Three-dimensional stack memory that provides both high-bandwidth access and large capacity is a promising technology for next-generation computer systems. While a large number of memory cubes increase the aggregate memory capacity, the communication latency and power consumption would become significant due to its low-radix large-diameter packet network. In this context, we propose a memory-cube network called Diagonal Memory Network (DMN). A diagonal network topology, its floor layout, and its lightweight router are designed for low-latency and low-voltage memory-read communication. Our evaluation results show that a DMN router decreases 31% of the hardware resources than a conventional virtual-channel router. The DMN router reduces 13% and 67% energy consumption to transit a packet along with the original datapath and bypassing datapath, respectively.