  In this paper it is shown that for any network there is a uniquely determined
network based on a structure tree that provides a convenient way of determining
a minimal cut separating a pair $s, t$ where each of $s, t$ is either a vertex
or an end in the original network. A Max-Flow Min-Cut Theorem is proved for any
network. In the case of a Cayley Graph for a finitely generated group the
theory provides another proof of Stallings' Theorem on the structure of groups
with more than one end.
