SIN is constructed to support real-time data acquisition, massive data transmission and processing, and systematized information services. Different from static networks, both the network topologies and the available network resources are dynamic in SIN. However, the existing networking technologies treat SIN as segmented static networks, and ignore the relationship among different segmented subnetworks, which results in low resource utilization and poor transmission QoS. This article exploits the time-varying graph theory to characterize and allocate the dynamic resources of SIN. We first introduce the overall SIN architecture, and discuss its key technologies in terms of network slicing and dynamic routing. Then, we construct a novel STAG to precisely depict the multi-dimensional time-varying resources and reveal their connection relationships in SIN. With STAG, we propose the dynamic network slicing strategy to build the dedicated network slices for different services, and design the intra-slice routing scheme to guarantee the service transmission QoS. Simulation results demonstrate our methods can complete more space missions with higher resource utilization. Finally, we discuss the promising future of the time-varying graph theory.