Quasi-stationary distributions as centrality measures of reducible graphs

TL;DR

This paper introduces parameter-free centrality measures based on quasi-stationary distributions for reducible graphs, addressing limitations of traditional random walk-based measures like PageRank.

Contribution

It proposes four new quasi-stationary distribution-based centrality measures and analyzes their effectiveness, providing a criterion-free alternative to PageRank.

Findings

The measures produce similar node rankings.

They can be applied to spam detection and image search.

The measures are parameter-free and theoretically grounded.

Abstract

Random walk can be used as a centrality measure of a directed graph. However, if the graph is reducible the random walk will be absorbed in some subset of nodes and will never visit the rest of the graph. In Google PageRank the problem was solved by introduction of uniform random jumps with some probability. Up to the present, there is no clear criterion for the choice this parameter. We propose to use parameter-free centrality measure which is based on the notion of quasi-stationary distribution. Specifically we suggest four quasi-stationary based centrality measures, analyze them and conclude that they produce approximately the same ranking. The new centrality measures can be applied in spam detection to detect ``link farms'' and in image search to find photo albums.