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.