Peer-to-peer (P2P) architectures have recently become a popular design choice for building scalable Networked Virtual Environments (NVEs). In P2P-based NVEs, system and data management is distributed among all participating users. Towards this end, a Delaunay Triangulation can be used to provide connectivity between the different NVE users depending on their positions in the virtual world. However, a Delaunay Triangulation clearly suffers from high maintenance cost as it is subject to high connection change rate due to continuous users' movement. In this paper, we propose a new triangulation algorithm that provides network connectivity to support P2P NVEs while dramatically decreasing maintenance overhead by reducing the number of connection changes due to users' insertion and movement. Performance evaluations show that our solution drastically reduces overlay maintenance cost in highly dynamic NVEs. More importantly, and beyond its quantitative advantages, this work questions the well accepted Delaunay Triangulation as a reference means for providing connectivity in NVEs, and paves the way for more research towards more practical alternatives for NVE applications.