  Real world network datasets often contain a wealth of complex topological
information. In the face of these data, researchers often employ methods to
extract reduced networks containing the most important structures or pathways,
sometimes known as `skeletons' or `backbones'. Numerous such methods have been
developed. Yet data are often noisy or incomplete, with unknown numbers of
missing or spurious links. Relatively little effort has gone into understanding
how salient network extraction methods perform in the face of noisy or
incomplete networks. We study this problem by comparing how the salient
features extracted by two popular methods change when networks are perturbed,
either by deleting nodes or links, or by randomly rewiring links. Our results
indicate that simple, global statistics for skeletons can be accurately
inferred even for noisy and incomplete network data, but it is crucial to have
complete, reliable data to use the exact topologies of skeletons or backbones.
These results also help us understand how skeletons respond to damage to the
network itself, as in an attack scenario.
