Vulnerability Assessment of Urban Rail Transit Network—A Case Study of Chongqing
Abstract
:1. Introduction
2. Literature Review
3. Methodology
3.1. Selection of Topological Network Model Construction Method
3.2. Construction of the Topological Structure Model of Rail Transit Network in Chongqing
3.2.1. Model Construction
- A.
- Since the distance between the track sites is relatively close, the site spacing is assumed to be equal. Moreover, the paper only studies the topological structure of the orbit network to find the stations with strong vulnerability, instead of considering the passenger flow intensity on each line. Therefore, the network is reduced to the unauthorized network;
- B.
- Since the urban rail transit can operate in both directions between any two stations, the urban rail transit network can be considered as an undirected network;
- C.
- Some of the same stations contained in the different lines are not in the same location due to unreasonable planning or excessive terrain height difference. The paper does not consider the hierarchical structure of the urban rail transit transfer station, and regards it as the same node;
- D.
- All stations and lines in the initial network of urban rail transit are not disturbed and can operate normally;
- E.
- Once a site or line is attacked, it is considered that the site is unable to play its original function.
3.2.2. Model Building
3.3. Analysis of Topological Structure Parameters of Rail Transit Network in Chongqing
3.3.1. Node Degree
3.3.2. Aggregation Coefficient
3.3.3. Average Shortest Path Length
3.4. Rail Transit Network Vulnerability Assessment in Chongqing
3.4.1. Frailty Evaluation Index Selection and Model Construction
3.4.2. Attack Strategy
Algorithm 1. Deliberate attack code. |
f = find(A > 0); L = length(f); %The query vector length; [m, m] = size(A); % Get the number of rows and columns of the matrix; sum(sum(A))~ = 0 % For summing over the elements of each column of the matrix; [n, n] = size(A); k = sum(A); % Each column degree value; j = 1:n; C = [j, k]; % Matrix table of the degree values of each node; [order, lo] = sort(C(:,2),’descend’); % An ascending sort of the array returns the sorted array; p = lo(1); % Obtain the serial number corresponding to the node with the highest degree value; A(p,:) = []; % The node with the highest median value in the original matrix is all in the column of 0; A(:,p) = []; % The node with the highest median value in the original matrix has all rows of 0; L = length(A); % Returns the length of the largest array dimension in A; E = Network_efficiency(A); % Calculate the network efficiency after a deliberate attack. |
4. Results and Discussions
4.1. Changes in the Ratio of the Network Efficiency
