This paper proposes a null-space-based behavior controller for spacecraft formation flying (SFF), considering the limitations of communication range. The multiple spacecraft network is represented as a distance-induced proximity graph. Two distinctive behaviors are designed to address the SFF control problem: a connectivity preservation behavior, and a formation configuration behavior. The connectivity preservation behavior aims to ensure connectivity preservation of the communication graph, while the formation behavior achieves the desired formation of all spacecraft. The least-square method is used to compute the desired velocities of the two behaviors. The desired trajectories for all spacecraft are generated by projecting the formation behavior velocity to the null space of the connectivity preservation behavior velocity to remove conflicting velocity components. Furthermore, we propose a distributed controller to accurately track the desired trajectories. Numerical simulations demonstrate that the proposed controller is capable of achieving the desired formation while preserving the network’s connectivity.