Eigensystems of Electrical Networks

The eigenvectors of an electrical network are voltages that, when placed at the boundary vertices, produce boundary currents that are a scalar multiple of the boundary voltage. The objective of this research is to gain information about a given electrical network using eigensystems. In particular, eigensystems are useful when an edges or multiple edges in a network have zero resistance or infinite resistance. Using the eigensystems of an electrical network which are based on the resistance and connectivity of edges in the network, one can determine the location of a dysfunctional resistor in a network or determine the expected number of dysfunctional resistors.