Passive, single-hop interconnections among N stations, each with several transmitters and receivers, provide a communication path between any two stations using one of the transmitters and receivers of each station. Such interconnections which permit a polylogarithmic (in N) number of concurrent transmissions using only spatial separation have recently been described. This paper shows how to optamally compose the layouts of any two fiber-optic single-hop interconnections to form that of the “product”interconnection. It presents a general method for optimally transforming a layered directed acyclac graph so as to balance the indegree and outdegree of intermediate vertices without altering (source, destination) connectivity.