  We present and analyze a methodology for numerical homogenization of spatial
networks, modelling e.g. diffusion processes and deformation of mechanical
structures. The aim is to construct an accurate coarse model of the network. By
solving decoupled problems on local subgraphs we construct a low dimensional
subspace of the solution space with good approximation properties. The coarse
model of the network is expressed by a Galerkin formulation and can be used to
perform simulations with different source and boundary data at a low
computational cost. We prove optimal convergence of the proposed method under
mild assumptions on the homogeneity, connectivity, and locality of the network
on the coarse scale. The theoretical findings are numerically confirmed for
both scalar-valued (heat conduction) and vector-valued (structural) models.
