  We study the PageRank mass of principal components in a bow-tie Web Graph, as
a function of the damping factor c. Using a singular perturbation approach, we
show that the PageRank share of IN and SCC components remains high even for
very large values of the damping factor, in spite of the fact that it drops to
zero when c goes to one. However, a detailed study of the OUT component reveals
the presence ``dead-ends'' (small groups of pages linking only to each other)
that receive an unfairly high ranking when c is close to one. We argue that
this problem can be mitigated by choosing c as small as 1/2.
