Google matrix analysis of directed networks

TL;DR

This paper reviews the Google matrix analysis method for directed networks, demonstrating its effectiveness in classifying and ranking complex networks like the Web, Wikipedia, social, and biological systems using advanced mathematical tools.

Contribution

It introduces and demonstrates the application of Google matrix analysis to various complex directed networks, highlighting its efficiency and versatility.

Findings

Effective classification of diverse networks

Demonstrated ranking capabilities on real-world data

Utilized advanced mathematical frameworks

Abstract

In past ten years, modern societies developed enormous communication and social networks. Their classification and information retrieval processing become a formidable task for the society. Due to the rapid growth of World Wide Web, social and communication networks, new mathematical methods have been invented to characterize the properties of these networks on a more detailed and precise level. Various search engines are essentially using such methods. It is highly important to develop new tools to classify and rank enormous amount of network information in a way adapted to internal network structures and characteristics. This review describes the Google matrix analysis of directed complex networks demonstrating its efficiency on various examples including World Wide Web, Wikipedia, software architecture, world trade, social and citation networks, brain neural networks, DNA sequences and Ulam networks. The analytical and numerical matrix methods used in this analysis originate from the fields of Markov chains, quantum chaos and Random Matrix theory.