Wireless sensor network design is critical and resource allocation is a major problem yet to be solved satisfactorily. The discrete nature of sensor networks renders existing skeleton extraction algorithms inapplicable. This paper considers 3D sensor network topologies and proposes a novel skeleton extraction method. Skeletal links are identified using an energy utilization function. A frequency-based weight assignment function identifies the root node. Topological clustering constructs layered topological sets to build the skeleton graph. Results indicate robustness of the method, and providing additional resources to skeletal nodes enhances network performance by 20%. © 2015 Elsevier B.V., All rights reserved.