Google matrix analysis of directed networks

LEONARDO ERMANN; KLAUS FRAHM; DIMA L. SHEPELYANSKY

REVIEWS OF MODERN PHYSICS

AMER PHYSICAL SOC

Lugar: New York; Año: 2015 vol. 87 p. 1261 - 1310

0034-6861

In the past decade modern societies have developed enormous communication and social networks.Their classification and information retrieval processing has become a formidable task for the society.Because of the rapid growth of the World Wide Web, and social and communication networks, newmathematical methods have been invented to characterize the properties of these networks in a moredetailed and precise way. Various search engines extensively use such methods. It is highly important todevelop new tools to classify and rank a massive amount of network information in a way that is adaptedto internal network structures and characteristics. This review describes the Google matrix analysis ofdirected complex networks demonstrating its efficiency using various examples including the WorldWide Web, Wikipedia, software architectures, world trade, social and citation networks, brain neuralnetworks, DNA sequences, and Ulam networks. The analytical and numerical matrix methods used inthis analysis originate from the fields of Markov chains, quantum chaos, and random matrix theory.