This article investigates a correlation between the thermal efficiency of ideal power cycles and a structural measure of the degree of interactions in networks known as cyclicity. Efficient design of networks that reuse materials and energy motivates the work. Corporate take-back plans, multi-company industrial symbioses and public recycling programs recover products, components and materials using partially closed loop networks. As resources become scarcer and more expensive, the prevalence of these networks is likely to increase, and the importance of designing efficient networks grows. Multiple structural and material flow metrics that one might use to aid network design exist. One novel approach to network design involves patterning industrial networks on ecological ones. This latter idea lays at the heart of industrial symbiosis efforts. However, neither the materials metric approach nor the bioinspired ecological patterns approach stands upon a strong theoretical base. As a test of both approaches, this work uses a structural cycling metric, cyclicity, previously used to quantify patterns in ecosystems, to quantify energy flow in ideal thermodynamic cycles. The objective is not to learn about thermodynamic cycles. Rather, the intent of the comparison is to reveal whether trends in network structure as given by cyclicity relate to the fundamental laws of thermodynamics. Familiar ideal power cycles are first redrawn as energy flow networks. Cyclicity values are then calculated for these networks. A comparison shows that thermal efficiency increases with increasing cyclicity for fixed source and sink temperatures within a cycle. This results from the practice of adding cyclical energy paths (i.e. a regenerator) to an ideal power cycle, to increase thermal efficiency. The remainder of the article comments on the potential ramifications of this finding for the design of cycling industrial networks.