  PageRank, the prestige measure for Web pages used by Google, is the
stationary probability of a peculiar random walk on directed graphs, which
interpolates between a pure random walk and a process where all nodes have the
same probability of being visited. We give some exact results on the
distribution of PageRank in the cases in which the damping factor q approaches
the two limit values 0 and 1. When q -> 0 and for several classes of graphs the
distribution is a power law with exponent 2, regardless of the in-degree
distribution. When q -> 1 it can always be derived from the in-degree
distribution of the underlying graph, if the out-degree is the same for all
nodes.
