For many islands, the answer to the question “why a locally, self-sustaining, and regenerative economy is needed?” is clear. The struggle often lies in the “how”. Here, we argue that tools from regenerative economics, which follow an island economy-as-an-organism analogy, offer valuable and complementary insights to socio-metabolic research. Indicators from flow-based and information-based ecological network analysis can quantify properties of an island's socio-economic metabolism (SEM) which are related to cycling, resilience, and degree of mutualism, among others. To illustrate the applicability of these methods, we select Samothraki in Greece as a case study. Results show that over the years the island became very efficient in streamlining imported resources, experiencing physical growth as indicated by a substantial increase in its total material throughput. This growth was attributed to a high degree of order (i.e., network efficiency) endowed by the constraining (ordered) part of the linear structure of the island's SEM. The disordered part of its SEM which is related to resilience, played a much smaller role which became progressively more important over the years, albeit to a limited degree. While the island exhibits an increasing trend in its robustness, its value over the years studied was well below what is typically observed for healthy natural ecosystems, and its current SEM has a very low ability to generate internal flow activity and cycling of resources per unit input. This limited robustness is due to the island's dependency on imports but also due to its linear SEM which had a very small number of feedback loops in its network. A scenario analysis showed that a reticulated network structure would theoretically endow the island with increased resilience, and hence robustness, by allowing for more internal resource flow activity to be circulated as regenerative re-investment. This article highlights that methods from regenerative economics can be used as diagnostic tools to assess and monitor the impact of strategies related to circular economy interventions on network properties, and to illuminate their effect on the regenerative potential of islands.