A rooted network consists of a connected, locally finite graph G , equipped with edge conductances and a distinguished vertex o . A nonnegative function on the vertices of G which vanishes at o , has Laplacian 1 at o , and is harmonic at all other vertices is called a potential. We prove that every infinite recurrent rooted network admits a potential tending to infinity. This is an analogue of classical theorems due to Evans and Nakai in the settings of Euclidean domains and Riemannian surfaces.