ALGORITHMS FOR FRACTAL DIMENSION CALCULATION

Algorithms to calculate the fractal dimension of a complex network are presented. One of the algorithms is applied to a parametrized class of models whose fractal dimension transitions from one to two. For the system size we considered here (16384 nodes), the transition takes place from one at p = 0 to essentially two at the small value p = 0.03. This seems to indicate that the transition is likely to become infinitely sharp and occur at p = 0 as the system size increases to infinity.