Comparison of methods of ranking scientists based on the Hirsch and PageRank indices: contradictory situations

Experiments aimed at comparing different methods of estimating and ranking scientists and researchers on the base of their publication activity are reported. Scientometric indicators based on h-index and PageRank are being compared. For such a comparison, a graph of citations represented by a matrix was applied. An example when different methods lead to opposite results was described. For example, authors having the best PageRank-based estimations may have the least h-indices. Such a situation is possible when a high-cited author managed to obtain a key result cited by all the other authors but this author has few papers. A comparison with methods of expert estimations was carried out, which appears to be very useful for building automated systems combining various methods of algorithmic estimating and ranking. The Analytic Hierarchy Process was applied. For building pairwise comparison matrices, transitive scales with a parameter representing how much times the next level of advantage is bigger than the previous one were harnessed.