  We investigate the problem of designing a minimum cost flow network
interconnecting n sources and a single sink, each with known locations and
flows. The network may contain other unprescribed nodes, known as Steiner
points. For concave increasing cost functions, a minimum cost network of this
sort has a tree topology, and hence can be called a Minimum Gilbert
Arborescence (MGA). We characterise the local topological structure of Steiner
points in MGAs for linear cost functions. This problem has applications to the
design of drains, gas pipelines and underground mine access.
