  Spatial network models are used as a simplified discrete representation in a
wide range of applications, e.g., flow in blood vessels, elasticity of fiber
based materials, and pore network models of porous materials. Nevertheless, the
resulting linear systems are typically large and poorly conditioned and their
numerical solution is challenging.
  This paper proposes a numerical homogenization technique for spatial network
models which is based on the Super Localized Orthogonal Decomposition (SLOD),
recently introduced for elliptic multiscale partial differential equations. It
provides accurate coarse solution spaces with approximation properties
independent of the smoothness of the material data. A unique selling point of
the SLOD is that it constructs an almost local basis of these coarse spaces,
requiring less computations on the fine scale and achieving improved sparsity
on the coarse scale compared to other state-of-the-art methods. We provide an
a-posteriori analysis of the proposed method and numerically confirm the
method's unique localization properties. In addition, we show its applicability
also for high-contrast channeled material data.
