Matrices of forests, analysis of networks, and ranking problems

TL;DR

This paper explores the use of spanning rooted forest matrices to analyze network structures, measure properties like vertex proximity, and develop ranking methods, providing new insights into network analysis and information dissemination.

Contribution

It introduces a vertex accessibility measure based on spanning forests with desirable properties and offers an interpretation of the stochastic out-forest matrix in terms of information flow.

Findings

Vertex accessibility measure has desirable properties

Stochastic out-forest matrix relates to information dissemination

Method aids in network structure analysis and ranking

Abstract

The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic bicomponents, measuring vertex proximity, and ranking from preference relations / sports competitions are considered. It is shown that the vertex accessibility measure based on spanning forests has a number of desirable properties. An interpretation for the stochastic matrix of out-forests in terms of information dissemination is given.