R_eff formula
R_eff(u,v) = sum over spanning trees containing edge (u,v)-shortcut vs not, weighted appropriately. Kirchhoff's laws.
Advertisement
Commute time
Expected round-trip time of random walk from u to v = 2|E| · R_eff(u,v).
Advertisement
Spielman-Srivastava
Effective resistances used in graph sparsification. Preserve cuts approximately with much fewer edges.
Computation
Solve L x = e_u - e_v where L = Laplacian. Effective resistance = (e_u - e_v)^T x.