In this paper we analyze the relationship between scalability, minimality and rigidity, and its application to cooperative control. As a case study, we address the problem of multi-agent formation control by proposing a distributed control strategy that stabilizes a formation described with bearing (direction) constraints, and that only requires bearing measurements and parallel rigidity of the interaction graph. We also consider the possibility of having different graphs modeling the interaction network in order to explicitly take into account the conceptual difference between sensing, communication, control, and parameters stored in the network. We then show how the information can be ‘moved’ from a graph to another making use of decentralized estimation, provided the parallel rigidity property. Finally we present simulative examples in order to show the validity of the theoretical analysis in some illustrative cases.