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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 ofnodes and will never visit the rest of the graph. In Google PageRank theproblem was solved by introduction of uniform random jumps with someprobability. Up to the present, there is no clear criterion for the choice thisparameter. We propose to use parameter-free centrality measure which is basedon the notion of quasi-stationary distribution. Specifically we suggest fourquasi-stationary based centrality measures, analyze them and conclude that theyproduce approximately the same ranking. The new centrality measures can beapplied in spam detection to detect ``link farms'' and in image search to findphoto albums.

Quasi-stationary distributions as centrality measures of reducible graphs