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 Chidamber and Kemerer, it is observed that Weyuker's 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 Brito and Carapuca. In this correspondence, we formally show that particular clas ses of inheritance metrics (that include the above proposals) that are defi ned on a directed graph abstraction of the inheritance structure and that a re contrived on the assumptions and definitions given by Chidamber and Keme rer, can never satisfy Property 9. Furthermore, it is also argued that the formalisation can be generalized to include other classes of structural met rics that are not necessarily inheritance metrics.