A weighted local-world evolving network model with aging nodes

In this paper, the dynamical behaviors of a class of weighted local-world evolving networks with aging nodes are investigated. As the network grows, each newly added node is connected to some existing nodes through strength–age preferential attachment. Each time step, the newly added node with randomly determined initial degree is connected to some existing nodes through a local strength–age preferential attachment. By using tools from stochastic analysis and continuous approximation, it is theoretically proved that the strength distribution of the generated network has a power-law form with exponent depending nontrivially on a decay factor α∈[0,1). In addition, the clustering coefficient, correlation and small-world properties of this class of networks are examined via simulations. It is shown that clustering coefficient is a monotone decreasing function of the decay factor, and the assortative degree correlation and small-world properties appear simultaneously. Finally, the new model is used to characterize the Internet topology as a typical application.