Many graph parameters are the optimal value of an objective function over selected subsets S of vertices with some constraint on how many selected neighbors vertices in S, and vertices not in S, can have. Classic examples are minimum dominating set and maximum independent set. We give a characterization of these graph parameters that unifies their definitions, facilitates their common algorithmic treatment and allows for their uniform complexity classi­fication. We investigate the computational complexity of problems admitting this characterization, identify classes of NP-complete problems and classes of problems solvable in polynomial time. We distinguish vertex subset properties admitting the characterization which have the feature that any such set in a graph has the same size.