Convexity and independence in software metric theory

Much work has been published in recent years relating to the field of hierarchical software metrics. These are structural measures, defined recursively over the program or flowgraph decomposition into sequences of prime flowgraphs, nested level-by-level. The theory of hierarchical metrics is generalised and extended well beyond its original framework, introducing a notion of convexity that permits combinations of (generalised) hierarchical metrics to be studied, so that weights can be given to various software attributes of interest to the individual investigator. It is found that certain concepts, e.g. those of independence and rank, that have their roots in linear algebra are applicable in this case. Examples are described that show the range of application of these fundamental notions