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Control of mobile networks raises fundamental and novel problems in controlling the structure of the resulting dynamic graphs. In particular, in applications involving mobile sensor networks and multiagent systems, a great new challenge is the development of distributed motion algorithms that guarantee connectivity of the overall network. Motivated by the inherently discrete nature of graphs as combinatorial objects, we address this challenge using a key control decomposition. First, connectivity control of the network structure is performed in the discrete space of graphs and relies on local estimates of the network topology used, along with algebraic graph theory, to verify link deletions with respect to connectivity. Tie breaking, when multiple such link deletions can violate connectivity, is achieved by means of gossip algorithms and distributed market-based control. Second, motion control is performed in the continuous configuration space, where nearest-neighbor potential fields are used to maintain existing links in the network. Integration of the earlier controllers results in a distributed, multiagent, hybrid system, for which we show that the resulting motion always ensures connectivity of the network, while it reconfigures toward certain secondary objectives. Our approach can also account for communication time delays as well as collision avoidance and is illustrated in nontrivial computer simulations.