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In this paper, we propose an unorthodox topology for datacenters that eliminates all hierarchical switches in favor of connecting nodes at random according to a small-world-inspired distribution. Specifically, we examine topologies where the underlying nodes are connected at the small scale in a regular pattern, such as a ring, torus or cube, such that every node can route efficiently to nodes in its immediate vicinity, and amended by the addition of random links to nodes throughout the datacenter, such that a greedy algorithm can route packets to far away locations efficiently. Coupled with geographical address assignment, the resulting network can provide content routing in addition to traditional routing, and thus efficiently implement key-value stores. The irregular but self-similar nature of the network facilitates constructing large networks easily using prewired, commodity racks. We show that Small-World Datacenters can achieve higher bandwidth and fault tolerance compared to both conventional hierarchical datacenters as well as the recently proposed CamCube topology. Coupled with hardware acceleration for packet switching, small-world datacenters can achieve an order of magnitude higher bandwidth than a conventional datacenter, depending on the network traffic.