Planar networks and inverse boundary problems. Consider a planar network where you know only what's happening on "the boundary". It's natural to ask what information about the network we can recover just from the boundary information. We can get some information from the following. There exists an isomorphism from planar networks with k boundary sources and n-k boundary sinks to the totally nonnegative Grassmannian, which essentially sends a network to an encoding of its boundary information.