Three novel indirect indicators for the assessment of papers and authors based on generations of citations

A new indirect indicator is introduced for the assessment of scientific publications. The proposed indicator ($$fp^{k}$$fpk-index) takes into account both the direct and indirect impact of scientific publications and their age. The indicator builds on the concept of generations of citations and acts as a measure of the accumulated impact of each scientific publication. A number of cases are examined that demonstrate the way the indicator behaves under well defined conditions in a Paper-Citation graph, like when a paper is cited by a highly cited paper, when cycles exist and when self-citations and chords are examined. Two new indicators for the assessment of authors are also proposed (fa-index and fas-index) that utilize the $$fp^{k}$$fpk-index values of the scientific publications included in the Publication Record of an author. Finally, a comparative study of the $$fp^{k}$$fpk and $$fa^{k}$$fak indices and a list of well known direct (Number of Citations, Mean number of citations, Contemporary h-index) and indirect (PageRank, SCEAS) indicators is presented.

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