Wireless sensor network design is critical and resource allocation is a major problem which remains to be solved satisfactorily. The discrete nature of sensor networks renders the existing skeleton extraction algorithms inapplicable. 3D topologies of sensor networks for practical scenarios are considered in this paper and the research carried out in the field of skeleton extraction for three dimensional wireless sensor networks. The skeletal links are identified on the basis of a novel energy utilization function computed for the transmissions carried out through the network. The frequency based weight assignment function is introduced to identify the root node of the skeleton graph. Topological clustering is used to construct the layered topological sets to preserve the nature of the topology in the skeleton graph. The skeleton graph is constructed with the help of the layered topological sets and the experimental results prove the robustness of the skeleton extraction algorithm introduced. Provisioning of additional resources to skeletal nodes enhances the sensor network performance by 20% as proved by the results presented in this paper.