Router virtualization is becoming more common as a method that uses network (NW) equipment effectively and robustly similar to server virtualization. Edge routers, which are gateways of core NWs, should be virtualized because they have many functions and resources just as servers do. To virtualize edge routers, a metro NW, which is a wide area layer-2 NW connecting each user's residential gateway to edge routers, must trace dynamic edge router re-allocation by changing the route of each Ethernet flow. Therefore, we propose a scalable centralized control architecture of a virtual layer-2 switch on a metro NW to trace virtual router re-allocation and use metro NW equipment effectively. The proposed scalable control architecture improves the centralized route control performance by processing in parallel on a flow-by-flow basis taking into account route information even in the worst case where edge routers fail. In addition, the architecture can equalize the load among parallel processes dynamically by using two proposed load re-allocation methods to increase the route control performance stably while minimizing the amount of resources for the control. We evaluate the scalability of the proposed architecture through theoretical analysis and experiments on a prototype and show that the proposed architecture increases the number of flows accommodated in a metro NW. Moreover, we evaluate the load re-allocation methods through simulation and show that they can evenly distribute the load among parallel processes. Finally, we show that the proposed architecture can be applied to not only large-scale metro NWs but also to data center NWs, which have recently become an important type of large-scale layer-2 NW.