Comparative analysis of evolving software systems using the Gini coefficient

Abstract

Software metrics offer us the promise of distilling useful information from vast amounts of software in order to track development progress, to gain insights into the nature of the software, and to identify potential problems. Unfortunately, however, many software metrics exhibit highly skewed, nonGaussian distributions. As a consequence, usual ways of interpreting these metrics -for example, in terms of "average" values -can be highly misleading. Many metrics, it turns out, are distributed like wealth -with high concentrations of values in selected locations. We propose to analyze software metrics using the Gini coefficient, a higherorder statistic widely used in economics to study the distribution of wealth. Our approach allows us not only to observe changes in software systems efficiently, but also to assess project risks and monitor the development process itself. We apply the Gini coefficient to numerous metrics over a range of software projects, and we show that many metrics not only display remarkably high Gini values, but that these values are remarkably consistent as a project evolves over time.

Partition Refinement of Component Interaction Automata: Why Structure Matters More Than Size

“…States that are already well connected attract new transitions more easily than others. This "rich-get-richer" strategy is typical for software systems [25]. The distribution of functionality in a software system is neither regular nor random.…”

“…There is a narrow margin, ±4%, that determines the success or failure of partition refinement. This value is of specific significance, as it corresponds exactly to the threshold defined by Vasa et al [25] for the identification of major shifts in evolving software systems. In other words, a deviation from the mean value µ G OUT by more than 4% significantly influences the success of partition refinement.…”

“…The distribution of functionality in a software system is neither regular nor random. Developers prefer to organize and maintain software systems around a small number of highly complex abstractions [25]. These abstractions constitute virtual hubs in the systems and appear to guarantee not only the proper function of a software, but also the ability to evolve a software system in order to meet changing requirements in the future [25].…”

“…We can measure these structural features using two concepts: the scaling exponent β [27,26] to denote the power-scaling relationship between the number of states and the number of transitions of an automaton and the Gini coefficients [10,25] of the incoming and outgoing transitions in an automaton in order to quantify the degree of inequality in the distribution of these attributes in a given automaton. Both measures provide suitable summary metrics of the underlying directed graph topology of an automaton.…”

“…The Gini coefficient is a well-established measure to quantify the inequality of income distributions in moderns societies [23] that we have previously applied in the analysis of evolving software systems [25]. The Gini coefficient is a number between 0 and 1, where 0 denotes a perfect equality (e.g., every state in the system possesses the same number of outgoing transitions) and 1 signifies a perfect inequality (e.g., all states except one have no incoming transitions).…”