Research on multilayer network structure characteristics from a higher-order model: The case of a Chinese high-speed railway system

In this paper, we integrate the non-Markovian higher-order model with the multilayer network analysis method for the first time to analyse the transportation system with route dependencies. An empirical study on the Chinese high-speed rail (HSR) system was conducted. The non-Markovian higher-order model is used to describe the theoretical high-speed railway network (THSRN), and weighted k-core decomposition is used to divide the THSRN into the core layer, bridge layer and periphery layer. We analyse the importance of cities and HSR routes. Ten important hub cities in the HSR system are discovered, and a finding against the common belief is revealed that the importance rank of cities is not completely consistent with their train flow. In addition, nine complete HSR lines and seven sections of the HSR lines were found to be the most important routes in the HSR system. Finally, the weaknesses of the HSR system are identified and some optimization suggestions are presented. Our work provides important insight for forming a new framework for analysing the transportation systems with route dependencies, which may assist in the future study of transportation systems. (C) 2021 Elsevier B.V. All rights reserved.