Recent advances in bibliometric indexes and the PaperRank problem

Bibliometric indexes are customary used in evaluating the impact of scientific research, even though it is very well known that in different research areas they may range in very different intervals. Sometimes, this is evident even within a single given field of investigation making very difficult (and inaccurate) the assessment of scientific papers. On the other hand, the problem can be recast in the same framework which has allowed to efficiently cope with the ordering of web-pages, i.e., to formulate the PageRank of Google. For this reason, we call such problem the PaperRank problem, here solved by using a similar approach to that employed by PageRank. The obtained solution, which is mathematically grounded, will be used to compare the usual heuristics of the number of citations with a new one here proposed. Some numerical tests show that the new heuristics is much more reliable than the currently used ones, based on the bare number of citations. Moreover, we show that our model improves on recently proposed ones.