The cross cyclomatic complexity: a bi-dimensional measure for program complexity on graphs

Reduce and control complexity is an essential practice in software design. Cyclomatic complexity (CC) is one of the most popular software metrics, applied for more than 40 years. Despite CC is an interesting metric to highlight the number of branches in a program, it clearly not sufficient to represent the complexity in a piece of software. In this paper, we introduce the cross cyclomatic complexity (CCC), a new bi-dimensional complexity measure on graphs that combines the cyclomatic complexity and the weight of a minimum-weight cycle basis in as pair on the Cartesian plan to characterize program complexity using control flow graphs. Our postulates open a new venue to represent program complexity, and we discuss its implications and opportunities.