Network virtualization promises a future Internet that inherently supports technological advancement. Extensive literature studies have been devoted to the fundamental problem, namely Virtual Network Embedding (VNE) in network virtualization, which instantiates the virtual network request (VNR) customized by the Service Provider (SP) to the substrate network managed by the Infrastructure Provider (InP). Different from prior studies, in this work, we identify security issues that are associated with the VNE process, which is further incorporated and addressed in the Security-Aware Virtual Network Embedding (SVNE) problem. Our efforts aim to fill the major gaps in the literature studies on the VNE problem: first, we assess the security issues in VNE at node, topology and network levels and explicitly define open, flexible and fine-granular security plans that can address above issues; second, we present and evaluate a comprehensive framework that implements the proposed security plans and address the SVNE problem.