  In this work a Green function approach for scattering quantum walks is
developed. The exact formula has the form of a sum over paths and always can be
cast into a closed analytic expression for arbitrary topologies and position
dependent quantum amplitudes. By introducing the step and path operators, it is
shown how to extract any information about the system from the Green function.
The method relevant features are demonstrated by discussing in details an
example, a general diamond-shaped graph.
