Re-Gauging Groupoid, non--commutative 2--cocycles and wire networks

We study a class of graph Hamiltonians given by groupoid representations to which we can
associate (non)-commutative geometries. By  selecting  gauging  data,  these  geometries 
are  realized  by  matrices. We describe the changes in gauge via the action of a re-gauging
groupoid. It acts via a second set of matrices that give rise to a noncommutative 2-cocycle
and hence to a groupoid extension (gerbe).  This is applicable to concrete cases, where we
find  extended graph symmetries determined by the above construction. These give rise to
projective representations,  iso-typical decompositions and super-selection rules, thus
realizing the higher structure inside materials.