Graph where PageRank will not converge I have been stuck on a homework problem for days.

Construct a strongly connected graph in which the basic PageRank computation does not converge.

I tried everything and still cannot find a solution.  My latest attempt is to brute force generate all possible 4 and 5 node graphs and to solve for their eigenvectors and look for cases where none of the eigenvectors are all the same sign.  Not working so far so I would greatly appreciate some hint.  I'm beginning to think no such graph exists....
If I can find a Matrix that will continually oscillate a vector with entries (1/n, 1/n, 1/n..., where is the number of dimensions) I believe that is the solution.  But how can I find such a Matrix?  I tried a 2D or 3D rotation matrix but that doesn't work as it gives a matrix with negative entries.

Maybe you should try with 


*

*an ergodic Markov chain which is not regular (and therefore MUST be cyclic)

*no dumping factor (aka alpha=1)


A directed cycle should work.
