Quasi-stationary distributions as centrality measures for the giant strongly connected component of a reducible graph

Authors:
Konstantin Avrachenkov;Vivek Borkar;Danil Nemirovsky
Affiliations:
INRIA Sophia Antipolis, France;Tata Institute of Fundamental Research, India;INRIA Sophia Antipolis, France and St. Petersburg State University, Russia
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

A 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 the introduction of uniform random jumps with some probability. Up to the present, there is no final answer to the question about the choice of this probability. We propose to use a parameter-free centrality measure which is based on the notion of a quasi-stationary distribution. Specifically, we suggest four quasi-stationary based centrality measures, analyze them and conclude that they produce approximately the same ranking.