Pruned Three-Dimensional Toroidal Networks

Using a unified framework, we show that a pruned 3D torus can be. explicitly specified by its pruning direction along which the links are uniformly removed from a complete 3D torus. The resulting networks, that offer the advantages of lower node degree and simpler layout, are inherently node-symmetric and maintain the same diameter as the original torus. It nuns out that the simplest pruning scheme is also best in preserving regularity, symmetry, and performance properties of the torus.