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Memory bandwidth has been one of the most critical system performance bottlenecks. As a result, the HMC (Hybrid Memory Cube) has recently been proposed to improve DRAM bandwidth as well as energy efficiency. In this paper, we explore different system interconnect designs with HMCs. We show that processor-centric network architectures cannot fully utilize processor bandwidth across different traffic patterns. Thus, we propose a memory-centric network in which all processor channels are connected to HMCs and not to any other processors as all communication between processors goes through intermediate HMCs. Since there are multiple HMCs per processor, we propose a distributor-based network to reduce the network diameter and achieve lower latency while properly distributing the bandwidth across different routers and providing path diversity. Memory-centric networks lead to some challenges including higher processor-to-processor latency and the need to properly exploit the path diversity. We propose a pass-through microarchitecture, which, in combination with the proper intra-HMC organization, reduces the zero-load latency while exploiting adaptive (and non-minimal) routing to load-balance across different channels. Our results show that memory-centric networks can efficiently utilize processor bandwidth for different traffic patterns and achieve higher performance by providing higher memory bandwidth and lower latency.