The structural and spatial evolution of the China Railway Express network

To illustrate the structural and spatial evolution of the China Railway Express (CR-Express) network, this paper adopts the Space-P method to construct three complex networks of the CR-Express routes respectively by the block train data in 2013, 2016 and 2019, and the indices of overall network structure (average degree, average path length, and average clustering coefficient) and indices of node importance (degree centrality and betweenness centrality) in the networks are comparatively analyzed. It is shown that the CR-Express network has become more complicated, but in 2016 the overall structure was basically stable, and consistently presents clear small-world and scale-free characteristics. The nodes in the network can be partitioned into four groups based on their influence on network connectivity and the number of block trains departing from them, namely core nodes, freight demand nodes, key nodes and edge nodes. Among them, core nodes and freight demand nodes are located in the central and western regions during the whole study period, and the newly added nodes in the eastern region from 2016 to 2019 are edge nodes. Based on the above analysis, we capture the evolving nature of the CR-Express network across distinct development stages under the influence of policy, economy, geographical location and other factors, and put forward operational suggestions to optimize the CR-Express service, strengthen the maintenance of key nodes, and ensure the efficient operation of China-Europe trains.