To absorb the traffic uncertainty and map the service network to the physical network of the data center flexibly and efficiently, this paper studies the dynamic virtual data center mapping problem in an elastic optical data center network, where the service model is a hose model. First, the mapping model of a flexible virtual machine is established in an elastic optical data center network, and then the virtual machine placement algorithm based on virtual topology (VT-VMPA) is proposed. The VT-VMPA first converts the hose model into the pipe model before looking for the core virtual machine using the maximization of traffic volume as a guideline. Then, in descending order of service volume, the virtual machines that adhere to the resource constraints and are linked to the core virtual machines are combined into clusters. The communication bandwidth requirement is reduced after the cluster is mapped to the server. Finally, the cluster sets are mapped to the servers and virtual links between clusters are mapped to optical paths of the elastic optical data center network according to hop distance adaptive and shortest path principles. In comparison to previous methods, the proposed algorithm has decreased blocking rate by 27%, increased average time revenue by 117%, and decreased average bandwidth usage by 21%. It demonstrates that this method may increase network mapping speed while consuming fewer network traffic.