基于复杂网络理论的城轨线网抗毁性对比分析

赵瑞琳; 牟海波; 肖丁; 杨景峰

doi:10.3963/j.jssn.1674-4861.2021.03.006

基于复杂网络理论的城轨线网抗毁性对比分析

doi: 10.3963/j.jssn.1674-4861.2021.03.006

兰州交通大学交通运输学院兰州 730070

基金项目:

国家自然科学基金项目 61563029

详细信息

作者简介:
赵瑞琳（1995—），硕士研究生.研究方向：交通运输规划与管理.E-mail：459368316@qq.com

通讯作者:
牟海波（1977—），博士，教授.研究方向：交通信息工程与控制.E-mail：mhbmmm@mail.lzjtu.cn

中图分类号: U231; X913.4
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出版历程
- 收稿日期: 2020-11-22

A Contrastive Analysis of Survivability of Urban Rail Network Based on Complex Network Theory

School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China

摘要

摘要: 为分析不同规模轨道交通路网面对突发事件的抗毁性能，选取中国10个典型城市的轨道交通网络，采用复杂网络理论分析模拟攻击下网络的抗毁程度。利用Pajek软件构建Space-L拓扑空间抽象路网，设定定量化评价指标，系统分析随机攻击、累计节点蓄意攻击下网络的抗毁性；利用改进网络效率公式分析单节点蓄意攻击下单一节点的失效对网络的影响程度。研究结果表明，轨道交通网络是无标度网络。随机攻击下，2种规模网络在指标为节点度、网络效率、最大连通子图的失效站点数占比分别达到10.44%和11.09%，17.99%和18.39%，13.27%和12.92%时路网崩溃；累计节点蓄意攻击下，2种规模网络在指标为节点度、网络效率、最大连通子图的失效站点数占比分别达到5.22%和5.17%，4.3%和3.19%，4.23%和2.43%时路网崩溃。与在发散型线路交点的失效节点相比，处在三角形顶点或网状结构内的失效节点对整体网络的抗毁性更强。
- 城市轨道交通 /
- 拓扑网络 /
- 抗毁性分析 /
- 模拟攻击 /
- 网络规模 /
- 复杂网络理论
Abstract: The metro networks of 10 typical cities in China are selected to analyze the resilience of different metro networks to emergencies.The complex network theory is used to analyze the resilience of networks under simulated attacks.Pajek software is used to construct an abstract road network of topological space Space-L.Quantitative evaluation indicators are set to systematically analyze the survivability of the network under random attacks and deliberate attacks of accumulated nodes.The improved network efficiency formula is used to analyze the influence of each node on the network under the single-node deliberate attack.The results show that the metro network is a scale-free network.Based on node degree, network efficiency, and the maximum connection sub-grap, the proportions of failed sites in the two networks reach 10.44%and 11.09%, 17.99%and 18.39%, and 13.27%and 12.92%under random attacks, and the net crashes.Under cumulative-node deliberate attacks, the proportions of failed sites in the two networks reach 5.22%and 5.17%, 4.3%and 3.19%, and 4.23%and 2.43%, and the net crashes.Compared with the failure node at the intersection of divergent lines, the node at the apex of the triangle or the mesh structure is more invulnerable to the network.
- urban-rail transit /
- topological network /
- survivability analysis /
- simulated attack /
- network scale /
- complex network theory

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图 1 构造拓扑网络步骤图

Figure 1. Steps for constructing a topological network

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图 2 深圳市现阶段地铁线路拓扑结构

Figure 2. Topology structure of current Shenzhen metro network

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图 3 各城市原始节点度分布

Figure 3. Degree distribution of original nodes in cities

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图 4 深圳市原始度分布幂律拟合图

Figure 4. Power-law fitting of original degree distribution in Shenzhen

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图 5 R攻击下各城市剩余节点为70%的节点度分布

Figure 5. Degree distribution of remaining 70%nodes in cities under R attack

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图 6 CM攻击下各城市剩余节点为75%的节点度分布

Figure 6. Degree distribution of remaining nodes 75%in cities under CMattack

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图 7 深圳R攻击70%个节点后度分布幂律拟合图

Figure 7. Power-law fitting of remaining 70%nodes degree distribution in Shenzhen under R attack

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图 8 深圳CM攻击75%个节点后度分布幂律拟合图

Figure 8. Power-law fitting of remaining 75%nodes degree distribution in Shenzhen under CMattack

