The design and operation of quantum networks are both decisive in the current push towards a global quantum internet. Although space-enabled quantum connectivity has already been identified as a beneficial candidate for long-range quantum channels for over two decades, the architecture of a hybrid space–ground network is still a work in progress. Here, we propose an analysis of such a network based on a best-path approach, where either fiber- or satellite-based elementary links can be concatenated to form a repeater chain. The network consisting of quantum information processing nodes, equipped with both ground and space connections, is mapped into a graph structure, where edge weights represent the achievable secret key rates, chosen as the figure of merit for the network analysis. A weight minimization algorithm allows for identifying the best path dynamically, i.e., as the weather conditions, stray light radiance, and satellite orbital position change. From the results, we conclude that satellite links will play a significant role in the future large-scale quantum internet, in particular when node distances exceed 500 km, and both a constellation of satellites—spanning 20 or more satellites—and significant advances in filtering technology are required to achieve continuous coverage.