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We present an approach for reducing redundancies in the design of reconfigurable antenna structures using graph models. The basics of graph models, their rules, and how they can be applied in the design of switch-based reconfigurable antennas are introduced. Based on these rules, a methodology is developed and formulated to reduce the number of switches and parts in the antenna structure, without sacrificing the desired antenna functions. This approach not only optimizes the overall structure of the antenna but it also reduces cost and overall losses. Several examples are presented and discussed to demonstrate the validity of this new approach through simulations and measurements that present good agreement.