  The problem of partitioning a large and sparse tensor is considered, where
the tensor consists of a sequence of adjacency matrices. Theory is developed
that is a generalization of spectral graph partitioning. A best
rank-$(2,2,\lambda)$ approximation is computed for $\lambda=1,2,3$, and the
partitioning is computed from the orthogonal matrices and the core tensor of
the approximation. It is shown that if the tensor has a certain reducibility
structure, then the solution of the best approximation problem exhibits the
reducibility structure of the tensor. Further, if the tensor is close to being
reducible, then still the solution of the exhibits the structure of the tensor.
Numerical examples with synthetic data corroborate the theoretical results.
Experiments with tensors from applications show that the method can be used to
extract relevant information from large, sparse, and noisy data.
