Computing the Fractal Dimension of Software Networks

Given a large software system, it is possible to associate to it a graph, also known as software network, where graph nodes are the software modules (packages, files, classes or other software entities), and graph edges are the relationships between modules. A recent paper by some of the authors demonstrated that the structure of software networks is also self-similar under a length-scale transformation, and calculated their fractal dimension using the “box counting” method. In this paper we describe three possible algorithms for the computation of the fractal dimension of software networks, and compare them. We show that a Merge Algorithm firt devised by the authors is the most efficient, while Simulated Annealing is the most accurate. A Greedy Coloring algorithm, based on the equivalence of the box counting problem with the graph coloring problem, seems nevertheless the best compromise, having speed comparable to the Merge Algorithm, and accuracy comparable with Simulated Annealing. Key-Words: Complex Systems, Complex Networks, Self-similarity, Software Graphs, Software Metrics, Object-Oriented Systems.