  We develop a framework for stress response in two dimensional granular media,
with and without friction, that respects vector force balance at the
microscopic level. We introduce local gauge degrees of freedom that determine
the response of contact forces between constituent grains on a given,
disordered, contact network, to external perturbations. By mapping this
response to the spectral properties of the graph Laplacian corresponding to the
underlying contact network, we show that this naturally leads to spatial
localization of forces. We present numerical evidence for localization using
exact diagonalization studies of network Laplacians of soft disk packings.
Finally, we discuss the role of other constraints, such as torque balance, in
determining the stability of a granular packing to external perturbations.
