Within-Journal Self-citations and the Pinski-Narin Influence Weights

The Journal Impact Factor (JIF) is linearly sensitive to self-citations because each self-citation adds to the numerator, whereas the denominator is not affected. Pinski & Narin (1976) derived the Influence Weight (IW) as an alternative to Garfield's JIF. Whereas the JIF is based on raw citation counts normalized by the number of publications, IWs are based on the eigenvectors in the matrix of aggregated journal-journal citations without a reference to size: the cited and citing sides are combined by a matrix approach. IWs emerge as a vector after recursive iteration of the normalized matrix. Before recursion, IW is a (vector-based) non-network indicator of impact, but after recursion (i.e. repeated improvement by iteration), IWs can be considered a network measure of prestige among the journals in the (sub)graph as a representation of a field of science. As a consequence (not intended by Pinski & Narin in 1976), the self-citations are integrated at the field level and no longer disturb the analysis as outliers. In our opinion, this is a very desirable property of a measure of quality or impact. As illustrations, we use data of journal citation matrices already studied in the literature, and also the complete set of data in the Journal Citation Reports 2017 (n = 11,579 journals). The values of IWs are sometimes counter-intuitive and difficult to interpret. Furthermore, iterations do not always converge. Routines for the computation of IWs are made available at http://www.leydesdorff.net/iw.