Abstract The brain’s connectivity is locally dense and globally sparse, forming a small-world graph—a principle prevalent in the evolution of various species, suggesting a universal solution for efficient information routing. However, current artificial neural network circuit architectures do not fully embrace small-world neural network models. Here, we present the neuromorphic Mosaic: a non-von Neumann systolic architecture employing distributed memristors for in-memory computing and in-memory routing, efficiently implementing small-world graph topologies for Spiking Neural Networks (SNNs). We’ve designed, fabricated, and experimentally demonstrated the Mosaic’s building blocks, using integrated memristors with 130 nm CMOS technology. We show that thanks to enforcing locality in the connectivity, routing efficiency of Mosaic is at least one order of magnitude higher than other SNN hardware platforms. This is while Mosaic achieves a competitive accuracy in a variety of edge benchmarks. Mosaic offers a scalable approach for edge systems based on distributed spike-based computing and in-memory routing.