Alfaro's conjecture on shortest directed networks

Let $A$ be the set of sources and $B$ the set of sinks in the Euclidean plane. A shortest $(A,B)$-network is a directed network of minimum length connecting the prescribed sources and sinks.

Alfaro's conjecture. If $A=B$, then a shortest $(A,B)$-network has no Steiner points and is a union of cycles.

This conjecture concerns the local and global structure of shortest directed networks when the source and sink sets coincide. It is presented as an attractive conjecture; no resolution is given here.