  Tensor network states are capable of describing many-body systems with
complex quantum entanglement, including systems with non-trivial topological
order. In this paper, we study methods to calculate the topological properties
of a tensor network state from the tensors that form the state. Motivated by
the concepts of gauge group and projective symmetry group in the
slave-particle/projective construction, and by the low-dimensional gauge-like
symmetries of some exactly solvable Hamiltonians, we study the $d$-dimensional
gauge structure and the $d$-dimensional symmetry structure of a tensor network
state, where $d\leq d_{space}$ with $d_{space}$ the dimension of space. The
$d$-dimensional gauge structure and $d$-dimensional symmetry structure allow us
to calculate the string operators and $d$-brane operators of the tensor network
state. This in turn allows us to calculate many topological properties of the
tensor network state, such as ground state degeneracy and quasiparticle
statistics.
