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A program should have several properties including being easy to read, maintain, and test. Complexity of a program is strongly related to these properties and is a significant determinant of a software system's success or failure [MeCabe89]. There are a large number of program complexity metrics that have been proposed and studied for conventional, procedural programming languages. The most basic and still widely used complexity metric is "program length", which is actually only a measure of program size. On the other hand, several graph-theoretic complexity metrics have been developed that demonstrate that software complexity to a large extent is independent of program size and dependent on the decision structure of a program [McCabe76 and Elshoff77]. Software metrics that are based on the flow graph of a program are in general insensitive to code bulk, e.g., adding or deleting functional statements (assignment statements), while affecting bulk, does not change the decision structure complexity of a program. We can also investigate the sensitivity of graph-theoretic metrics to edge directions. For instance, McCabe's cyclomatic complexity [McCabe76] is based on some concepts from graph theory that were originally defined for undirected graphs. This work explores the notion of changing the directions of the edges of a flow graph and its impact on some of the graph-theoretic metrics including cyclomatic complexity [McCabe76], track number (a generalization of cyclomatic complexity)[Culik81], and normal number [Culik77]. This question is investigated analytically and empirically. Both structured and unstructured flow graphs are considered in this study. Suppose G is a flow graph and G' is the same graph with reversed edges. Some of the results of this stuly indicate that the cyclomatic and track numbers of G and G' are the same for structured and unstructured flow graphs, the normal numbers of G and G' are not necessarily the same either for structured or unstructured flow graphs, and the number of spanning trees of G and G' are the same for structured flow graphs but not necessarily the same for unstructured flow graphs.

Sensitivity of graph-theoretic metrics to edge directions for structured and unstructured programs (abstract and references only)