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摘要: 构建了多模式复合交通网络拓扑模型；在传统测度指标的基础上，从各交通方式的差异性、资源公平性和网络可达性相结合的新视角提出了适用于多模式复合交通网的脆弱性测度，分别为子网敏感度、站点分布均衡度和可达指数；选取3种不同攻击策略进行Python仿真，以特点鲜明的东南沿海发达地区和西南边境山区的实际综合交通网为例，对比分析了网络结构脆弱性的差异性和共同点，多重验证了指标的有效性、稳定性和适用性。研究结果表明：浙江省和云南省多模式复合交通网络均符合小世界网络特性，能够使各交通方式间优势互补，降低网络脆弱性；在3组贡献度参数取值下，无论采取何种攻击策略，当失效节点数量相同时，浙江省子网敏感度从大到小总体趋势为公路网、水运网、铁路网，云南省子网敏感度从大到小总体趋势为航空网、公路网、铁路网；浙江省和云南省的公路网站点分布的基尼系数分别为0.196和0.086，均为分布绝对平均，铁路网站点分布的基尼系数分别为0.559和0.702，均为分布差距悬殊，云南省机场分布的基尼系数为0.363，分布相对合理，浙江省水运网港口分布的基尼系数为0.672，分布差距悬殊，说明需要进一步完善铁路网、水运网和航空网的布局；持续攻击会造成多模式复合交通网络分裂出多个连通子图或孤立节点，使得网络可达性发生突变性下降，为避免这种现象的发生应尽早采取恢复措施。可见，提出的脆弱性测度可以有效刻画综合交通网脆弱性，并发现网络间脆弱性的差异性和共同点。Abstract: A topological model for multimodal composite transportation networks was constructed. The vulnerability metrics applicable to multimodal composite transportation networks were proposed from a new perspective combining the differences in each transportation mode, resource equity, and network accessibility. The metrics were sub-network sensitivity, station distribution balance, and accessibility index. Three different attack strategies were selected for Python simulation. The actual comprehensive transportation networks in developed coastal areas of Southeast China and mountainous border areas of Southwest China were taken as examples to comprehensively analyze the differences and commonalities of network structure vulnerability. In this way, the validity, stability, and applicability of the metrics were verified in multiple cases. Research results show that multimodal composite transportation networks in Zhejiang Province and Yunnan Province are in agreement with the characteristics of small-world networks. They are capable of making the advantages of each transportation mode complement each other and reducing network vulnerability. Under the three sets of contribution parameter values, regardless of the attack strategy, when the number of failed nodes is the same, the overall trend of the sub-network sensitivities from large to small in Zhejiang Province is highway network, waterway network and railway network, and Yunnan Province is aviation network, highway network and railway network. The Gini coefficients of the distribution of highway network stations in Zhejiang Province and Yunnan Province are 0.196 and 0.086, respectively, indicating equal distribution. The Gini coefficients of the distribution of railway network stations are 0.559 and 0.702, respectively, indicating highly unequal distribution. In addition, the Gini coefficient of the distribution of airports in Yunnan Province is 0.363, denoting a relatively reasonable distribution. The Gini coefficient of the distribution of ports in Zhejiang Province is 0.672, denoting highly unequal distribution. It can be concluded that the layouts of railway networks, waterway networks, and aviation networks should be further improved. The multimodal composite transportation network should be separated into multiple connected subgraphs or isolated nodes when subjected to continuous attacks. As a result, network accessibility is suddenly degraded. Recovery measures should be taken as early as possible to avoid this phenomenon. Therefore, the proposed vulnerability metrics are able to effectively describe the comprehensive transportation network vulnerability and discover the differences and commonalities of vulnerability among networks.
