Impact functions on the citation network of scientific articles

Scientometric models, which consider papers in a undifferentiated way, are blind to important features of the citation network. We propose an approach for the definition of a function PS, for any set of scientific articles S, which reflects global properties of the citation network associated to S. Such a function, that we propose as a measure of the impact of scientific papers, is constructed as solution of an iterated system of Perron-eigenvalue problems. We discuss differences with previously defined measures, in particular of the PageRank type.

Research Highlights
► Whatever it measures, we expect that a function ranking the scientific papers reflects an intuitive idea of quality rather than the quantity of citations.
► We propose a number of properties (P1) to (P6) that a function has to fulfill in order to be considered as an impact function for scientific articles.
► We construct functions satisfying these properties by calculating, using Perron–Frobenius theory, the spectral radius of matrices associated to the citation network with some weights in the links.
► We provide an algorithmic definition of the impact functions that can be carried out by simple calculations.
► The proposed impact functions yield rankings of papers different than the PageRank algorithm.