  We consider the resonances of a quantum graph $\mathcal G$ that consists of a
compact part with one or more infinite leads attached to it. We discuss the
leading term of the asymptotics of the number of resonances of $\mathcal G$ in
a disc of a large radius. We call $\mathcal G$ a \emph{Weyl graph} if the
coefficient in front of this leading term coincides with the volume of the
compact part of $\mathcal G$. We give an explicit topological criterion for a
graph to be Weyl. In the final section we analyze a particular example in some
detail to explain how the transition from the Weyl to the non-Weyl case occurs.
