空铁综合运输网络结构特征实证分析

为探究中国空铁综合运输网络结构特性，以城市为节点，若城市间有航班或高铁则连边，以航班数量和高铁数量为权重，分别建立了3个加权网络：高铁子网络、航空子网络和空铁综合运输网络。首先，通过均值关联、三角中介中心度、加权谐波中心度指标对比研究了不同网络的关键节点；其次，通过聚类系数和平均最短路径长度研究了三个网络的小世界特性；再次，通过Newman算法研究了三个网络的社团结构；最后，通过加权网络效率为指标，研究了三个网络的鲁棒性。研究结果表明，北上广深是三个网络的三种不同加权中心度的排名都很靠前，是共有的最为关键的节点。三个网络都具有小世界特性，但只有高铁子网络的模块度值大于0.3,存在明显的社团结构，并被划分为了10个社团。空铁综合运输网络具有更好的加权网络效率，约为0.32,为三个网络中最高，节点失效时的加权效率变化最小，鲁棒性最强。可见空铁综合运输网络集成了高铁网络、航空网络的互补优势，网络结构特征优于单一运输网络。

Empirical analysis of the structural characteristics of an integrated air-rail transportation network

In order to explore the structural characteristics of Chinese aviation and high-speed rail integrated transportation network, this study treated cities as nodes and established three weighted networks: a high-speed rail sub-network, an aviation sub-network, and a comprehensive air-rail transportation network by connecting cities with flight or high-speed rail services, with flight numbers and high-speed rail numbers as weights. Firstly,mean correlation, triangle betweenness centrality, and weighted harmonic centrality were used to analyze key nodes in different networks. Secondly,clustering coefficients and average shortest path lengths were used to analyze the small-world properties of the three networks. Thridly,the Newman algorithm was used to study the community structure of the three networks. Lastly,weighted network efficiency was used as an indicator to compare the robustness of the three networks. The results show that Beijing, Shanghai, Guangzhou, and Shenzhen ranked high in all three weighted centrality measures and were the most critical nodes in all three networks. All three networks had small-world properties, but only the high-speed rail sub-network had a modularity value greater than 0.3, indicating significant community structures, which were divided into ten communities. The comprehensive air-rail transportation network had a better weighted network efficiency, approximately 0.32, which was the highest among the three networks. It also had the strongest robustness and the smallest change in weighted efficiency when nodes failed. It is concluded that the comprehensive air-rail transportation network integrates the complementary advantages of the high-speed rail and aviation networks and has better structural characteristics than single transportation networks.