  Recent milestone experiments establishing satellite-to-ground quantum
communication are paving the way for the development of the quantum internet, a
network interconnected by quantum channels. Here we employ network theory to
study the properties of the photonic networks that can be generated by
satellite-based quantum communication and compare it with the optical-fiber
counterpart. We predict that satellites can generate small-world networks,
implying that physically distant nodes are actually near from a network
perspective. We also analyse the connectivity properties of the network and
show, in particular, that they are robust against random failures. This puts
satellite-based quantum communication as the most promising technology to
distribute entanglement across large distances in quantum networks of growing
size and complexity.
