Effective resistance ($R_{\mathrm{eff}}(a,z)$)

The effective resistance between vertices $a$ and $z$ is the voltage difference required to send one unit of current from $a$ to $z$.

Thomson principle says that effective resistance is the minimum energy among unit flows from $a$ to $z$:

If ${\Pi }_1,\dots ,{\Pi }_m$ are pairwise edge-disjoint cutsets separating $a$ from $z$ in an electrical network, then

For a random walk on a finite electrical network,