  We present and analyze a multiscale method for wave propagation problems,
posed on spatial networks. By introducing a coarse scale, using a finite
element space interpolated onto the network, we construct a discrete multiscale
space using the localized orthogonal decomposition (LOD) methodology. The
spatial discretization is then combined with an energy conserving temporal
scheme to form the proposed method. Under the assumption of well-prepared
initial data, we derive an a priori error bound of optimal order with respect
to the space and time discretization. In the analysis, we combine the theory
derived for stationary elliptic problems on spatial networks with classical
finite element results for hyperbolic problems. Finally, we present numerical
experiments that confirm our theoretical findings.
