Dynamic Evolution Analysis of Complex Topology and Node Importance in Shenzhen Metro Network from 2004 to 2021
Abstract
:1. Introduction
2. Methodology
2.1. Complex Topology Modeling of Metro Network
2.2. Statistical Measurement of Node Centrality
2.3. Identification and Ranking of Node Importance
3. Numerical Analysis and Discussions
3.1. Dynamic Evolution Analysis of Network Topology
3.2. Dynamic Evolution Analysis of Node Centrality
3.3. Dynamic Evolution Analysis of Node Importance
4. Conclusions and Future Work
- (1)
- With the spatiotemporal evolution of the network, the SZMN gradually developed from a loop network to a tree network after 2011, and the number of loops grew linearly. The nodes in the SZMN became more and more intensive. Moreover, the proportion of low-degree nodes declined gradually, and the small-world effect was increasingly weakened. For the information transmission between nodes, the global efficiency decreased over time, but the local efficiency became higher. The fault-tolerant ability of the SZMN became stronger and the network became more and more assortative;
- (2)
- The proportion of high-degree nodes gradually increased, and the scale-free and heterogeneous characteristics of the SZMN become more and more obvious. The nodes with high ECs tended to form the core areas of the network. The nodes with high BCs in each period are all multiline transfer stations, and their control over the physical network is stronger. The three new lines that opened in 2016 (L-11/7/9) had a significant impact on the network topology. The CCs of all the nodes had the same overall development trend over time. Generally, the DCs, BCs and PRs of the transfer stations in the network were usually at a higher level, which should be focused on management to prevent the vulnerability caused by deliberate attack. The shortest travel distance from one node to others became shorter with the network development, and the evolution trend tended to be reasonable;
- (3)
- In the node-importance evaluation, the multi-attribute decision-making method is better than a single attribute. The EC occupies the highest influence weight of the five indicators. With the evolution over time, the node importance of the SZMN gradually dispersed from the core area of Chegongmiao–Futian to the direction of the Airport and Shenzhen North (high-speed railway station). So far, the network development trend looks rational, and it can avoid the vulnerability caused by deliberate attack. Moreover, the node importance is closely related to the changes in the node type, surrounding nodes and network environment. Thus, we should consider the spatiotemporal development trend of the network and the changes in the importance of adjacent nodes when evaluating the metro node importance.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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No. | Periods | Existing Lines |
---|---|---|
1 | 2004 | L-1/4 |
2 | 2009 | L-1/4 |
3 | 2010 | L-1/2/3/4 |
4 | 2011 | L-1/2/3/4/5 |
5 | 2016 | L-1/2/3/4/5/7/9/11 |
6 | 2019 | L-1/2/3/4/5/7/9/11 |
7 | 2020 | L-1/2/3/4/5/6/7/8/9/10/11 |
8 | 2021 | L-1/2/3/4/5/6/7/8/9/10/11/20 |
Index | Definition | Formula |
---|---|---|
[28] | measures the total number of connected edges of a node. | |
[8,28] | can identify the different effects of neighbor ones on a node on it. | |
[29] | is the shortest number of paths through a node. | |
[29] | is used to measure the ability of a station to affect another node through the network. | |
[30] | is used to calculate the ranking of nodes in a graph based on the structure of incoming links. |
Period | N | E | L | β | γ | APL | D | ρ | |||
---|---|---|---|---|---|---|---|---|---|---|---|
2004 | 18 | 17 | 2 | 0.944 | 1 | 5.19 | 14 | 0.1111 | 0 | 0.3179 | −0.2289 |
2009 | 22 | 21 | 2 | 0.955 | 1 | 6.16 | 17 | 0.0909 | 0 | 0.2799 | −0.0194 |
2010 | 49 | 47 | 4 | 0.959 | 2 | — | — | 0.0400 | 0 | 0.1281 | −0.0066 |
2011 | 118 | 126 | 5 | 1.068 | 13 | 13.62 | 43 | 0.0183 | 0.0042 | 0.1239 | 0.1534 |
2016 | 166 | 190 | 8 | 1.145 | 32 | 11.64 | 43 | 0.0139 | 0.0026 | 0.1323 | −0.0431 |
2019 | 181 | 207 | 8 | 1.144 | 34 | 11.70 | 43 | 0.0127 | 0.0024 | 0.1292 | −0.0283 |
2020 | 236 | 271 | 11 | 1.148 | 46 | 13.60 | 42 | 0.0098 | 0.0037 | 0.1110 | 0.0603 |
2021 | 240 | 275 | 12 | 1.146 | 47 | 13.70 | 42 | 0.0096 | 0.0036 | 0.1099 | 0.0608 |
Period | |||||
---|---|---|---|---|---|
2004 | 0.1111 | 0.1763 | 0.2618 | 0.2036 | 0.0556 |
2009 | 0.0909 | 0.1475 | 0.2580 | 0.1715 | 0.0455 |
2010 | 0.0400 | — | 0.0854 | 0.0719 | 0.0204 |
2011 | 0.0183 | 0.0328 | 0.1088 | 0.0771 | 0.0085 |
2016 | 0.0139 | 0.0315 | 0.0649 | 0.0915 | 0.0060 |
2019 | 0.0127 | 0.0294 | 0.0598 | 0.0908 | 0.0055 |
2020 | 0.0098 | 0.0248 | 0.0538 | 0.0783 | 0.0042 |
2021 | 0.0096 | 0.0244 | 0.0534 | 0.0776 | 0.0042 |
DC | EC | BC | CC | PR | |
---|---|---|---|---|---|
2004 | 0.139 | 0.353 | 0.303 | 0.09 | 0.116 |
2009 | 0.121 | 0.404 | 0.29 | 0.087 | 0.098 |
2010 | 0.155 | — | 0.569 | 0.152 | 0.125 |
2011 | 0.077 | 0.65 | 0.166 | 0.049 | 0.057 |
2016 | 0.094 | 0.527 | 0.257 | 0.052 | 0.07 |
2019 | 0.09 | 0.521 | 0.274 | 0.049 | 0.067 |
2020 | 0.088 | 0.553 | 0.245 | 0.053 | 0.062 |
2021 | 0.087 | 0.551 | 0.249 | 0.052 | 0.061 |
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Meng, Y.; Qi, Q.; Liu, J.; Zhou, W. Dynamic Evolution Analysis of Complex Topology and Node Importance in Shenzhen Metro Network from 2004 to 2021. Sustainability 2022, 14, 7234. https://doi.org/10.3390/su14127234
Meng Y, Qi Q, Liu J, Zhou W. Dynamic Evolution Analysis of Complex Topology and Node Importance in Shenzhen Metro Network from 2004 to 2021. Sustainability. 2022; 14(12):7234. https://doi.org/10.3390/su14127234
Chicago/Turabian StyleMeng, Yangyang, Qingjie Qi, Jianzhong Liu, and Wei Zhou. 2022. "Dynamic Evolution Analysis of Complex Topology and Node Importance in Shenzhen Metro Network from 2004 to 2021" Sustainability 14, no. 12: 7234. https://doi.org/10.3390/su14127234