I do understand that there is a big analogy between graphs and electrical circuits, so that nodes are being treated as voltage sources and edges as resistor, where each resistor has a conductance that is denoted as the weight of an edge in a graph. I also know that spectral graph theory uses eigenvalues and eigenvectors in order to learn more about graph properties. The thing I am missing and cannot understand very well is that how the eigenvalues can be related to voltages. In other words, what is the relationship between voltages of nodes in electrical circuits and eigenvalues?
Thanks!
