The problem of process structure driven distributed controller structure selection is addressed in this paper using graph-theoretical methods. The process structure is represented by a directed graph describing the variable structure of the lumped non-linear state space model of the process system. Weights can also be associated to the edges of the structure graph and a one-to-one correspondence can be made between a linearized state space model and the weighted digraph. Two types of distributed controller structures: the stabilizing and disturbance rejective ones are investigated. The optimal stabilizing structures minimize the coupling and the optimal disturbance rejective ones have minimal interaction defined in both of the unweighted and weighted cases. For single input single output stabilizing and disturbance rejective controllers the formulated optimal controller structure selection problem is shown to be solvable in polynomial time. Efficient algorithms for determining the optimal stabilizing controller structure are proposed, based on the algorithms solving the well known Maximum Weighted Matching problem. The concepts and methods are illustrated on a simple example and on the Tennessee Eastman benchmark problem.