中国城市航空网络的实证研究与分析

以城市为节点，城市间直航线路为边，实证地研究了中国城市航空网络的拓扑性质.研究表明，中国城市航空网络是一个小世界网络，具有短的平均路径长度和大的簇系数，且其度分布服从双段幂律分布.它的度度相关性质与世界航空网络和北美航空网络都不相同.当度较小时，世界航空网络和北美航空网络都是正相关的，但中国城市航空网络未表现出度度相关性；而对于度较大的节点，世界航空网络中其邻点平均度几乎是一个常值，但中国城市航空网络却呈现出负相关性.以往的实证研究暗示，节点具有明确几何位置的网络，如计算机互联网、电力网络等，不表现层次性.但是中国城市航空网络展现出明显的层次性，表明地理因素对其结构演化的影响并不强烈.进一步地，以城市间直航计划每周提供的座位数为边权，研究了网络的含权性质，发现该网络节点度权之间是幂律相关的，相关指数为1.37.

Empirical study of Chinese city airline network

We investigate the empirical properties of Chinese city airline network, where nodes and edges denote cities and direct fights. The present network is a small-world network with short average path length and high degree of clustering, and its degree distribution follows a double power law. The degree-degree correlation of the present network is different from that of the world airport network and the North American air network: The small-degree nodes of the world airport network and the North American air network are positively correlated, whereas those of the present network don't exhibit correlation behavior. And for large-degree nodes, the average neighboring degrees approach a constant in the world airport network, while the present network shows negatively correlated behavior. Previous studies suggested the absence of hierarchical structure in geographical networks, such as the Internet, the electrical power grids, and so on. However, the present network displays an obviously hierarchical property, which provides us an evidence that the geographical ingredient may have no effect on the structural evolution of Chinese city airline network. Furthermore, by setting the number of available seats per week as the edge weight, we investigate the correlation between weight and degree, and find a power-law weight-degree correlation with exponent 1.37.