4.2. Site Vulnerability
4.3. Improvement Strategy
4.3.1. Planning Principles
4.3.2. Network Optimization
5. Conclusions
5.1. Theoretical Implications
5.2. Practical Implications
5.3. Limitations and Future Research
5.3.1. Limitations
5.3.2. Future Research
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
Num. | Site | Num. | Site | Num. | Site | Num. | Site | Num. | Site |
---|---|---|---|---|---|---|---|---|---|
1 | Chongqing University | 47 | Gaomiaocun | 93 | Gongmao | 139 | Dalongshan | 185 | Hongyancun |
2 | Yudaishan | 48 | Shiqiaopu | 94 | Tongyuanju | 140 | Xingfu Square | 186 | Fuhualu |
3 | Nanqiaosi | 49 | Xietaizi | 95 | Huaxinjie | 141 | Renhe | 187 | Hualongqiao |
4 | Sports Park | 50 | Shiyoulu | 96 | Guanyinqiao | 142 | Hemulu | 188 | Lijiaping |
5 | Ranjiaba | 51 | Daping | 97 | Hongqihegou | 143 | Chongguang | 189 | Mahuangliang |
6 | Dongbu Park | 52 | Eling | 98 | Jiazhoulu | 144 | Huxiajie | 190 | Liyuchi |
7 | Honghu East Road | 53 | Lianglukou | 99 | Zhengjiayuanzi | 145 | Danhe | 191 | Liujiatai |
8 | Min’an Ave. | 54 | Qixinggang | 100 | Tangjiayuanzi | 146 | The EXPO Garden Center | 192 | Gailanxi |
9 | Chongqing North Station South Square | 55 | Jiaochangkou | 101 | Shiziping | 147 | Beibei | 193 | Cruise Home Port |
10 | Yulu | 56 | Xiaoshizi | 102 | Longtousi | 148 | Southwest University | 194 | Hejialiang |
11 | Wulidian | 57 | Chaotianmen | 103 | Tongjiayuanzi | 149 | Zhuangyuanbei | 195 | Shipanhe |
12 | Danzishi | 58 | Yudong | 104 | Jinyu | 150 | Longfengxi | 196 | Shangwanlu |
13 | Tushan | 59 | Dajiang | 105 | Jintonglu | 151 | Xiangjiagang | 197 | Qinggangping |
14 | Renji | 60 | Baijusi | 106 | Yuanyang | 152 | Caijia | 198 | Baoshenghu |
15 | Shangxinjie | 61 | Liujiaba | 107 | The EXPO Garden | 153 | Caojiawan | 199 | Xingke Ave. |
16 | Shanghao | 62 | Jinjiawan | 108 | Cuiyun | 154 | Jinshansi | 200 | Chunhua Ave. |
17 | Haitangxi | 63 | Jianqiao | 109 | Changfulu | 155 | Lijia | 201 | Langui Ave. |
18 | Luojiaba | 64 | Tiantangbao | 110 | Huixing | 156 | Jiuquhe | 202 | Center Park East |
19 | Sigongli | 65 | Xinshancun | 111 | Shuanglong | 157 | Kangzhuang | 203 | Congyansi |
20 | Nanhu | 66 | Dadukou | 112 | Bijin | 158 | Dazhulin | 204 | Huashigou |
21 | Haixialu | 67 | Ping’an | 113 | Shuangfengqiao | 159 | Guangdianyuan | 205 | Longtousi Park |
22 | Xiejiawan | 68 | Mawangchang | 114 | Jiangbei Airport Terminal 2 | 160 | Huahuiyuan | 206 | Minxinjiayuan |
23 | Olympic Sports Center Station | 69 | Dayancun | 115 | Konggang Square | 161 | Huangnibang | 207 | Sanyawan |
24 | Chenjiaping | 70 | Zoo | 116 | Gaohubao | 162 | Hongtudi | 208 | Huanshan Park |
25 | Caiyunhu | 71 | Yangjiaping | 117 | Guanyuelu | 163 | Jiangbecheng | 209 | Changhe |
