The Astrometry.net system sees a huge amount of heterogeneous data, from wide-field snapshots to very narrow-field professional images, to all-sky fish-eye cloud cameras. Any image that is successfully calibrated by the system has been matched to a dataabase of four-star figures (quads) and then verified probabilistically using all the stars in the image and in the USNO-B1.0 Catalog in that region (down to some effective magnitude cut). Of course the quad index and the catalog are both suspect, in the sense that they both contain stars that are either non-existent or else have wrong properties. The amusing thing is that we could construct a graph in which the nodes are catalog entries and the edges are instances in which pairs of stars have been observed in the same image.
This graph would contain an enormous amount of information about the sky. For example, the network could be used to create a brightness ordering of stars on the sky, which would be amusing. But more importantly for us, the covisibility information would tell us what pairs of stars we should be using together in quads, and what pairs we shouldn't. That analysis would take account not just of their relative magnitudes, but also the typical angular scales of the images in which stars of that magnitude tend to be detected. It would also identify (as nodes with few or no edges) catalog entries that don't correspond to stars, and groups of catalog entries that are created by certain kinds of artifacts (like handwriting on the photographic plates, etc) that generate certain kinds of false positive matches in our calibrations.
This idea was first suggested to Dustin Lang (CMU) and me by Sven Dickinson (Toronto) at Lang's PhD defense. Advanced goal: Make a directed graph, with arrows going from brighter to fainter. Then use statistics of edge directions to do a better job on brightness ranking and also classify images by bandpass, etc. Even more advanced goal: Evolve away from star catalogs to covisible-asterism catalogs! At the bright end (first or second magnitude), we might be able to propose a better set of constellations.