A large number of real networks are characterized by two fundamental properties: they are small world and scale-free. A recent paper demonstrated that the structure of many complex networks is also self-similar under a length-scale transformation, and calculated their fractal dimension using the "box counting" method. We studied nine large object-oriented software systems, finding that the graphs associated to these networks are self-similar. We also studied the time evolution of the fractal dimension during system growth, finding a significant correlation between the fractal dimension and object-oriented complexity metrics known to be correlated with software fault-proneness. Thus, in software systems the fractal dimension could be considered as a measure of internal complexity, and consequently of the system quality.( 1 )See Supplementary Information of paper [2].c EDP Sciences Article published by EDP Sciences and available at http://www.edpsciences.org/epl or http://dx.
The distribution of bugs in software systems has been shown to satisfy the Pareto principle, and typically shows a power-law tail when analyzed as a rank-frequency plot. In a recent paper, Zhang showed that the Weibull cumulative distribution is a very good fit for the Alberg diagram of bugs built with experimental data. In this paper, we further discuss the subject from a statistical perspective, using as case studies five versions of Eclipse, to show how log-normal, Double-Pareto, and Yule-Simon distributions may fit the bug distribution at least as well as the Weibull distribution. In particular, we show how some of these alternative distributions provide both a superior fit to empirical data and a theoretical motivation to be used for modeling the bug generation process. While our results have been obtained on Eclipse, we believe that these models, in particular the Yule-Simon one, can generalize to other software systems
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