Journal of Shandong University(Engineering Science) ›› 2022, Vol. 52 ›› Issue (6): 14-22.doi: 10.6040/j.issn.1672-3961.0.2022.214

• Transportation Engineering—Special Issue for Intelligent Transportation • Previous Articles     Next Articles

Study on topological characteristics and node centrality of high-speed railway complex network

Fengbo LAI(),Bing XU,Ying XU,Lei ZHANG,Yirong SUN   

  1. Shandong Transportation and Regional Development Research Center, Shandong Jiaotong University, Jinan 250357, Shandong, China
  • Received:2022-06-10 Online:2022-12-20 Published:2022-12-23

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Abstract:

Taking the main representative cities in China as the research object, this study analyzed the characteristics and topological characteristics of high-speed railway network, and identifies node cities and their functions in high-speed railway network. The Space-P method was used to build a high-speed network model, and the complex network theory and Pajek analysis software were used to analyze the topological structure and node centrality of of China′s high-speed rail network from the aspects of degree values, average path length, aggregation coefficient and node city centrality. The results showed that China′s high-speed rail network highly aggregated and connected as a whole, the eastern, central and coastal cities showed high aggregation, while the western cities had low high-speed rail network connectivity and weak aggregation. High-speed rail network had the characteristics of a small world, any two nodes could be connected by a small number of transit times, and a few cities need three transit times to be connected. In the high-speed rail network, the cities with large degree values were mainly concentrated in the east, central and coastal regions of China, while the cities in the west and northeast regions had less degree values and large degree centrality, and their proximity centrality was also large. Cities with smaller degree value and greater intermediate centrality had stronger transit ability.

Key words: high-speed rail complex network, topological structure, node centrality, Space-P method

CLC Number: 

  • U268.6

Table 1

Filter criteria and city list"

筛选条件 城市名称
直辖市、省会、首府 北京、天津、上海、重庆、西安、兰州、西宁、南宁、成都、郑州、合肥、武汉、贵阳、长沙、南昌、杭州、昆明、广州、银川、拉萨、石家庄、乌鲁木齐、长春、沈阳、呼和浩特、福州、南京、海口、哈尔滨、济南、太原
各省、自治区、直辖市GDP居首位城市 北京、天津、上海、重庆、乌鲁木齐、西宁、南宁、成都、郑州、合肥、武汉、杭州、昆明、海口、银川、拉萨、长春、福州、南京、唐山、大连、青岛、贵阳、长沙、南昌、深圳、鄂尔多斯、海口、哈尔滨、太原、西安、兰州

Fig.1

High speed railway complex network connectivity diagram"

Table 2

Calculation results of node degree value"

城市 度数 城市 度数 城市 度数
北京 31 重庆 25 深圳 20
西安 31 广州 24 昆明 19
郑州 31 福州 24 长春 15
上海 30 天津 23 哈尔滨 14
武汉 30 青岛 23 大连 14
济南 30 兰州 22 银川 14
石家庄 30 贵阳 22 呼和浩特 7
南京 29 太原 22 西宁 6
成都 28 沈阳 21 乌鲁木齐 4
长沙 28 南昌 21 鄂尔多斯 3
合肥 27 唐山 21
杭州 27 南宁 20

Table 3

Shortest path length distribution"

最短路径长度 节点对数量
lmin=1 349
lmin=2 204
lmin=3 8

Fig.2

Distribution of agglomeration coefficient of node cities"

Table 4

Judgment index value of small world network"

节点数 平均度 聚集系数 平均路径长度
34 21.65 0.829 1.39

Fig.3

Centrality comparison chart"

Table 5

Degree centrality Calculation results"

城市 度中心性 城市 度中心性 城市 度中心性
北京 0.886 重庆 0.714 深圳 0.571
西安 0.886 广州 0.686 昆明 0.543
郑州 0.886 福州 0.686 长春 0.429
上海 0.857 天津 0.657 哈尔滨 0.400
武汉 0.857 青岛 0.657 大连 0.400
济南 0.857 兰州 0.629 银川 0.400
石家庄 0.857 贵阳 0.629 呼和浩特 0.200
南京 0.829 太原 0.629 西宁 0.171
成都 0.800 沈阳 0.600 乌鲁木齐 0.114
长沙 0.800 南昌 0.600 鄂尔多斯 0.086
合肥 0.771 唐山 0.600
杭州 0.771 南宁 0.571

Table 6

Calculation results of intermediate centrality"

城市 介数中心性 城市 介数中心性 城市 介数中心性
西安 0.108 太原 0.007 深圳 0.000
北京 0.027 合肥 0.006 大连 0.000
郑州 0.027 杭州 0.006 鄂尔多斯 0.000
兰州 0.026 天津 0.005 南昌 0.000
石家庄 0.026 呼和浩特 0.005 长春 0.000
济南 0.025 青岛 0.005 南宁 0.000
成都 0.020 唐山 0.004 哈尔滨 0.000
上海 0.016 沈阳 0.003 昆明 0.000
武汉 0.016 福州 0.003 乌鲁木齐 0.000
南京 0.013 广州 0.002 银川 0.000
重庆 0.013 西宁 0.001
长沙 0.009 贵阳 0.001

Table 7

Calculation results of near centrality"

城市 接近中心性 城市 接近中心性 城市 接近中心性
北京 0.890 重庆 0.763 深圳 0.682
西安 0.890 广州 0.746 昆明 0.668
郑州 0.890 福州 0.746 大连 0.605
上海 0.866 天津 0.729 银川 0.605
武汉 0.866 青岛 0.729 长春 0.583
济南 0.866 兰州 0.712 哈尔滨 0.572
石家庄 0.866 贵阳 0.712 呼和浩特 0.517
南京 0.843 太原 0.712 西宁 0.501
成都 0.822 沈阳 0.697 乌鲁木齐 0.486
长沙 0.822 南昌 0.697 鄂尔多斯 0.486
合肥 0.801 唐山 0.697
杭州 0.801 南宁 0.682
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