Fearful symmetry in system structures

Discusses the relationship between the level of symmetry in a system structure and loss of controllability. For a system consisting of a large number of modules, symmetrical structure is considered as the identity of modules and their interconnections. We especially deal with three basic structures: ring-type, bus-type and star-type structures. If the entire system becomes uncontrollable because of failures in a set of k submodules, this number k indicates the level of fault tolerance. On the other hand, the level of symmetry is evaluated by the number of transformations that keep the structure invariant. Through evaluation of the fault tolerance of the three basic structures, we consider the relationship between lowering the level of symmetry and the loss of controllability because of failures