26 | Erlang | 72 | Yuanjiagang | 118 | Lianhua | 164 | Grand Theater | 210 | Jiangbei Airport Terminal 3 |
27 | Hualong | 73 | Fotuguan | 119 | Jurenba | 165 | Liujiaping | 211 | Yubei Square |
28 | Chongqing West Station | 74 | Liziba | 120 | Chongqing North Station North Square | 166 | Changshengqiao | 212 | Lushan |
29 | Shangqiao | 75 | Niujiaotuo | 121 | Toutang | 167 | Qiujiawan | 213 | Central Park |
30 | Fengmingshan | 76 | Zengjiayan | 122 | Baoshuigang | 168 | Chayuan | 214 | Central Park west |
31 | Chongqing Library | 77 | Daxigou | 123 | Cuntan | 169 | Shaheba | 215 | Tieshanping |
32 | Tianxingqiao | 78 | Huanghuayuan | 124 | Heizi | 170 | Hongyanping | 216 | Luqi |
33 | Shapingba | 79 | Linjiangmen | 125 | Gangcheng | 171 | Fuxing | 217 | Guoyuan Logistics Hub |
34 | Bishan | 80 | Jinzhu | 126 | Taipingchong | 172 | Siyuan | 218 | Yuzui |
35 | Jiandingpo | 81 | Yuhulu | 127 | Tangjiatuo | 173 | Liujiayuanzi | 219 | Yanping |
36 | Daxuecheng | 82 | Xuetangwan | 128 | Tiaodeng | 174 | Qingxihe | 220 | Shiheqing |
37 | Chenjiaqiao | 83 | Dashancun | 129 | Huayan Center | 175 | Wangjiazhuang | 221 | Fusheng |
38 | Weidianyuan | 84 | Huaxi | 130 | Jinjianlu | 176 | Yuelai | 222 | Sanbanxi |
39 | Laijiaqiao | 85 | Chalukou | 131 | Zhongliangshan | 177 | International Expo Center | 223 | Longyi Ave. |
40 | Shuangbei | 86 | Jiugongli | 132 | Banshan | 178 | Gaoyikou | 224 | Longxing |
41 | Shijingpo | 87 | Linlong | 133 | Huachenglu | 179 | Huangmaoping | 225 | Gaoshita |
42 | Ciqikou | 88 | Bagongli | 134 | Huayansi | 180 | Huanlegu | 226 | Pufu |
43 | Lieshimu | 89 | Chongqing jiaotong University | 135 | Fengxilu | 181 | Xinqiao | 227 | Tongzilin |
44 | Yanggongqiao | 90 | Liugongli | 136 | Bashan | 182 | Gaotanyan | 228 | Shichuan |
45 | Xiaolongkan | 91 | Chongqing Technology and Business University | 137 | Shixinlu | 183 | Tianlilu | 229 | Huangling |
46 | Majiayan | 92 | Nanping | 138 | Dashiba | 184 | Tuwan |
Appendix B
Num. | Adjacency | Num. | Adjacency | Num. | Adjacency | Num. | Adjacency | Num. | Adjacency |
---|---|---|---|---|---|---|---|---|---|
1 | 1–2 | 51 | 31–32 | 101 | 74–75 | 151 | 121–122 | 201 | 173–174 |
2 | 1–33 | 52 | 32–33 | 102 | 75–76 | 152 | 121–192 | 202 | 174–175 |
3 | 2–3 | 53 | 33–44 | 103 | 75–95 | 153 | 122–123 | 203 | 175–176 |
4 | 3–4 | 54 | 33–45 | 104 | 76–77 | 154 | 122–193 | 204 | 176–177 |
5 | 4–5 | 55 | 33–183 | 105 | 77–78 | 155 | 123–124 | 205 | 176–214 |
6 | 5–6 | 56 | 34–35 | 106 | 78–79 | 156 | 124–125 | 206 | 177–178 |
7 | 5–139 | 57 | 35–36 | 107 | 80–81 | 157 | 125–126 | 207 | 178–179 |
8 | 5–140 | 58 | 36–37 | 108 | 81–82 | 158 | 126–127 | 208 | 179–180 |
9 | 5–159 | 59 | 37–38 | 109 | 82–83 | 159 | 127–215 | 209 | 181–182 |
