Decomposing is one way to gain efficiency when dealing with large scale systems. In addition, the breakdown into subsystems may be mandatory to reflect some geographic or confidentiality constraints. In this context, the selection of diagnostic tests must comply with decomposition and it is desired to minimize the number of subsystem intercon-nections while still guaranteeing maximal diagnosability. On the other hand, it should be noticed that there is often some flexibility in the way to decompose a system. By placing itself in the context of structural analysis, this paper provides a solution to the double overlinked problem of choosing the decomposition of the system by leveraging existing flexibility and of selecting the set of diagnostic tests so as to minimize subsystem interconnections while maximizing diagnosability .