Multi-resolution Wavelet Decomposition of Chinese Aviation Network

In order to alleviate the high computational load of overall feature analysis caused by too large a number of nodes and edges in aviation network, a complex network data compression method based on wavelet decomposition theory was put forward. The applicability and decomposition forms of Haar wavelet basis that was applied to the wavelet decomposition in the aviation network were discussed. The way to determine the number of network decomposition layers and parameter restoration after decomposition was developed. In addition, with respect to the complicated aviation network constituted by 163 air traffic cities and 2 198 air lines in China in May 2011, Haar wavelet basis was adopted to the adjacent matrix of the network to carry out a 4-level wavelet decomposition. The obtained lowest frequency sub-band of the network was a 10?10 matrix and contained most information of the original network. An empirical study showed that the average degree, average shortest path length, and cluster coefficient of the node cities in the original network could be restored by using the lowest frequency sub-band after decomposition.