  We prove an approximation result showing how operators of the type $-\Delta
-\gamma \delta (x-\Gamma)$ in $L^2(\mathbb{R}^2)$, where $\Gamma$ is a graph,
can be modeled in the strong resolvent sense by point-interaction Hamiltonians
with an appropriate arrangement of the $\delta$ potentials. The result is
illustrated on finding the spectral properties in cases when $\Gamma$ is a ring
or a star. Furthermore, we use this method to indicate that scattering on an
infinite curve $\Gamma$ which is locally close to a loop shape or has multiple
bends may exhibit resonances due to quantum tunneling or repeated reflections.
