Connectivity refers to the problem that the initial information flow between a group of agents is required to be preserved for all time in order to achieve a given set of system-level objectives. This technical note focuses on a new connectivity control architecture for networked multiagent systems based on hybrid protocols. Specifically, for a group of agents subject to Delta-disk proximity graphs, we consider the consensus problem while preserving connectedness with a priori given bounds on the control inputs. The bounds on the control inputs are shown neither to depend on potential functions nor system states. Instead the bounds are user selected continuous functions. Using the proposed framework, we show that the maximum distance among neighboring agents strictly decreases, and hence, the connectivity problem is solved while satisfying the consensus objective. Illustrative numerical examples are provided to demonstrate the efficacy of the proposed bounded hybrid connectivity control architecture.