10 | 6–7 | 60 | 38–39 | 110 | 83–84 | 160 | 128–129 | 210 | 182–183 |
11 | 7–8 | 61 | 39–40 | 111 | 84–85 | 161 | 129–130 | 211 | 184–185 |
12 | 8–9 | 62 | 40–41 | 112 | 85–86 | 162 | 130–131 | 212 | 185–186 |
13 | 8–120 | 63 | 41–42 | 113 | 86–87 | 163 | 131–132 | 213 | 186–187 |
14 | 9–10 | 64 | 42–43 | 114 | 87–88 | 164 | 132–133 | 214 | 187–188 |
15 | 9–101 | 65 | 43–44 | 115 | 88–89 | 165 | 133–134 | 215 | 188–189 |
16 | 9–102 | 66 | 45–46 | 116 | 89–90 | 166 | 135–136 | 216 | 190–191 |
17 | 9–120 | 67 | 45–184 | 117 | 90–91 | 167 | 136–137 | 217 | 193–194 |
18 | 9–205 | 68 | 46–47 | 118 | 92–93 | 168 | 138–139 | 218 | 194–195 |
19 | 10–11 | 69 | 47–48 | 119 | 93–94 | 169 | 139–160 | 219 | 195–196 |
20 | 11–12 | 70 | 48–49 | 120 | 95–96 | 170 | 140–141 | 220 | 196–197 |
21 | 11–162 | 71 | 48–137 | 121 | 96–97 | 171 | 141–142 | 221 | 196–207 |
22 | 11–163 | 72 | 49–50 | 122 | 96–189 | 172 | 142–143 | 222 | 196–208 |
23 | 11–192 | 73 | 50–51 | 123 | 96–190 | 173 | 143–144 | 223 | 197–198 |
24 | 12–13 | 74 | 51–52 | 124 | 97–98 | 174 | 144–145 | 224 | 198–199 |
25 | 13–14 | 75 | 51–72 | 125 | 97–160 | 175 | 145–146 | 225 | 199–200 |
26 | 14–15 | 76 | 51–73 | 126 | 97–161 | 176 | 147–148 | 226 | 200–201 |
27 | 15–16 | 77 | 52–53 | 127 | 98–99 | 177 | 148–149 | 227 | 201–202 |
28 | 15–56 | 78 | 53–54 | 128 | 99–100 | 178 | 149–150 | 228 | 202–203 |
29 | 15–165 | 79 | 53–75 | 129 | 100–101 | 179 | 150–151 | 229 | 202–212 |
30 | 16–17 | 80 | 53–94 | 130 | 102–103 | 180 | 151–152 | 230 | 202–213 |
31 | 17–18 | 81 | 54–55 | 131 | 103–104 | 181 | 152–153 | 231 | 203–204 |
32 | 18–19 | 82 | 55–56 | 132 | 104–105 | 182 | 153–154 | 232 | 206–207 |
33 | 19–20 | 83 | 55–79 | 133 | 105–106 | 183 | 154–155 | 233 | 208–209 |
34 | 19–91 | 84 | 56–57 | 134 | 106–107 | 184 | 155–156 | 234 | 209–210 |
35 | 19–92 | 85 | 56–164 | 135 | 107–108 | 185 | 155–180 | 235 | 211–212 |
36 | 20–21 | 86 | 58–59 | 136 | 108–109 | 186 | 156–157 | 236 | 213–214 |
37 | 21–22 | 87 | 58–80 | 137 | 109–110 | 187 | 157–158 | 237 | 215–216 |
38 | 22–23 | 88 | 59–60 | 138 | 110–111 | 188 | 158–159 | 238 | 216–217 |
39 | 22–71 | 89 | 60–61 | 139 | 111–112 | 189 | 161–162 | 239 | 217–218 |
40 | 22–72 | 90 | 61–62 | 140 | 112–113 | 190 | 162–190 | 240 | 218–219 |
41 | 23–24 | 91 | 62–63 | 141 | 112–114 | 191 | 162–205 | 241 | 219–220 |
42 | 24–25 | 92 | 63–64 | 142 | 113–115 | 192 | 163–164 | 242 | 220–221 |
43 | 25–26 | 93 | 64–65 | 143 | 114–210 | 193 | 163–191 | 243 | 221–222 |
44 | 26–27 | 94 | 65–66 | 144 | 114–211 | 194 | 165–166 | 244 | 222–223 |
45 | 27–28 | 95 | 66–67 | 145 | 115–116 | 195 | 166–167 | 245 | 223–224 |
46 | 28–29 | 96 | 67–68 | 146 | 116–117 | 196 | 167–168 | 246 | 224–225 |
47 | 28–134 | 97 | 68–69 | 147 | 117–118 | 197 | 169–170 | 247 | 225–226 |
