A Contrastive Analysis of Survivability of Urban Rail Network Based on Complex Network Theory
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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。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.
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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
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
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
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
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
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
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
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 Ln 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 -0.131K0.568+0.373 0.729 3 -0.167K0.50+0.413 0.716 7 上海 -0.145K0.52+0.381 0.779 5 -0.118K0.616+0.366 0.567 5 成都 -0.115K0.619+0.362 0.756 4 -0.163K0.512+0.412 0.730 1 深圳 -0.115K0.615+0.359 0.698 8 -0.149K0.543+0.399 0.693 6 广州 -0.136K0.554+0.379 0.709 5 -0.122K0.622+0.377 0.647 2 重庆 -0.149K0.524+0.391 0.713 6 -0.111K0.645+0.361 0.542 8 天津 -0.117K0.608+0.362 0.670 6 -0.117K0.639+0.374 0.632 9 苏州 -0.123K0.60+0.372 0.614 2 -0.104K 0.68+0.36 0.598 1 杭州 -0.11K0.637+0.356 0.676 9 -0.113K0.649+0.367 0.622 3 西安 -0.134K0.563+0.38 0.680 6 -0.115K0.645+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
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