title: Are there more than one families of flow networks with non unique minimum cuts?
body: <p>I'm wondering if the only way to construct a flow network with several minimum cuts is to include at least 2 consecutive edges with the same capacity, such that any one of them will be in the minimum cut edge set.</p>
  
  <p>It's clear that the simplest kind of such a network is a path with all edges of the same capacity, so in that case any one of |E| edges can be the edge separating S from T.</p>
  
  <p>Is this the only way to construct such networks? If so, how can I prove it?</p>