Rich-Core Structure And Load Distribution Of Metro Networks

Metro network is the product of traffic science and network science,which makes it possible for us to use complex network theory in metro system,and deepens our understanding of metro system.In the field of complex network,the research on complex traffic network is always an important topic.This paper studies 28 metro networks from the two aspects of the core structure and the load of network nodes.We explore the similarities and differences in the topological structure of different metro networks.In terms of the core structure,we first discuss whether there is rich-club phenomenon in 28 metro networks.The result shows that rich-club phenomenon exists in 18 metro networks,and there is no rich-club phenomenon in the other 10 metro networks.Then,based on the“corner”in rich-club coefficient curve,we propose an algorithm for calculating the rich-core structure of networks.This algorithm can obtain good results not only in metro network,but also in other networks with scale-free properties.This is because in the scale-free network,we find that there is a power-law relationship between rich-club coefficient and betweenness centrality.It is this power law relation that makes the curve have obvious“corner”.In terms of the load of network nodes,we first discuss the relationship between shortest path length and betweenness centrality,and then prove their relationship.After,we use a method that equates the betweenness centrality of nodes to the load for calculating the load of nodes in the metro network.By comparing the average load ratios between the rich-core and the outside of different metro networks,it is found that in typical metro networks of large size,the average load ratios are greatly different.In order to explore the reason for this difference,we use four network models with different topological characteristics.The result shows that preferred connection increases the average load ratio,while the existence of the edge loop decreases the average load ratio.After comparing the results of metro networks with these four network models,we divide metro networks into two types:“tree”network and“mesh”network.Among them,the"tree" network is represented by the metro networks of New York,London and Berlin.In these networks,the rich-club phenomenon is common,and their average load ratios are usually large.The "mesh" network is represented by the metro networks of Beijing,Shanghai and Seoul.There is usually no rich-club phenomenon in these networks,and their average load ratios are usually small.