The small-world effect of fractal networks modeled on ‘dust-like’ cubes

In this paper, the sequence of evolving networks is generated from some ‘dust-like’ cubes by applying the encoding methods in fractal and symbolic dynamical systems. Based on the self-similar structures of fractals, we study the mean clustering coefficient, the mean geodesic distance and the mean Fermat distance. The relevant results show the small-world effect of our evolving networks.