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