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The Journal Impact Factor (JIF) is linearly sensitive to self-citationsbecause each self-citation adds to the numerator, whereas the denominator isnot affected. Pinski & Narin (1976) derived the Influence Weight (IW) as analternative to Garfield's JIF. Whereas the JIF is based on raw citation countsnormalized by the number of publications, IWs are based on the eigenvectors inthe 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 avector after recursive iteration of the normalized matrix. Before recursion, IWis a (vector-based) non-network indicator of impact, but after recursion (i.e.repeated improvement by iteration), IWs can be considered a network measure ofprestige among the journals in the (sub)graph as a representation of a field ofscience. As a consequence (not intended by Pinski & Narin in 1976), theself-citations are integrated at the field level and no longer disturb theanalysis as outliers. In our opinion, this is a very desirable property of ameasure of quality or impact. As illustrations, we use data of journal citationmatrices already studied in the literature, and also the complete set of datain the Journal Citation Reports 2017 (n = 11,579 journals). The values of IWsare sometimes counter-intuitive and difficult to interpret. Furthermore,iterations do not always converge. Routines for the computation of IWs are madeavailable at http://www.leydesdorff.net/iw.

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