Three-dimensional stacked memory is considered to be one of the innovative elements for the next-generation computing system, for it provides high bandwidth and energy efficiency. Particularly, packet routing ability of Hybrid Memory Cubes (HMCs) enables new interconnects for the memories, giving flexibility to its topological design space. Since memory-processor communication is latency-sensitive, our challenge is to alleviate latency of the memory interconnection network, which is subject to high overheads from hop-count increase. Interestingly, random network topologies are known to have remarkably low diameter that is even comparable to theoretical Moore graph. In this context, we first propose to exploit the random topologies for the memory networks. Second, we also propose several optimizations to leverage the random topologies to be further adaptive to the latency-sensitive memory-processor communication: communication path length based selection, deterministic minimal routing, and page-size granularity memory mapping. Finally, we present interesting results of our evaluation: the random networks with universal memory access outperformed non-random networks of which memory access was optimally localized.