Low communication latency becomes a main concern in highly parallel computers and supercomputers that reach millions of processing cores. Random network topologies are better suited to achieve low average shortest path length and low diameter in terms of the hop counts between nodes. However, random topologies lead to two problems: (1) increased aggregate cable length on a machine room floor that would become dominant for communication latency in next-generation custom supercomputers, and (2) high routing complexity that typically requires a routing table at each node (e.g., topology-agnostic deadlock-free routing). In this context, we first propose low-degree non-random topologies that exploit the small-world effect, which has been well modeled by some random network models. Our main idea is to carefully design a set of various-length shortcuts that keep the diameter small while maintaining a short cable length for economical passive electric cables. We also propose custom routing that uses the regularity of the various-length shortcuts. Our experimental graph analyses show that our proposed topology has low diameter and low average shortest path length, which are considerably better than those of the counterpart 3-D torus and are near to those of a random topology with the same average degree. The proposed topology has average cable length drastically shorter than that of the counterpart random topology, which leads to low cost of interconnection networks. Our custom routing takes non-minimal paths to provide lower zero-load latency than the minimal custom routings on different counterpart topologies. Our discrete-event simulation results using SimGrid show that our proposed topology is suitable for applications that have irregular communication patterns or non-nearest neighbor collective communication patterns.