  In this paper, a simple dynamical model in which fractal networks are formed
by self-organized critical (SOC) dynamics is proposed; the proposed model
consists of growth and collapse processes. It has been shown that SOC dynamics
are realized by the combined processes in the model. Thus, the distributions of
the cluster size and collapse size follow a power-law function in the
stationary state. Moreover, through SOC dynamics, the networks become fractal
in nature. The criticality of SOC dynamics is the same as the universality
class of mean-field theory. The model explains the possibility that the fractal
nature in complex networks emerges by SOC dynamics in a manner similar to the
case with fractal objects embedded in a Euclidean space.
