  We prove an analogue of the magnetic nodal theorem on quantum graphs: the
number of zeros $\phi$ of the $n$-th eigenfunction of the Schr\"odinger
operator on a quantum graph is related to the stability of the $n$-th
eigenvalue of the perturbation of the operator by magnetic potential. More
precisely, we consider the $n$-th eigenvalue as a function of the magnetic
perturbation and show that its Morse index at zero magnetic field is equal to
$\phi - (n-1)$.
