Characterizing traffic time series based on complex network theory

A complex network is a powerful tool to research complex systems, traffic flow being one of the most complex systems. In this paper, we use complex network theory to study traffic time series, which provide a new insight into traffic flow analysis. Firstly, the phase space, which describes the evolution of the behavior of a nonlinear system, is reconstructed using the delay embedding theorem. Secondly, in order to convert the new time series into a complex network, the critical threshold is estimated by the characteristics of a complex network, which include degree distribution, cumulative degree distribution, and density and clustering coefficients. We find that the degree distribution of associated complex network can be fitted with a Gaussian function, and the cumulative degree distribution can be fitted with an exponential function. Density and clustering coefficients are then researched to reflect the change of connections between nodes in complex network, and the results are in accordance with the observation of the plot of an adjacent matrix. Consequently, based on complex network analysis, the proper range of the critical threshold is determined. Finally, to mine the nodes with the closest relations in a complex network, the modularity is calculated with the increase of critical threshold and the community structure is detected according to the optimal modularity. The work in our paper provides a new way to understand the dynamics of traffic time series.