Towards two-dimensional search engines

TL;DR

This paper explores the development of two-dimensional search engines by analyzing the statistical properties of directed networks using PageRank and CheiRank, offering a new approach to node ranking based on incoming and outgoing links.

Contribution

It introduces a two-dimensional ranking method combining PageRank and CheiRank, enabling more comprehensive search engine algorithms and analyzing their properties across various real-world networks.

Findings

PageRank correlates with number of ingoing links

CheiRank correlates with number of outgoing links

Two-dimensional ranking improves search engine capabilities

Abstract

We study the statistical properties of various directed networks using ranking of their nodes based on the dominant vectors of the Google matrix known as PageRank and CheiRank. On average PageRank orders nodes proportionally to a number of ingoing links, while CheiRank orders nodes proportionally to a number of outgoing links. In this way the ranking of nodes becomes two-dimensional that paves the way for development of two-dimensional search engines of new type. Statistical properties of information flow on PageRank-CheiRank plane are analyzed for networks of British, French and Italian Universities, Wikipedia, Linux Kernel, gene regulation and other networks. A special emphasis is done for British Universities networks using the large database publicly available at UK. Methods of spam links control are also analyzed.