48 | 28–135 | 98 | 69–70 | 148 | 118–119 | 198 | 170–171 | 248 | 226–227 |
49 | 29–30 | 99 | 70–71 | 149 | 120–121 | 199 | 171–172 | 249 | 227–228 |
50 | 30–31 | 100 | 73–74 | 150 | 120–206 | 200 | 172–173 | 250 | 228–229 |
Appendix C
Ranking | Num. | Network Efficiency | Vulnerability | Decline Ratio | Ranking | Num. | Network Efficiency | Vulnerability | Decline Ratio |
---|---|---|---|---|---|---|---|---|---|
1 | 2 | 0.0894 | 0.0107 | 10.69% | 116 | 83 | 0.0992 | 0.0009 | 0.90% |
2 | 4 | 0.0902 | 0.0099 | 9.89% | 117 | 130 | 0.0992 | 0.0009 | 0.90% |
3 | 26 | 0.0909 | 0.0092 | 9.19% | 118 | 29 | 0.0992 | 0.0009 | 0.90% |
4 | 33 | 0.092 | 0.0081 | 8.09% | 119 | 199 | 0.0993 | 0.0008 | 0.80% |
5 | 205 | 0.0928 | 0.0073 | 7.29% | 120 | 188 | 0.0993 | 0.0008 | 0.80% |
6 | 8 | 0.0934 | 0.0067 | 6.69% | 121 | 184 | 0.0993 | 0.0008 | 0.80% |
7 | 5 | 0.094 | 0.0061 | 6.09% | 122 | 109 | 0.0993 | 0.0008 | 0.80% |
8 | 134 | 0.0945 | 0.0056 | 5.59% | 123 | 69 | 0.0993 | 0.0008 | 0.80% |
9 | 28 | 0.0945 | 0.0056 | 5.59% | 124 | 68 | 0.0993 | 0.0008 | 0.80% |
10 | 67 | 0.0948 | 0.0053 | 5.29% | 125 | 56 | 0.0993 | 0.0008 | 0.80% |
11 | 122 | 0.095 | 0.0051 | 5.09% | 126 | 49 | 0.0993 | 0.0008 | 0.80% |
12 | 17 | 0.0955 | 0.0046 | 4.60% | 127 | 181 | 0.0994 | 0.0007 | 0.70% |
13 | 66 | 0.0956 | 0.0045 | 4.50% | 128 | 151 | 0.0994 | 0.0007 | 0.70% |
14 | 23 | 0.0957 | 0.0044 | 4.40% | 129 | 136 | 0.0994 | 0.0007 | 0.70% |
15 | 6 | 0.0959 | 0.0042 | 4.20% | 130 | 128 | 0.0994 | 0.0007 | 0.70% |
16 | 30 | 0.0959 | 0.0042 | 4.20% | 131 | 118 | 0.0994 | 0.0007 | 0.70% |
17 | 7 | 0.0959 | 0.0042 | 4.20% | 132 | 82 | 0.0994 | 0.0007 | 0.70% |
18 | 206 | 0.096 | 0.0041 | 4.10% | 133 | 73 | 0.0994 | 0.0007 | 0.70% |
19 | 15 | 0.0961 | 0.0040 | 4.00% | 134 | 48 | 0.0994 | 0.0007 | 0.70% |
20 | 160 | 0.0963 | 0.0038 | 3.80% | 135 | 47 | 0.0994 | 0.0007 | 0.70% |
21 | 65 | 0.0963 | 0.0038 | 3.80% | 136 | 39 | 0.0994 | 0.0007 | 0.70% |
22 | 1 | 0.0963 | 0.0038 | 3.80% | 137 | 215 | 0.0995 | 0.0006 | 0.60% |
23 | 207 | 0.0964 | 0.0037 | 3.70% | 138 | 201 | 0.0995 | 0.0006 | 0.60% |
24 | 13 | 0.0964 | 0.0037 | 3.70% | 139 | 200 | 0.0995 | 0.0006 | 0.60% |
25 | 156 | 0.0965 | 0.0036 | 3.60% | 140 | 194 | 0.0995 | 0.0006 | 0.60% |
26 | 132 | 0.0965 | 0.0036 | 3.60% | 141 | 169 | 0.0995 | 0.0006 | 0.60% |
27 | 144 | 0.0966 | 0.0035 | 3.50% | 142 | 168 | 0.0995 | 0.0006 | 0.60% |
28 | 208 | 0.0968 | 0.0033 | 3.30% | 143 | 163 | 0.0995 | 0.0006 | 0.60% |
29 | 159 | 0.0968 | 0.0033 | 3.30% | 144 | 101 | 0.0995 | 0.0006 | 0.60% |
30 | 145 | 0.0968 | 0.0033 | 3.30% | 145 | 72 | 0.0995 | 0.0006 | 0.60% |
31 | 64 | 0.0969 | 0.0032 | 3.20% | 146 | 59 | 0.0995 | 0.0006 | 0.60% |
32 | 140 | 0.097 | 0.0031 | 3.10% | 147 | 55 | 0.0995 | 0.0006 | 0.60% |