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图 6 云南省MCTN的网络效率变化曲线
Figure 6. Change curves of network efficiency of MCTN in Yunnan Province
图 7 浙江省MCTN的网络效率变化曲线
Figure 7. Change curves of network efficiency of MCTN in Zhejiang Province
图 8 云南省MCTN最大连通子图相对大小变化曲线
Figure 8. Relative size change curves of largest connected subgraph of MCTN in Yunnan Province
图 9 浙江省MCTN最大连通子图相对大小变化曲线
Figure 9. Relative size change curves of largest connected subgraph of MCTN in Zhejiang Province
图 10 浙江省站点分布Lorenz曲线
Figure 10. Lorenz curves of station distribution in Zhejiang Province
图 11 云南省站点分布Lorenz曲线
Figure 11. Lorenz curves of station distribution in Yunnan Province
图 12 云南省机场分布Lorenz曲线
Figure 12. Lorenz curves of airport distribution in Yunnan Province
图 15 云南省铁路网络效率和最大连通子图相对大小变化曲线
Figure 15. Change curves of railway network efficiency and largest connected subgraph relative size in Yunnan Province
图 17 浙江省铁路网络效率和最大连通子图相对大小变化曲线
Figure 17. Change curves of railway network efficiency and largest connected subgraph relative size in Zhejiang Province
表 1 网络拓扑结构特性分析指标
Table 1. Analysis indexes of network topology structure characteristic
指标 公式 变量描述 网络效率 $ E=\frac{1}{N(N-1)} \sum_{i \neq j \in V} \frac{1}{d_{i j}}$ E为网络效率；N为网络节点数量；dij为节点vi与vj之间的最短路径长度，当2个节点间没有路径时dij=+∞ 最大连通子图相对大小 $ C_{\max }=\frac{n}{N}$ Cmax为最大连通子图相对大小；n为最大连通子图包含的节点数 聚类系数 $ C_i=\frac{2 e_i}{k_i\left(k_i-1\right)}$ Ci为节点vi的聚类系数; ki为节点vi的度，即vi有ki个邻居节点，则这ki个节点之间最多可能有ki(ki－1)/2条边；ei为这ki个节点之间实际存在的边数 平均聚类系数 $ \bar{C}_i=\frac{1}{N} \sum_{i=1}^N C_i$ $ \bar{C}_i$为平均聚类系数 平均最短路径长度 $ \bar{L}=\frac{2}{N(N-1)} \sum_{v_i, v_j \in V ; i \neq j} d_{i j}$ L为网络中任意2个节点vi与vj之间平均最短路径长度 
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表 2 国际基尼系数标准[31]
Table 2. Gini coefficient criterion of United Nations
基尼系数 [0, 0.2) [0.2, 0.3) [0.3, 0.4) [0.4, 0.5) [0.5, 1] 等级 绝对平均 比较平均 相对合理 差距较大 差距悬殊
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表 3 网络拓扑特性指标值
Table 3. Values of network topology characteristic indexes
参数 浙江省 云南省 公路网 铁路网 水运网 MCTN 公路网 铁路网 航空网 MCTN 节点数 106 60 62 89 142 52 15 129 边数 272 70 56 248 395 51 33 416 平均度 5.132 2.333 1.807 5.573 5.563 1.962 4.400 6.450 最大度 16 9 3 16 14 4 14 23 平均聚类系数 0.405 0.044 0.000 0.422 0.411 0.000 0.500 0.505 平均最短路径长度 5.043 7.001 8.457 4.337 5.159 8.042 1.686 3.303
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表 4 贡献度参数取值含义
Table 4. Meanings of contribution parameter values
参数取值 含义 α=0.3，β=0.7 最大连通子图相对大小贡献度较大 α=β=0.5 二者贡献度相同 α=0.7，β=0.3 网络效率贡献度较大
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表 5 站点分布均衡性
Table 5. Balance of station distribution
参数 浙江省 云南省 公路网 铁路网 水运网 公路网 铁路网 基尼系数 0.196 0.559 0.672 0.086 0.702 均衡等级 绝对平均 差距悬殊 差距悬殊 绝对平均 差距悬殊
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