Data centers are fundamental facilities that support high-performance computing and large-scale data processing. To guarantee that a data center can provide excellent properties of expanding and routing, the interconnection network of a data center should be designed elaborately. Herein, we propose a novel structure for the interconnection network of data centers that can be expanded with a variable coefficient, also known as a variable expanding structure (VES). A VES is designed in a hierarchical manner and built iteratively. A VES can include hundreds of thousands and millions of servers with only a few layers. Meanwhile, a VES has an extremely short diameter, which implies better performance on routing between every pair of servers. Furthermore, we design an address space for the servers and switches in a VES. In addition, we propose a construction algorithm and routing algorithm associated with the address space. The results and analysis of simulations verify that the expanding rate of a VES depends on three factors: n, m, and k where the n is the number of ports on a switch, the m is the expanding speed and the k is the number of layers. However, the factor m yields the optimal effect. Hence, a VES can be designed with factor m to achieve the expected expanding rate and server scale based on the initial planning objectives.