# Resilience Analysis of Container Port Shipping Network Structure: The Case of China

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## Abstract

**:**

## 1. Introduction

## 2. Resilience Framework of CPSN

- (1).
- Prevention state (t(0) ≤ t ≤ t(d))

- (2).
- Resistance state (t(d) ≤ t ≤ t(r))

- (3).
- Restoration state(t(r) ≤t ≤ t(ns))

- (4).
- Adaption and optimization state(t ≥ t(ns))

## 3. Materials and Methods

#### 3.1. Study Area and Data

#### 3.2. Methods

- (1)
- Degree and degree distribution

_{i}is the degree of node i; K

_{i}* indicates the ranking of degree of node i in the network; C is constant; a is the slope of the degree distribution.

- (2)
- Betweenness

_{j}and V

_{l}in the network will pass through some nodes. If many other shortest paths pass node V

_{i}, it means that the node is essentially important in the network, and its importance or influence can be characterized by the node’s betweenness B

_{i}[28].

_{jl}is the number of shortest paths between nodes V

_{j}and V

_{l}, and n

_{jl}(i) is the number of shortest paths between nodes V

_{j}and V

_{l}through node V

_{i}in the unweighted network.

- (3)
- Strength

_{i}is the sum of edge weights associated with node i. The formula is as follows [13]:

_{i}is the set of adjacent points with node V

_{i}, and w

_{ij}is the number of shipping routes between nodes V

_{i}and V

_{j}in the weighted CCPSN.

- (4)
- Clustering coefficient

_{i}and global clustering coefficient C. Global clustering coefficient C is the average local clustering coefficient of all nodes in the network. The clusters in the shipping network can be measured according to the network clustering coefficient. The more significant value of the clustering coefficient of the port network refers to the closer connections among nodes in the network, and it is easy for these nodes to form a closed thinking habit. The formula is as follows [28]:

_{i}is the local clustering coefficient of node i, and E

_{i}is the actual number of edges between the neighbors of node i. N is the number of nodes in the network.

- (5)
- Network efficiency

_{ij}is the shortest path between node i and node j in the unweighted network.

- (6)
- Network independent path

_{(G)}is the average number of independent paths; n

_{ij}is the number of independent paths between nodes i and j in the unweighted network.

- (7)
- Network connectivity

- (8)
- Resilience index

#### 3.3. Degree, Betweenness, and Strength of Nodes

## 4. Results

#### 4.1. Prevention State

#### 4.2. Resistance State

#### 4.3. Recovery State

#### 4.4. Adaption and Optimization State

- (1).
- Optimization strategy

- (2).
- Recovery strategy

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**MDPI and ACS Style**

He, Y.; Yang, Y.; Wang, M.; Zhang, X.
Resilience Analysis of Container Port Shipping Network Structure: The Case of China. *Sustainability* **2022**, *14*, 9489.
https://doi.org/10.3390/su14159489

**AMA Style**

He Y, Yang Y, Wang M, Zhang X.
Resilience Analysis of Container Port Shipping Network Structure: The Case of China. *Sustainability*. 2022; 14(15):9489.
https://doi.org/10.3390/su14159489

**Chicago/Turabian Style**

He, Yao, Yongchun Yang, Meimei Wang, and Xudong Zhang.
2022. "Resilience Analysis of Container Port Shipping Network Structure: The Case of China" *Sustainability* 14, no. 15: 9489.
https://doi.org/10.3390/su14159489