Towards the Fractal Dimension of Classes

Abstract

The fractal property has been regarded as a fundamental property of complex networks, characterizing the self-similarity of a network. Such a property is usually numerically characterized by the fractal dimension metric, and it not only helps the understanding of the relationship between the structure and function of complex networks, but also finds a wide range of applications in complex systems. The existing literature shows that class-level software networks (i.e., class dependency networks) are complex networks with the fractal property. However, the fractal property at the feature (i.e., methods and fields) level has never been investigated, although it is useful for measuring class complexity and predicting bugs in classes. Furthermore, existing studies on the fractal property of software systems were all performed on un-weighted software networks and have not been used in any practical quality assurance tasks such as bug prediction. Generally, considering the weights on edges can give us more accurate representations of the software structure and thus help us obtain more accurate results. The illustration of an approach’s practical use can promote its adoption in practice. In this paper, we examine the fractal property of classes by proposing a new metric. Specifically, we build an FLSN ( F eature L evel S oftware N etwork) for each class to represent the methods/fields and their couplings (including coupling frequencies) within the class, and propose a new metric, ( F ractal D imension for C lasses), to numerically describe the fractal property of classes using FLSNs, which captures class complexity. We evaluate theoretically against Weyuker’s nine properties, and the results show that adheres to eight of the nine properties. Empirical experiments performed on a set of twelve large open-source Java systems show that i) for most classes (larger than \(96\%\) ), there exists the fractal property in their FLSNs, ii) is capable of capturing additional aspects of class complexity that have not been addressed by existing complexity metrics, iii) significantly correlates with both the existing class-level complexity metrics and the number of bugs in classes, and iv), when used together with existing class-level complexity metrics, can significantly improve bug prediction in classes in three scenarios (i.e., bug-count , bug-classification , and effort-aware ) of the cross-project context, but in the within-project context, it cannot.