33 | 131 | 0.097 | 0.0031 | 3.10% | 148 | 54 | 0.0995 | 0.0006 | 0.60% |
34 | 158 | 0.0971 | 0.0030 | 3.00% | 149 | 46 | 0.0995 | 0.0006 | 0.60% |
35 | 209 | 0.0972 | 0.0029 | 2.90% | 150 | 45 | 0.0995 | 0.0006 | 0.60% |
36 | 155 | 0.0972 | 0.0029 | 2.90% | 151 | 193 | 0.0996 | 0.0005 | 0.50% |
37 | 133 | 0.0972 | 0.0029 | 2.90% | 152 | 189 | 0.0996 | 0.0005 | 0.50% |
38 | 174 | 0.0973 | 0.0028 | 2.80% | 153 | 180 | 0.0996 | 0.0005 | 0.50% |
39 | 157 | 0.0974 | 0.0027 | 2.70% | 154 | 177 | 0.0996 | 0.0005 | 0.50% |
40 | 25 | 0.0974 | 0.0027 | 2.70% | 155 | 166 | 0.0996 | 0.0005 | 0.50% |
41 | 63 | 0.0975 | 0.0026 | 2.60% | 156 | 114 | 0.0996 | 0.0005 | 0.50% |
42 | 42 | 0.0975 | 0.0026 | 2.60% | 157 | 108 | 0.0996 | 0.0005 | 0.50% |
43 | 12 | 0.0975 | 0.0026 | 2.60% | 158 | 107 | 0.0996 | 0.0005 | 0.50% |
44 | 9 | 0.0975 | 0.0026 | 2.60% | 159 | 81 | 0.0996 | 0.0005 | 0.50% |
45 | 210 | 0.0976 | 0.0025 | 2.50% | 160 | 50 | 0.0996 | 0.0005 | 0.50% |
46 | 146 | 0.0976 | 0.0025 | 2.50% | 161 | 36 | 0.0996 | 0.0005 | 0.50% |
47 | 123 | 0.0976 | 0.0025 | 2.50% | 162 | 40 | 0.0996 | 0.0005 | 0.50% |
48 | 87 | 0.0976 | 0.0025 | 2.50% | 163 | 185 | 0.0997 | 0.0004 | 0.40% |
49 | 18 | 0.0976 | 0.0025 | 2.50% | 164 | 179 | 0.0997 | 0.0004 | 0.40% |
50 | 139 | 0.0977 | 0.0024 | 2.40% | 165 | 178 | 0.0997 | 0.0004 | 0.40% |
51 | 106 | 0.0977 | 0.0024 | 2.40% | 166 | 162 | 0.0997 | 0.0004 | 0.40% |
52 | 27 | 0.0977 | 0.0024 | 2.40% | 167 | 149 | 0.0997 | 0.0004 | 0.40% |
53 | 3 | 0.0977 | 0.0024 | 2.40% | 168 | 119 | 0.0997 | 0.0004 | 0.40% |
54 | 154 | 0.0978 | 0.0023 | 2.30% | 169 | 111 | 0.0997 | 0.0004 | 0.40% |
55 | 41 | 0.0978 | 0.0023 | 2.30% | 170 | 100 | 0.0997 | 0.0004 | 0.40% |
56 | 173 | 0.0979 | 0.0022 | 2.20% | 171 | 53 | 0.0997 | 0.0004 | 0.40% |
57 | 175 | 0.0979 | 0.0022 | 2.20% | 172 | 52 | 0.0997 | 0.0004 | 0.40% |
58 | 110 | 0.0979 | 0.0022 | 2.20% | 173 | 51 | 0.0997 | 0.0004 | 0.40% |
59 | 121 | 0.0979 | 0.0022 | 2.20% | 174 | 216 | 0.0998 | 0.0003 | 0.30% |
60 | 34 | 0.0979 | 0.0022 | 2.20% | 175 | 192 | 0.0998 | 0.0003 | 0.30% |
61 | 14 | 0.0979 | 0.0022 | 2.20% | 176 | 191 | 0.0998 | 0.0003 | 0.30% |
62 | 211 | 0.098 | 0.0021 | 2.10% | 177 | 190 | 0.0998 | 0.0003 | 0.30% |
63 | 164 | 0.098 | 0.0021 | 2.10% | 178 | 187 | 0.0998 | 0.0003 | 0.30% |
64 | 62 | 0.098 | 0.0021 | 2.10% | 179 | 182 | 0.0998 | 0.0003 | 0.30% |
65 | 115 | 0.0981 | 0.0020 | 2.00% | 180 | 143 | 0.0998 | 0.0003 | 0.30% |
66 | 86 | 0.0981 | 0.0020 | 2.00% | 181 | 126 | 0.0998 | 0.0003 | 0.30% |
67 | 19 | 0.0981 | 0.0020 | 2.00% | 182 | 120 | 0.0998 | 0.0003 | 0.30% |
68 | 11 | 0.0981 | 0.0020 | 2.00% | 183 | 99 | 0.0998 | 0.0003 | 0.30% |
69 | 124 | 0.0982 | 0.0019 | 1.90% | 184 | 91 | 0.0998 | 0.0003 | 0.30% |
