# Study on the Evolution of Multiple Network Resilience of Urban Agglomerations in the Yellow River Basin

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Study Area, Data, and Methods

#### 3.1. Study Area

#### 3.2. Data Source and Processing

#### 3.3. Research Methodology and Model Design

#### 3.3.1. Network Correlation Test Method

#### Maximum Inter-Class Difference Method

_{0}and 𝑁

_{1}, and the proportion of the number of matrices are 𝜔

_{0}and 𝜔

_{1}. The average grayscale is 𝜇

_{0}, and 𝜇

_{1.}The average grayscale of the total matrix is 𝜇, the threshold t0, t1, where the maximum interclass difference can be expressed by determining the g maximum interclass difference as follows.

_{0}𝜔

_{1}(𝜇

_{0}− 𝜇

_{1})

^{2}

#### Quadratic Assignment Procedure (QAP)

#### 3.3.2. Network Toughness Evolutionary Evaluation Model

#### Network Performance Measurement Index

^{∗}is the node 𝑖, the ranking of the nodes, and 𝑎 is the slope of the curve and is a negative number. Taking logarithms of both sides of Equation (2) simultaneously yields Equation (3), which means that the logarithm of the network node degree is linearly correlated with the logarithm of the city order.

#### Network Toughness Evolution Evaluation Method

## 4. Multiple Network Toughness Characteristics Analysis

#### 4.1. Hierarchy

#### 4.2. Matching

#### 4.3. Transportability

#### 4.4. Aggregation

## 5. Evolutionary Assessment of Network Resilience

#### 5.1. Network Type Determination

#### 5.2. Toughness Evolution Level

## 6. Multi-City Network Resilience Optimization Path

#### 6.1. Consolidate Core City Status

#### 6.2. Optimize the Structure of the Multi-City Network

#### 6.3. Optimize Factor Flow

## 7. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Distribution of multiple network degrees in the Yellow River basin during the study period. The red line indicates the fitted line, the blue dot indicates the node city, the horizontal coordinate indicates the bit order of the node degree after taking the log, and the vertical coordinate indicates the degree of the node after taking the log.

**Figure 5.**Spatial distribution of multiple network degree values in the Yellow River Basin urban agglomeration.

**Figure 6.**Multiple network degree correlation coefficients in the Yellow River basin during the study period. The red line indicates the fitted line, the blue dot indicates the node city, the horizontal coordinate indicates the degree of the node, and the vertical coordinate indicates the degree of the node’s neighbors.

**Figure 7.**Multiple network proximity correlation coefficients in the Yellow River basin during the study period. The red line indicates the fitted line, the blue dots indicate the node cities, the horizontal coordinates indicate the closeness centrality of the nodes, and the vertical coordinates indicate the closeness centrality of the node neighbors.

Urban Network 2014 | Transportation | Financial | Information | Innovation |

Transportation | —— | 0.3 *** | 0.223 *** | 0.413 *** |

Financial | 0.3 *** | —— | 0.282 *** | 0.545 *** |

Information | 0.223 *** | 0.282 *** | —— | 0.415 *** |

Innovation | 0.413 *** | 0.545 *** | 0.415 *** | —— |

Urban Network 2021 | Transportation | Financial | Information | Innovation |

Transportation | —— | 0.545 *** | 0.291 *** | 0.282 *** |

Financial | 0.545 *** | —— | 0.402 *** | 0.415 *** |

Information | 0.291 *** | 0.402 *** | —— | 0.212 *** |

Innovation | 0.282 *** | 0.415 *** | 0.212 *** | —— |

Year | Network Types | Average Shortest Path Length | Average Cluster Coefficient |
---|---|---|---|

2014 | Transportation | 1.59 | 0.758 |

Financial | 1 | 1 | |

Information | 1.06 | 0.96 | |

Innovation | 2.57 | 0.6 | |

2021 | Transportation | 1.53 | 0.761 |

Financial | 1 | 1 | |

Information | 1.95 | 0.84 | |

Innovation | 1.91 | 0.81 |

Transportation | Financial | Information | Innovation | |||||
---|---|---|---|---|---|---|---|---|

Coefficient | 2014 | 2021 | 2014 | 2021 | 2014 | 2021 | 2014 | 2021 |

a | −0.736 | −1.271 | −1.185 | −0.863 | −1.245 | −1.154 | −1.563 | −1.325 |

b | 4.819 | 6.751 | −37.03 | −24.05 | 5.743 | −1.965 | 2.563 | 5.472 |

c | −7.238 | −3.909 | −5.53 | −4.700 | −3.592 | −4.109 | −0.025 | −7.951 |

Coefficient | Transportation | Financial | Information | Innovation |
---|---|---|---|---|

Δ|a| | 0.5349 | −0.3222 | 2.399 | −0.238 |

Δb | 1.9328 | 12.9786 | −7.7077 | 2.9091 |

Δc | 3.3290 | 0.8726 | −0.5172 | −7.9268 |

P | 1.9757 | 10.4066 | 7.3565 | 7.8833 |

Q | 2.7670 | 10.1167 | 5.2734 | 7.9836 |

L | 3.8864 | 13.0119 | 8.0890 | 8.4471 |

P/Q | 0.7140 | 1.0286 | 1.3950 | 0.9874 |

R | 2.7750 | 13.3848 | 11.2842 | 8.3409 |

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**MDPI and ACS Style**

Liu, H.; Shi, X.; Yuan, P.; Dong, X.
Study on the Evolution of Multiple Network Resilience of Urban Agglomerations in the Yellow River Basin. *Sustainability* **2022**, *14*, 11174.
https://doi.org/10.3390/su141811174

**AMA Style**

Liu H, Shi X, Yuan P, Dong X.
Study on the Evolution of Multiple Network Resilience of Urban Agglomerations in the Yellow River Basin. *Sustainability*. 2022; 14(18):11174.
https://doi.org/10.3390/su141811174

**Chicago/Turabian Style**

Liu, Huifang, Xiaoyi Shi, Pengwei Yuan, and Xiaoqing Dong.
2022. "Study on the Evolution of Multiple Network Resilience of Urban Agglomerations in the Yellow River Basin" *Sustainability* 14, no. 18: 11174.
https://doi.org/10.3390/su141811174