  We propose a dynamical model in which a network structure evolves in a
self-organized critical (SOC) manner and explain a possible origin of the
emergence of fractal and small-world networks. Our model combines a network
growth and its decay by failures of nodes. The decay mechanism reflects the
instability of large functional networks against cascading overload failures.
It is demonstrated that the dynamical system surely exhibits SOC
characteristics, such as power-law forms of the avalanche size distribution,
the cluster size distribution, and the distribution of the time interval
between intermittent avalanches. During the network evolution, fractal networks
are spontaneously generated when networks experience critical cascades of
failures that lead to a percolation transition. In contrast, networks far from
criticality have small-world structures. We also observe the crossover behavior
from fractal to small-world structure in the network evolution.
