Virtual networks are sets of virtual devices that are interconnected through a physical network to provide services to end users. These services are usually heterogeneous (VOIP, VoD, streaming, etc.), exploit various amounts of resources (bandwidth, computing power, servers, etc.), and have topologies different from those of the substrate network. These variations in requirements are traditionally known as the architectural flexibility of virtual networks. Each virtual service is provided through a server called a virtual service resource. When a virtual service resource can no longer provide a good quality of service to end users due to the traffic variation generated by their mobility, two approaches are commonly implemented: provisioning the virtual network with resources or replacing the virtual service resource by migrating the service to another node that offers the most suitable amount of resource to satisfy the quality of service (QoS). In this paper, we propose a flow splitting-based dynamic virtual service resource replacement approach that allows for virtual service replacement across multiple virtual paths. Our approach is based on a graph topology that differs from those in the literature, which are based on tree topologies. The simulations performed in this study show that our approach significantly reduces the virtual service resource replacement time compared to other approaches.