Fractal and Small-World Networks Formed by Self-Organized Critical Dynamics

摘要

We propose a dynamical model in which a network structure evolves in aself-organized critical (SOC) manner and explain a possible origin of theemergence of fractal and small-world networks. Our model combines a networkgrowth and its decay by failures of nodes. The decay mechanism reflects theinstability of large functional networks against cascading overload failures.It is demonstrated that the dynamical system surely exhibits SOCcharacteristics, such as power-law forms of the avalanche size distribution,the cluster size distribution, and the distribution of the time intervalbetween intermittent avalanches. During the network evolution, fractal networksare spontaneously generated when networks experience critical cascades offailures that lead to a percolation transition. In contrast, networks far fromcriticality have small-world structures. We also observe the crossover behaviorfrom fractal to small-world structure in the network evolution.