Axiomatic measures of intellectual influence

Measuring influence allows the study of such issues as the impact and reputation of scientists and scientific publications, the dynamics of innovation, and the construction of ranking algorithms for search engines in the world wide web. Ranking methods that measure influence are typically based on the information contained in the network of communications between different entities (scholarly publications, patents, web pages). This paper presents within the same framework recent developments that use the axiomatic approach to derive ranking methods. Two related but essentially different ranking problems are studied: journal ranking problems and scholar ranking problems. The paper concludes with open theoretical and empirical questions for future research.