  For a directed graph, the Pagerank algorithm emulates a random walker on the
graph that occasionally "jumps" to a random vertex based on a jumping parameter
$\alpha$. Upon completion, the algorithm generates a stochastic vector whose
entries correspond to the limiting probability that the walker will be at that
vertex. This vector is a right eigenvector of a corresponding Markov trasition
matrix. Undoubtedly, this vector can drastically change based upon the jumping
parameter $\alpha$.
  In this article, we investigate the maximum possible discrepancy for
different Pagerank vectors on the same unweighted directed (perhaps with loops)
graph as measured by the 2-norm. We show that the limsup of this discrepancy
can be as large as $\sqrt{\frac{67}{50}}$ using a very specific construction.
(For contrast, the norm of the difference for any two stochastic vectors is at
most $\sqrt{2}$.) Interestingly, on this construction this discrepancy occurs
when $\alpha = 1$ and when $\alpha$ is very close to 1.
