Google matrix analysis of directed networks

Abstract

How can information from communication and social networks in modern societies be processed, classified, and retrieved? For this new mathematical methods have to be invented for a precise characterization of the existing networks and their search engines. This article describes the properties of the Google matrix and its efficiency in analyzing directed networks by way of several examples like the World Wide Web, Wikipedia, world trade, social and citation networks, DNA sequences and Ulam networks, and others. The underlying analytical and numerical tools used thereby originate from fields like quantum chaos and random matrix theory.