First we review the basic facts about Ihara zeta functions. Then we discuss two topics. 1)A condition on edge weights will be given that insures that the natural Ihara zeta function associated to a weighted graph has a 3-term determinant formula. 2)The distribution of poles of zeta functions of abelian graph coverings of a fixed small irregular graph will be compared with with those for a random covering.
This is joint work with H. Stark and M. Horton.