  We consider the problem of graph matchability in non-identically distributed
networks. In a general class of edge-independent networks, we demonstrate that
graph matchability can be lost with high probability when matching the networks
directly. We further demonstrate that under mild model assumptions,
matchability is almost perfectly recovered by centering the networks using
Universal Singular Value Thresholding before matching. These theoretical
results are then demonstrated in both real and synthetic simulation settings.
We also recover analogous core-matchability results in a very general core-junk
network model, wherein some vertices do not correspond between the graph pair.
