GENERAL SCIENTIFIC SUMMARY
Introduction and background. The question of how to measure the scientific influence of scientists and their publications is a long-term debate. Citation counts have been widely used to evaluate scientific impact. However, a paper with fewer citations, but those from prestigious scientists, is of greater influence than those papers with more citations, but from less prestigious sources. The value of each citation should depend on its source. We therefore propose an iterative algorithm to quantify the scientists' prestige and the quality of their publications via their interrelationship on an author–paper bipartite network; we call this the AP rank.

Main results. We apply AP rank to classify scientists and papers in the field of econophysics. Although some overlap exists between AP rank and citation counts, the outliers reveal the remarkable and meaningful differences. The figure shows the co-authorship network. With AP rank, we also identify the top-five mainstream journals in econophysics, Physica A, Physical Review E, European Physical Journal B, Quantitative Finance and Physical Review Letters.

Wider implications. The main advantages of AP rank are obvious: (1) it is parameter-free; (2) it considers the interaction between the prestige of scientists and the quality of their publications; and (3) it is effective in distinguishing prestige from popularity. Our algorithm can be generalized to applications in a wide range of systems. For example, on Twitter we can build an online reputation system to identify the influential users and evaluate the quality of their tweets by constructing a bipartite network where the retweets can be considered as a kind of citation.