  Tensor network states provide successful descriptions of strongly correlated
quantum systems with applications ranging from condensed matter physics to
cosmology. Any family of tensor network states possesses an underlying
entanglement structure given by a graph of maximally entangled states along the
edges that identify the indices of the tensors to be contracted. Recently, more
general tensor networks have been considered, where the maximally entangled
states on edges are replaced by multipartite entangled states on plaquettes.
Both the structure of the underlying graph and the dimensionality of the
entangled states influence the computational cost of contracting these
networks. Using the geometrical properties of entangled states, we provide a
method to construct tensor network representations with smaller effective bond
dimension. We illustrate our method with the resonating valence bond state on
the kagome lattice.
