# Flows on hypergraphs

We consider the capacitated minimum cost flow problem on directed
hypergraphs. We define spanning hypertrees so generalizing the spanning
tree of a standard graph, and show that, like in the standard and in the
generalized minimum cost flow problems, a correspondence exists between
bases and spanning hypertrees. Then, we show that, like for the
network simplex algorithms for the standard and for the generalized
minimum cost flow problems, most of the computations performed at each
pivot operation have direct hypergraph interpretations.