Dynamic fluctuation model of complex networks with weight scaling behavior and its application to airport networks

Airport networks are a kind of complex systems that display significant fluctuations. To describe this kind of phenomena a dynamical fluctuation model is proposed. In this model the fluctuations in growth rates of weight are exponential. There are two adjustable parameters: the exponent β and the creation probability Pd of a new node. β characterizes the tendency to retain an “optimal” allocation of weights (size of components) for a given kind of networks. Pd reflects the interactive effect between the weight fluctuation and variation of nodes and links (topological structure) for each real network. For airport networks the exponent β is 0.4 and the creation probability Pd is equal to 0.018 (China), 0.025 (US), 0.03 (Brazil) and 0.04 (Europe). This model quantitatively describes and reproduces these real airport networks.