  We introduce a new coarse-graining algorithm, tensor network skeletonization,
for the numerical computation of tensor networks. This approach utilizes a
structure-preserving skeletonization procedure to remove short-range
correlations effectively at every scale. This approach is first presented in
the setting of 2D statistical Ising model and is then extended to higher
dimensional tensor networks and disordered systems. When applied to the
Euclidean path integral formulation, this approach also gives rise to new
efficient representations of the ground states for 1D and 2D quantum Ising
models.
