  We characterize the tail behavior of the distribution of the PageRank of a
uniformly chosen vertex in a directed preferential attachment graph and show
that it decays as a power law with an explicit exponent that is described in
terms of the model parameters. Interestingly, this power law is heavier than
the tail of the limiting in-degree distribution, which goes against the
commonly accepted {\em power law hypothesis}. This deviation from the power law
hypothesis points at the structural differences between the inbound
neighborhoods of typical vertices in a preferential attachment graph versus
those in static random graph models where the power law hypothesis has been
proven to hold (e.g., directed configuration models and inhomogeneous random
digraphs). In addition to characterizing the PageRank distribution of a typical
vertex, we also characterize the explicit growth rate of the PageRank of the
oldest vertex as the network size grows.
