Dynamical evolution of weighted scale-free network models

Inspired by the weighted network model proposed by Barrat, Barthélemy, and Vespignani (BBV), we construct a new evolving model that characterizes the weighted scale-free networks with community structure by adjusting one parameter. In the process of the evolution, a new node or a new community with a probability is added to the network, and new links are added to the network according to the strength preferential attachment rule. Theoretical analyses and numerical simulations show that our model captures power-law distributions of node strengths and link weights, as confirmed in several real-world systems.