  We review quantum chaos on graphs. We construct a unitary operator which
represents the quantum evolution on the graph and study its spectral and
wavefunction statistics. This operator is the analogue of the classical
evolution operator on the graph. It allow us to establish a connection between
the corresponding periodic orbits and the statistical properties of eigenvalues
and eigenfunctions. Specifically, for the energy-averaged spectral form factor
we derived an exact combinatorial expression which illustrate the role of
correlations between families of isometric orbits. We also show that enhanced
wave function localization due to the presence of short unstable periodic
orbits and strong scarring can rely on completely different mechanisms.
