  Generalized integer splines on a graph $G$ with integer edge weights are
integer vertex labelings such that if two vertices share an edge in $G$, the
vertex labels are congruent modulo the edge weight. We introduce collapsing
operations that reduce any simple graph to a single vertex, carrying with it
the edge weight information. This corresponds to a sequence of surjective maps
between the associated spline modules, leading to an explicit construction of a
module basis in terms of the edge weights.
