To analyze the dynamics of air pollution, a homogenous partition of the coarse graining process is employed to transform the daily air pollution index series in Lanzhou into a character series consisting of five characters ( R, r, e, d and D ). The nodes of the pollution fluctuation network are 125 three‐symbol strings (i.e. 125 fluctuation patterns in a duration of 3 days) linked in the network's topology by a time sequence. The network contains integrated information about the interconnections and interactions among the fluctuation patterns of pollution in the network topology. After calculating the dynamical statistics of degree and degree distribution, we find that the distribution follows a three‐stage power‐law distribution characterized by a scale‐free property with hierarchy structure and small‐world effect. Therefore, the pollution fluctuation network is not only a scale‐free network with hierarchy but also a small‐world network. The higher the degree of the node is, the greater the probability that the pollution fluctuation modes will occur. The main nodes of pollution fluctuation networks generally contain the symbols R and r , which demonstrates that the feature of pollution fluctuation is mainly ascending.
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