In tensegrity networks, we are given a realization of a graph and we ask the question if the realization is rigid with inequality constraints on the length of edges. We propose an analog for disk packings: Given a disk packing that realizes a graph, we want to know if the packing is rigid with inequality constraints on the radii. We show that a result similar to that of Roth & Whiteley's holds in this type of rigidity problem in a very intuitive way. We can define the uniformity of a packing as the ratio of its minimal radius to its maximal radius.We show the global rigidity for disk packings would help us identify the second most uniform triangulated packing of the plane (with the most being hexagonal packing, obviously), which would then be a good estimate of how uniform a packing can be in order to beat the density of hexagonal packing.