The Cloud computing paradigm entails a challenging networking scenario. Due to the economy of scale, the Cloud is mainly supported by Data Center infrastructures. Therefore, virtualized environment manageability, seamless migration of virtual machines, inter-domain communication issues and scalability problems are some of the main concerns that should be addressed. A recently proposed abstract model is used as a reference for the Cloud computing architecture. This paper introduces a network virtualization framework for the Cloud based on this model. Accordingly, a proper abstraction of network elements (vhost, vnode and vlink) is defined in order to virtualize the physical infrastructure. Moreover, a novel Layer 2 network virtualization approach based on a new MAC addressing scheme is presented: we propose to build locally administered MAC addresses that hold context information, such as virtual operator, domain, node and host identifiers. In addition, implementation details are suggested, describing how the Open Flow technology can lead to an implementation of the proposed approach.