中国国内航空网络的分形特征研究

A Study of Fractal Features of Chinese Domestic Airline Network

为进一步探索中国航空网络拓扑结构的复杂性,以2015和2019年夏秋航季国内航班正班计划数据为例,以分形理论为基础,对中国航空网络分形特征进行实证分析。研究表明,中国航空网络具有较高的聚类系数和较短的平均路径长度,且度服从幂律分布,其具有小世界特征和无标度特征。度度相关性表现为负相关,网络为异配的。盒子尺寸l_(B)与最小盒子数N_(B)在双对数图中线性关系显著,表明中国航空网络在结构上具有自相似功能模块,具有分形特征。与2015年网络结构比较,2019年网络的平均最短路径和聚类系数均下降,而节点数和节点平均度增大,无权盒维数由2015年的5.065增长到5.079,加权盒维数从2.164增长到2.262,中国航空网络的分形结构随时间推移逐步演进,网络整体结构在趋好。

To further explore the complexity of Chinese airline network topology,based on the schedule data of domestic flights in the summer and autumn seasons of 2015 and 2019,an empirical analysis of the fractal characteristics of Chinese airline network is conducted by using the fractal theory.The research shows that:Chinese airline network has shorter average path length and clustering coefficient,and follows power-law distribution,having the characteristics of small world and scale-free feature.Degree correlation shows negative correlation and the network is heterotopic.The linear relationship between the box size l_(B) and the minimum box number N_(B) is significant in the log-log graph,which indicates that Chinese airline network has self-similar functional modules in structure,and it has fractal characteristics.Compared with network structure in 2015,in 2019 the average Chinese airline network shortest path and cluster coefficient decreased,and the number of nodes,the average degree of node,the dimension of no weight box increased from 5.065 in 2015 to 5.079,the weighted box dimension increased from 2.164 to 2.262,and as the fractal structure of Chinese airline network evolved over time,the overall structure of the network was getting better.