Considering its relatively low circularity rate (11.8% in 2019), the EU set several waste management targets as part of its roadmap to a circular economy yet the decision about which transition pathway to follow is not trivial. The maximization of circularity in human made systems is intended to function as a catalyst for this transition albeit at the risk of establishing fragile techno-economic systems. To provide insights for a balanced transition to a circular economy its link with the ecological concepts of “resilience” and “robustness” is illuminated by assessing the theoretical robustness of the material and energy flow networks of the EU27 countries between 2010-2018 using Eurostat data. Results show that despite the high degrees of order (efficiencies) which all European countries developed over the years studied, none of them achieved near-maximum robustness. The identified relationships between the average circularity rate and the average energy efficiency with the theoretical robustness of these material and energy flow networks (for the years studied), respectively, suggest that ascendency analysis is a credible tool for supporting policy making. Both on a national and on a local level for developing circular and robust urban waste management systems given data availability. The contribution to the underlying theory of ascendency analysis is the introduction of the concepts of “technological boundaries” and “windows of efficiency” of these human-made networks which are juxtaposed with the “window of vitality” that is often used to describe healthy natural ecosystems. Finally, the limitations of ascendency analysis and directions for future research are presented.