As the scales of parallel applications and platforms increase the negative impact of communication latencies on performance becomes large. Random network topologies can be used to achieve low hop counts between nodes and thus low latency. However, random topologies lead to increased aggregate cable length and cable packaging complexity on a machine room floor. In this work we propose two new methods for generating random topologies and their physical layout on a floorplan: randomize links after optimizing the physical layout, or optimize the layout after randomizing links. The first method randomly swaps link endpoints for a given non-random topology for which a good physical layout is known. The resulting topology has the same cable length and cable packaging as the original topology, but achieves lower communication latency. The second method creates a random topology with random links picked so that they will not lead to a long physical cable length, and then solves a constrained optimization problem to compute a physical layout that minimizes aggregate cable length. We quantitatively compare these two methods using both graph analysis and cycle-accurate network simulation, including comparisons with previously proposed random topologies and non-random topologies.