Quantum key distribution constellation is the key to achieve global quantum networking. However, the networking feasibility of quantum constellation that combines satellite-to-ground accesses selection and inter-satellite routing is faced with a lack of research. In this paper, satellite-to-ground accesses selection is modeled as problems to find the longest paths in directed acyclic graphs. The inter-satellite routing is interpreted as problems to find a maximum flow in graph theory. As far as we know, the above problems are initially understood from the perspective of graph theory. Corresponding algorithms to solve the problems are provided. Although the classical discrete variable quantum key distribution protocol, i.e., BB84 protocol, is applied in simulation, the methods proposed in our paper can also be used to solve other secure key distributions. The simulation results of a low-Earth-orbit constellation scenario show that the Sun is the leading factor in restricting the networking. Due to the solar influence, inter-planar links block the network periodically and, thus, the inter-continental delivery of keys is restricted significantly.