Self-organized Criticality on Growing Scale-Free Networks

Abstract

This paper explores a universal property in the behavior of growing scale-free networks. The characteristic of scale-free networks is that the degree distribution follows the power-law. This structure has been found in various kinds of self-organized networks. Most investigations conducted so far have demonstrated that network topologies are scale-free at a specific point in time. On the other hand, we focus attention on universality in the growing process of networks. In our proposed model, each node has its own fitness to designate the tendency allowing the node to acquire new links. From the simulation results, spread of the network follows the power-law, and power spectrum of the growing process shows 1/f noise, not to mention that the network has scale-free structure. It is found that those properties are in common with self-organized criticality. In conclusion, self-organizational growing networks follow the power-law not only in the sense of scale-free characteristic but also in the spatial and temporal sense.