Collective adaptation evolution of weighted complex networks: On syncronizability dependence

Abstract

An innovated evolving network representation model to characterize weighted, complex, scale-free networks is proposed. A new node or a community is added to network in the process of evolution while emergences of new links occur according to the ‘Triad Formation’ possessing symmetry and the random selection mechanism. A weighted scale-free network with high-value clustering coefficient can be obtained by adjusting two parameters only. The evolution of degree, strength, weights exhibit the power-law distributions. Highly correlated with the degree, the average strength displays scale-free property. The average clustering coefficient is found to exhibit well power-law decay as a function of the node degree. Triad Formation and Community Structure in weighted scale-free evolving networks, as building mechanisms, can distinctly enhance the clustering coefficient of networks. Both type I and type II networks are found their synchronizability to decrease as the average clustering coefficient increases in weighted scale-free networks of communities.