  The goal of this paper is to describe the connections between
Perron-Frobenius theory and vertex maps on graphs. In particular, it is shown
how Perron-Frobenius theory gives results about the sets of integers that can
arise as periods of periodic orbits, about the concepts of transitivity and
topological mixing, and about horseshoes and topological entropy.
  This is a preprint. The final version will appear in the Journal of
Difference Equations and Applications.