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图 9 2种攻击下各城市变化趋势

Figure 9. Variation trend of under two attacks in cities

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图 10 1次不同攻击下各城市平均失效边

Figure 10. Average edge failure for each city under different attacks

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图 11 2种攻击下各城市变化趋势

Figure 11. Variation trend of under two attacks in cities

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图 12 2种攻击下各城市变化趋势

Figure 12. Variation trend of under two attacks in cities

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图 13 2种攻击下各城市变化趋势

Figure 13. Variation trend of under two attack in cities

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图 14 单节点蓄意攻击下各城市影响趋势

Figure 14. Variation trend of under single-node malicious attacks in cities

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图 15 城市轨道交通局部标点图

Figure 15. Local punctuation of an urban-rail transit

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表 1 突发事件与网络攻击对应关系

Table 1. Relationship between the emergency and network attack

攻击类别	突发事件种类
随机攻击（R攻击）	技术设备类、自然灾害类
累计节点蓄意攻击（CM攻击）	社会治安类、运营故障类
单节点蓄意攻击	社会治安类、大客流类

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表 2 各城市轨道交通网络静态表征指标

Table 2. Static representation indices of the metro network in China

城市	S	n	m	L_n	K	E(G)	C	α
北京	23	338	380	56	2.248 52	0.044 28	0.001 97	0.376 98
上海	16	337	398	56	2.362 02	0.047 69	0.005 64	0.396 02
成都	11	279	314	45	2.250 90	0.048 67	0.001 79	0.377 86
深圳	11	237	273	39	2.303 80	0.055 55	0.003 80	0.387 23
广州	13	226	245	32	2.168 14	0.046 69	0	0.364 58
重庆	8	164	176	18	2.146 34	0.054 81	0	0.362 14
天津	6	143	153	15	2.139 86	0.061 42	0	0.361 70
苏州	4	126	130	9	2.063 49	0.059 03	0	0.349 46
杭州	5	123	131	14	2.130 08	0.058 95	0	0.360 88
西安	5	102	104	6	2.039 22	0.064 41	0	0.346 67

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表 3 各城市原始度分布尾部度分布拟合函数

Table 3. Tail-fitting function of each city's original degree distribution

城市	拟合函数	R²
北京	410K^-9.1 + 0.00243	0.972 0
上海	1.04×10⁸K^-27.07+0.029	0.975 5
成都	1.9×10⁶K^-21.27+0.027	0.972 3
深圳	8.39×10⁷K^-26.66+0.024	0.984 7
广州	54.53K^-6.1+0.01	0.993 4
重庆	208.8K^-8+0.012	0.995 4
天津	6.1×10⁸K^-29.5+0.018	0.986 0
苏州	2.5×10⁶K^-21.47+0.012	0.995 0
杭州	703.8K^-9.789+0.016	0.988 5
西安	4.675×10⁷K^-25.71+0.01	0.995 4

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表 4 各城市模拟攻击后尾部度分布拟合函数

Table 4. Tail-fitting function of each city's degree distribution under attack

	随机攻击（R攻击）	R²	蓄意累计攻击（M攻击）	R²
北京	-0.131K^0.568+0.373	0.729 3	-0.167K^0.50+0.413	0.716 7
上海	-0.145K^0.52+0.381	0.779 5	-0.118K^0.616+0.366	0.567 5
成都	-0.115K^0.619+0.362	0.756 4	-0.163K^0.512+0.412	0.730 1
深圳	-0.115K^0.615+0.359	0.698 8	-0.149K^0.543+0.399	0.693 6
广州	-0.136K^0.554+0.379	0.709 5	-0.122K^0.622+0.377	0.647 2
重庆	-0.149K^0.524+0.391	0.713 6	-0.111K^0.645+0.361	0.542 8
天津	-0.117K^0.608+0.362	0.670 6	-0.117K^0.639+0.374	0.632 9
苏州	-0.123K^0.60+0.372	0.614 2	-0.104K ^0.68+0.36	0.598 1
杭州	-0.11K^0.637+0.356	0.676 9	-0.113K^0.649+0.367	0.622 3
西安	-0.134K^0.563+0.38	0.680 6	-0.115K^0.645+0.371	0.624 8

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表 5 R攻击下不同规模网络指标边界

Table 5. Network-index boundary of different scale under R attacks %

指标边界	规模1	规模2
节点度80	10.44	11.09
网络效率50	17.99	18.39
最大连通子图 60	13.27	12.92

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表 6 CM攻击下不同规模网络指标边界

Table 6. Network index boundary of different scales under CM attacks %

指标边界	规模1	规模2
节点度80	5.22	5.17
网络效率50	4.30	3.19
最大连通子图 60	4.23	2.43

下载: 导出CSV

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