A weighted scale-free network model with high clustering and its synchronizability

The detecting of clusters or communities in large real-world networks such as large social or information networks is of considerable significance. We propose a new weighted evolving model of high clustering scale-free network incorporating a community structure mechanism, which means the addition of the new node depends on not only a single node but also a community. In the process of the evolution, a new node with probability p and a new community with the probability 1 - p are added to the network. Different from the existing studies where new links are additionally established, some links with probability phi according to the triad formation mechanism and other links with the probability 1 phi according to the random selection mechanism are connected between neighbors in the model. The topology and weights of links of the network evolve as time goes on. Moreover, the evolving model gives power-law distributions of degree, weight, and strength as confirmed in several real world systems. Especially, the average clustering coefficient exhibits power-law decay as a function of degree of node. Both the community structure and the triad formation can enhance the average clustering coefficient of scale-free networks. Furthermore, we investigate how the synchronization of the network is influenced by the evolution mechanism of the network. Numerical simulation results show that the network synchronizability is optimized when the average clustering coefficient decreases in the model.