Sandbox fixed-mass algorithm for multifractal unweighted complex networks

Abstract

The study of multifractal properties is one of the current scopes in the analysis of complex networks. Last decade, several multifractal algorithms have been proposed, both adding new approaches and improving their accuracy or time consumption. One of the methods that provide more advantages is the sandbox method, which does not require to solve the NP-hard problem of covering the whole networks in non-overlapping boxes by means of an approximation. Unlike the box-covering methods, the sandbox method allows the complete reconstruction of the multifractal dimension functions D(q). However, sandbox algorithms for complex networks have been developed exclusively from a Fixed-Size approach. Hence, the applicability of the Fixed-Mass approach with a sandbox procedure (FM-SB) in this framework is explored for the first time. The accuracy of the FM-SB is evaluated in deterministic networks, and subsequently applied for determining multifractal properties in synthetic networks generated by the Barabási–Albert model (scale-free) and the Watts–Strogatz model (small-world and random), as well as in real ones. The FM-SB algorithm is capable to completely characterize multifractal properties in these networks, like the mass exponent function and generalized fractal dimensions. This work completes the algorithms proposed in the literature for the multifractal analysis of unweighted complex networks, using a Fixed-Mass procedure.