A defining feature of a Digital Twin (DT) is its level of "entanglement": the degree of strength to which the twin is interconnected with its physical counterpart. Despite its importance, this characteristic has not been yet fully investigated, and its impact on applications' design is underestimated. In this paper, we define the concept of "Degree of Entanglement" (DoE), which provides an operational model for assessing the strength of the entanglement between a DT and its physical counterpart. We also propose an interoperable representation of DoE within the Web of Things (WoT) framework, which enables DT-driven applications to dynamically adapt to changes in the physical environment. We evaluate our proposal using two realistic use cases, demonstrating the practical utility of DoE in supporting, for instance, context-awareness decisions and adaptiveness.