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Sensor and network topologies of rigid formations with distance information between mobile autonomous agents are considered. An approach based on rigidity for creating such topologies was suggested in our previous work. Here, we first illustrate some potential scenarios on formations that require unambiguity in the knowledge of distances between every pair of agents in a formation. Then, we show how a stronger type of rigidity, namely global rigidity, plays a role in creating such unambiguous formations. We draw out and summarize some relevant results from the related mathematical theory of global rigidity; and present some new results on globally rigid formations.