70 | 105 | 0.0982 | 0.0019 | 1.90% | 185 | 90 | 0.0998 | 0.0003 | 0.30% |
71 | 10 | 0.0982 | 0.0019 | 1.90% | 186 | 80 | 0.0998 | 0.0003 | 0.30% |
72 | 138 | 0.0983 | 0.0018 | 1.80% | 187 | 38 | 0.0998 | 0.0003 | 0.30% |
73 | 44 | 0.0983 | 0.0018 | 1.80% | 188 | 37 | 0.0998 | 0.0003 | 0.30% |
74 | 43 | 0.0983 | 0.0018 | 1.80% | 189 | 186 | 0.0999 | 0.0002 | 0.20% |
75 | 212 | 0.0984 | 0.0017 | 1.70% | 190 | 142 | 0.0999 | 0.0002 | 0.20% |
76 | 170 | 0.0984 | 0.0017 | 1.70% | 191 | 141 | 0.0999 | 0.0002 | 0.20% |
77 | 153 | 0.0984 | 0.0017 | 1.70% | 192 | 135 | 0.0999 | 0.0002 | 0.20% |
78 | 147 | 0.0984 | 0.0017 | 1.70% | 193 | 129 | 0.0999 | 0.0002 | 0.20% |
79 | 161 | 0.0985 | 0.0016 | 1.60% | 194 | 125 | 0.0999 | 0.0002 | 0.20% |
80 | 85 | 0.0985 | 0.0016 | 1.60% | 195 | 204 | 0.0999 | 0.0002 | 0.20% |
81 | 61 | 0.0985 | 0.0016 | 1.60% | 196 | 35 | 0.0999 | 0.0002 | 0.20% |
82 | 32 | 0.0985 | 0.0016 | 1.60% | 197 | 117 | 0.0999 | 0.0002 | 0.20% |
83 | 24 | 0.0985 | 0.0016 | 1.60% | 198 | 116 | 0.0999 | 0.0002 | 0.20% |
84 | 20 | 0.0985 | 0.0016 | 1.60% | 199 | 94 | 0.0999 | 0.0002 | 0.20% |
85 | 176 | 0.0986 | 0.0015 | 1.50% | 200 | 89 | 0.0999 | 0.0002 | 0.20% |
86 | 104 | 0.0986 | 0.0015 | 1.50% | 201 | 79 | 0.0999 | 0.0002 | 0.20% |
87 | 213 | 0.0987 | 0.0014 | 1.40% | 202 | 222 | 0.1 | 0.0001 | 0.10% |
88 | 195 | 0.0987 | 0.0014 | 1.40% | 203 | 219 | 0.1 | 0.0001 | 0.10% |
89 | 112 | 0.0987 | 0.0014 | 1.40% | 204 | 167 | 0.1 | 0.0001 | 0.10% |
90 | 165 | 0.0988 | 0.0013 | 1.30% | 205 | 150 | 0.1 | 0.0001 | 0.10% |
91 | 137 | 0.0988 | 0.0013 | 1.30% | 206 | 98 | 0.1 | 0.0001 | 0.10% |
92 | 127 | 0.0988 | 0.0013 | 1.30% | 207 | 93 | 0.1 | 0.0001 | 0.10% |
93 | 88 | 0.0988 | 0.0013 | 1.30% | 208 | 92 | 0.1 | 0.0001 | 0.10% |
94 | 31 | 0.0988 | 0.0013 | 1.30% | 209 | 58 | 0.1 | 0.0001 | 0.10% |
95 | 21 | 0.0988 | 0.0013 | 1.30% | 210 | 97 | 0.1001 | 0.0000 | 0.00% |
96 | 16 | 0.0988 | 0.0013 | 1.30% | 211 | 96 | 0.1001 | 0.0000 | 0.00% |
97 | 196 | 0.0989 | 0.0012 | 1.20% | 212 | 95 | 0.1001 | 0.0000 | 0.00% |
98 | 183 | 0.0989 | 0.0012 | 1.20% | 213 | 78 | 0.1001 | 0.0000 | 0.00% |
99 | 171 | 0.0989 | 0.0012 | 1.20% | 214 | 77 | 0.1001 | 0.0000 | 0.00% |
100 | 152 | 0.0989 | 0.0012 | 1.20% | 215 | 76 | 0.1001 | 0.0000 | 0.00% |
101 | 103 | 0.0989 | 0.0012 | 1.20% | 216 | 75 | 0.1001 | 0.0000 | 0.00% |
102 | 84 | 0.0989 | 0.0012 | 1.20% | 217 | 74 | 0.1001 | 0.0000 | 0.00% |
103 | 71 | 0.0989 | 0.0012 | 1.20% | 218 | 217 | 0.1001 | 0.0000 | 0.00% |
104 | 203 | 0.099 | 0.0011 | 1.10% | 219 | 172 | 0.1001 | 0.0000 | 0.00% |
105 | 202 | 0.099 | 0.0011 | 1.10% | 220 | 228 | 0.1001 | 0.0000 | 0.00% |
106 | 197 | 0.099 | 0.0011 | 1.10% | 221 | 227 | 0.1001 | 0.0000 | 0.00% |
