficients being 4/9, 3/9 and 2/9, respectively, where 9 = 4 + 3 + 2. Similarly, for the kth author in a paper with n authors, c(k,n) = 2(n – k + 1)/(n + 1)(n – 2), n ≥ 4, 2 ≤ k ≤ n – 1 (a special case is c(2,3) = 0.7 based on the extra polation of c(2,n), n ≥ 4). By this definition, except the first and corresponding authors, the sum of weights for the remaining authors is 1. Weighted citation numbers, calculated by multiplying regular cit ations by weight coefficients, remain the same as reg ular citations for the first and corres ponding authors, but decrease linearly for authors with increasing rank. The h index is based on total citation numbers, which disregard author rank. Therefore, we define w, the weighted h index, based their contrib utions are hardly equal and not all of them should take full credit. Nevertheless, routinely every author in a paper claims all cit ations as his or her own. Although the author rank is evident in the byline of a publication, it is invisible in citation numbers. For example, SCI and Scopus both disregard author rank when computing the total citation number and h index for a scientist. Indeed, multiple authorship is considered to be damaging to the credit system and the situation is becoming more severe as the average author number per paper continues to increase (Greene, 2007; Kennedy, 2003). Ten years ago, Nature introduced a policy advising authors to include a statement about their contributions for each paper (Campbell, 1999). This policy, increasingly being adopted by other scientific journals, is doubtlessly useful and necessary. However, this information becomes invisible when citation numbers are concerned and it is completely qualitative; author contributions should be quantified.