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In this paper, distributed control algorithms and event-based communication strategies are developed to achieve formation control with connectivity preservation among a group of networked mobile agents. Each agent transmits its current state information to its neighbors when its own triggering condition is satisfied or when the time elapsed from its last event time is going to exceed the agent's maximal admissible inter-event time. We have focused our studies on two types of systems' dynamics: agents that can be modeled as first order integrators and agents that can be modeled as double integrators. Simulations are provided to validate our results.