107 | 60 | 0.099 | 0.0011 | 1.10% | 222 | 225 | 0.1001 | 0.0000 | 0.00% |
108 | 214 | 0.0991 | 0.0010 | 1.00% | 223 | 223 | 0.1001 | 0.0000 | 0.00% |
109 | 148 | 0.0991 | 0.0010 | 1.00% | 224 | 226 | 0.1001 | 0.0000 | 0.00% |
110 | 113 | 0.0991 | 0.0010 | 1.00% | 225 | 224 | 0.1001 | 0.0000 | 0.00% |
111 | 70 | 0.0991 | 0.0010 | 1.00% | 226 | 221 | 0.1001 | 0.0000 | 0.00% |
112 | 57 | 0.0991 | 0.0010 | 1.00% | 227 | 220 | 0.1001 | 0.0000 | 0.00% |
113 | 22 | 0.0991 | 0.0010 | 1.00% | 228 | 218 | 0.1001 | 0.0000 | 0.00% |
114 | 198 | 0.0992 | 0.0009 | 0.90% | 229 | 229 | 0.1001 | 0.0000 | 0.00% |
115 | 102 | 0.0992 | 0.0009 | 0.90% |
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The Initial Network | After Suffering From a Node Attack | After Suffering From the Edge Attack | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N1 | N2 | N3 | N4 | N5 | N1 | N2 | N3 | N4 | N5 | N1 | N2 | N3 | N4 | N5 | |||
N1 | 0 | 1 | 1 | 0 | 0 | N1 | 0 | 0 | 1 | 0 | 0 | N1 | 0 | 0 | 1 | 0 | 0 |
N2 | 1 | 0 | 1 | 0 | 0 | N2 | 0 | 0 | 0 | 0 | 0 | N2 | 0 | 0 | 1 | 0 | 0 |
N3 | 1 | 1 | 0 | 1 | 1 | N3 | 1 | 0 | 0 | 1 | 1 | N3 | 1 | 1 | 0 | 1 | 1 |
N4 | 0 | 0 | 1 | 0 | 1 | N4 | 0 | 0 | 1 | 0 | 1 | N4 | 0 | 0 | 1 | 0 | 1 |
N5 | 0 | 0 | 1 | 1 | 0 | N5 | 0 | 0 | 1 | 1 | 0 | N5 | 0 | 0 | 1 | 1 | 0 |
Number | Site | Network Efficiency | Vulnerability | Decline Ratio |
---|---|---|---|---|
2 | Yudaishan | 0.0894 | 0.0107 | 10.69% |
4 | Sports Park | 0.0902 | 0.0099 | 9.89% |
26 | Erlang | 0.0909 | 0.0092 | 9.19% |
33 | Shapingba | 0.092 | 0.0081 | 8.09% |
205 | Longtousi Park | 0.0928 | 0.0073 | 7.29% |
8 | Min’an Ave | 0.0934 | 0.0067 | 6.69% |
5 | Ranjiaba | 0.094 | 0.0061 | 6.09% |
134 | Huayansi | 0.0945 | 0.0056 | 5.59% |
28 | Chonogqing West Station | 0.0945 | 0.0056 | 5.59% |
67 | Ping’an | 0.0948 | 0.0053 | 5.29% |
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Xu, L.; Xiang, P.; Qian, Y.; Yang, S.; Zhou, T.; Wang, F. Vulnerability Assessment of Urban Rail Transit Network—A Case Study of Chongqing. Buildings 2025, 15, 170. https://doi.org/10.3390/buildings15020170
Xu L, Xiang P, Qian Y, Yang S, Zhou T, Wang F. Vulnerability Assessment of Urban Rail Transit Network—A Case Study of Chongqing. Buildings. 2025; 15(2):170. https://doi.org/10.3390/buildings15020170
Chicago/Turabian StyleXu, Lan, Pengcheng Xiang, Yan Qian, Simai Yang, Tao Zhou, and Feng Wang. 2025. "Vulnerability Assessment of Urban Rail Transit Network—A Case Study of Chongqing" Buildings 15, no. 2: 170. https://doi.org/10.3390/buildings15020170
APA StyleXu, L., Xiang, P., Qian, Y., Yang, S., Zhou, T., & Wang, F. (2025). Vulnerability Assessment of Urban Rail Transit Network—A Case Study of Chongqing. Buildings, 15(2), 170. https://doi.org/10.3390/buildings15020170