Context-aware applications are intrinsically complex to develop and maintain. Many frameworks were proposed aiming to support the development of these applications by providing developers with tools and design guidelines. However, these proposals constrain applications to share specific semantic for the modeled context data. This constraint may also be propagated to context reasoning which is the feature that enables application's adaptive behavior. This paper proposes a new context management framework that relies on graph-based context modeling. This approach takes into account context presentation, while it gives the freedom to each application to define its own semantic for the manipulated context. The implementation of this framework and its evaluation in a case study shows the benefits, in terms of flexibility, for the development of context-aware applications