  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.
