Structure Characteristics Of Multi-layer Network Based On High Speed Railway And Ordinary Railway

Most of the studies on complex network simply transfer the systems into a single network,in which nodes in a single network can only represent one type of object,and the link between nodes represent only one type of relationship.However,in many biological and man-made networked systems are characterized by the simultaneous presence of different sub-networks organized in separate layers,with links and nodes of qualitatively different types.There are enormous limitations in the traditional single-layer networks,which are used to express complex systems.Therefore,the research on the structure and function of double-layer and even multi-layer networks has become an important direction in the study of complex networks in recent years.Moreover,with the rapid development of high-speed railway,China's high-speed railway was also developed from a line to a network.A single railway network research is not uncommon,the study of high-speed railway network is rarely involved,and a comparative analysis of high-speed railway network and ordinary railway network has not yet appeared.Based on complex network theory,multi-layer network of high-speed railway and ordinary railway is built and we analysis the topological properties of high-speed railway network,ordinary railway network and multi-layer railway network.These results provide new references for the empirical study of multi-layer network and optimizing the traffic network.First,according to the 2016 Chinese train timetable,this paper extracts 453 high-speed railway stations and 2293 ordinary railway stations as the research object.Through analyzing the topological properties of node degree,average shortest path,clustering coefficient in the complex network,we find that the degree distribution of high-speed railway network and ordinary railway network all follow the power-law distribution,the two networks are also scale-free and small-world networks,the high-speed railway networks has better scale-free and clustering characteristics.Second,the paper builds a network model based on the Chinese high-speed railway and ordinary railway from the perspective of double-layer network.Some characteristics in a single-layer network is extended to multi-layer complex networks and verified in actual railway network data.It turns out that in the double-layer network,there also exists a negative correlation between the degree and the clustering coefficient.At last,by using the size of largest component we research the reliability of the high-speed railway network,ordinary railway network and multi-layer railway network.The results implied that the robustness of three networks is basically same under random attack.Under the deliberate attack,due to the connection between the network layers of the double-layer railway network,although the robustness of the high-speed railway network remains the strongest as a whole.However,when the multiple nodes exist,the double-layer railway network is more robust than the other two single-layer railway networks.