Higher radix networks, such as high-dimensional tori and multi-level directly connected networks, are being used for supercomputers as they become larger but need lower diameter. These networks have more resources (e.g. links) in order to provide good performance for a range of applications. We observe that a sizeable fraction of the links in the interconnect are never used or underutilized during execution of common parallel applications. Thus, in order to save power, we propose addition of hardware support for on/off control of links in software and their management using adaptive runtime systems. We study the effectiveness of our approach using real applications (NAMD, MILC), and application benchmarks (NAS Parallel Benchmarks, Jacobi). They are simulated on representative topologies such as 6-D Torus and Dragonfly (e.g. IBM PERCS, Cray Aries). For common applications, our approach can save up to 16% of total machine's power and energy, without any performance penalty.