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This technical note proposes a general class of distributed potential-based control laws with the connectivity preserving property for single-integrator agents. The potential functions are designed in such a way that when an edge in the information flow graph is about to lose connectivity, the gradient of the potential function lies in the direction of that edge, aiming to shrink it. The results are developed for a static information flow graph first, and then are extended to the case of dynamic edge addition. Connectivity preservation for problems involving static leaders is covered as well. The potential functions are chosen to be smooth, resulting in bounded control inputs. Other constraints may also be imposed on the potential functions to satisfy various design criteria such as consensus, containment, and formation convergence. The effectiveness of the proposed control strategy is illustrated by simulation for examples of consensus and containment.