Computer systems and methods using efficient module and backplane tiling to interconnect computer nodes via a Kautz-like digraph. A multinode computing system includes a large plurality of computing nodes interconnected via a Kautz topology having order O, diameter n, and degree k. The order equals (k+1)kn−1. The interconnections from a node x to a node y in the topology satisfy the relationship y=(−x*k−j) mod O, where 1≦j≦k, and the computing nodes are arranged onto a plurality of modules. Each module has an equal plurality of computing nodes on it. A majority of the inter-node connections are contained on the plurality of modules and a minority of the inter-node connections are inter-module connections. Inter-module connections are routed among modules in parallel on an inter-module connection plane.