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In this paper, we investigate the nonlinear observability properties of bearing-only cooperative localization. We establish a link between observability and a graph that represents measurements and communication between the robots. It is shown that graph theoretic properties like the connectivity and the existence of a path between two nodes can be used to explain the observability of the system. We obtain the maximum rank of the observability matrix without global information and derive conditions under which the maximum rank can be achieved. Furthermore, we show that for complete observability, all of the nodes in the graph must have a path to at least two different landmarks of known location.