A hierarchy of unidirectional rings has been used successfully in distributed shared-memory multiprocessors. The fixed cluster size of the hierarchy prevents full exploitation of communication locality. The bidirectional ring is presented as an alternative to the hierarchy. Its relative performance is evaluated for a variety of memory access patterns and network sizes. It gives superior performance for low communication locality and for large networks. Another useful feature of the bidirectional ring is that the network load tends to be balanced over the two constituent unidirectional rings. These features make the bidirectional ring an attractive possibility as a network structure for scalable NUMA multiprocessors.