中国航空网络的多分辨率小波分解研究

为解决航空网络中节点与边数量过多导致整体特征分析计算量大的困难,提出了基于多分辨率小波分解理论的复杂网络数据压缩方法,论证了选用Haar小波基进行航空网络小波分解的适用性及分解形式,提出了确定网络分解层数和分解后还原参数的方法.对2011年5月我国163座通航城市和2 198条航线构成的复杂航空网络,选用Haar小波基对该网络的邻接矩阵进行4层小波分解,得到的网络最低频子带10×10阶矩阵,包含了原网络的大部分信息.实证研究结果表明:利用分解后的最低频子带可以还原出原网络节点城市的平均度、平均最短路径长度和聚类系数. 

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.