  A definition for functions of multidimensional arrays is presented. The
definition is valid for third-order tensors in the tensor t-product formalism,
which regards third-order tensors as block circulant matrices. The tensor
function definition is shown to have similar properties as standard matrix
function definitions in fundamental scenarios. To demonstrate the definition's
potential in applications, the notion of network communicability is generalized
to third-order tensors and computed for a small-scale example via block Krylov
subspace methods for matrix functions. A complexity analysis for these methods
in the context of tensors is also provided.
