  The choice of the PageRank damping factor is not evident. The Google's choice
for the value c=0.85 was a compromise between the true reflection of the Web
structure and numerical efficiency. However, the Markov random walk on the
original Web Graph does not reflect the importance of the pages because it
absorbs in dead ends. Thus, the damping factor is needed not only for speeding
up the computations but also for establishing a fair ranking of pages. In this
paper, we propose new criteria for choosing the damping factor, based on the
ergodic structure of the Web Graph and probability flows. Specifically, we
require that the core component receives a fair share of the PageRank mass.
Using singular perturbation approach we conclude that the value c=0.85 is too
high and suggest that the damping factor should be chosen around 1/2. As a
by-product, we describe the ergodic structure of the OUT component of the Web
Graph in detail. Our analytical results are confirmed by experiments on two
large samples of the Web Graph.
