The stochastic weighted complexity of a group covering of a digraph

We consider the (stochastic) weighted complexity of a digraph D and a stochastic function from A(D) to nonnegative real numbers. Furthermore, we consider the weighted zeta function of a digraph, and present a determinant expression of it. We present a decomposition formula for the weighted zeta function of a group covering of a digraph. As an application, we give an explicit formula for the stochastic weighted complexity of a group covering of a digraph by using its stochastic weighted complexity.