Network reconstruction is a useful tool in a number of areas reaching from medical imaging to oil exploration.
How can one reconstruct the internal structure of an object by external measurements? Electrical impedance tomography (EIT) attempts reconstruction using resistance measurements between pairs of exterior points. When the hidden structure is a planar network, the reconstruction problem has a long history and was studied by Colin de Verdière, Curtis, Ingerman, Morrow and others. Kenyon and Wilson’s work gives an efficient algorithm for exact reconstruction and continues to study the space of all possible external responses for planar networks.