  We consider compact metric graphs with an arbitrary self adjoint realisation
of the differential Laplacian. After discussing spectral properties of
Laplacians, we prove several versions of trace formulae, relating Laplace
spectra to sums over periodic orbits on the graph. This includes trace formulae
with, respectively, absolutely and conditionally convergent periodic orbit
sums; the convergence depending on properties of the test functions used. We
also prove a trace formula for the heat kernel and provide small-$t$
asymptotics for the trace of the heat kernel.
