  In this note we define L-functions of finite graphs and study the particular
case of finite cycles in the spirit of a previous paper that studied spectral
zeta functions of graphs. The main result is a suggestive equivalence between
an asymptotic functional equation for these L-functions and the corresponding
case of the Generalized Riemann Hypothesis. We also establish a relation
between the positivity of such functions and the existence of real zeros in the
critical strip of the classical Dirichlet L-functions with the same character.
