Fractal dimension in software networksG. Concas, M. F. Locci, M. Marchesi, S. Pinna and I. Turnu
Dipartimento di Ingegneria Elettrica ed Elettronica Università di Cagliari - piazza d'armi, 09123 Cagliari, Italy
received 5 June 2006; accepted in final form 19 October 2006
published online 16 November 2006
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.
89.75.-k - Complex systems.
89.75.Da - Systems obeying scaling laws.
61.43.Hv - Fractals; macroscopic aggregates (including diffusion-limited aggregates).
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