On the applicability of Weyuker Property 9 to object-oriented structural inheritance complexity metrics

In the metric suite for object oriented design put forward by S.R. Chidamber and C.F. Kemerer (1994), it is observed that E. Weyuker's (1988) Property 9 is not satisfied by any of the structural inheritance complexity metrics. The same is also observed for candidate structural inheritance complexity metrics proposed by A.F. Brito and R. Carapuca (1994). The authors formally show that particular classes of inheritance metrics (that include the above proposals) that are defined on a directed graph abstraction of the inheritance structure and that are contrived on the assumptions and definitions given by Chidamber and Kemerer, can never satisfy Property 9. Furthermore, it is also argued that the formalisation can be generalized to include other classes of structural metrics that are not necessarily inheritance metrics.