## 3 Results
### Influencing Factor Analysis of the Network Structure of UAs in the Context of COVID-19
#### 3.3.3. QAP Regression Analysis  
This study excludes the UAs that did not meet the significance level threshold as indicated in Figure 5, then selects 10,000 random permutations to obtain the QAP regression analysis results, as shown in Figure 6.  
Note: In the table, areas shaded in light red signify that the results did not pass the significance level test, indicating an absence of discernible correlation in the variable matrix. Conversely, green shading indicates that the variable successfully cleared the significance level test, with the depth of color indicating the magnitude of correlation, wherein darker hues signify higher correlation levels. Since the constructed dimension involves a difference matrix, significant negative variable regression results suggest that a smaller disparity in the variable matrix is conducive to enhancing the stability of UA network structures. Conversely, when variable regression results are significantly positive, it implies that a greater disparity in the variable matrix is less favorable for improving the stability of UA network structures. The dependent variable  
Figure 5: QAP correlation analysis of UA network structures in the context of COVID-19. Figure 6: QAP regression analysis of UA network structures in the context of COVID-19. in this analysis is the spatial correlation matrix representing UA network stability. The independent variables consist of absolute difference matrices for various variable values. These matrices are standardized to eliminate dimensional influence. A comparative examination of the data in Figure 6 yielded the following outcomes:  
Spatial proximity exerts a significant adverse influence on the UA network structures. This arises from the heightened geographical distances and the presence of cross-provincial connections between cities, which escalate the costs associated with intercity interactions. Consequently, this scenario imposes restrictions on communication and collaborative efforts among cities within UAs. Consequently, After COVID-19, the deleterious impact of spatial proximity on the UA network structures is exacerbated. The level of economic development exhibits discernible variations among the UAs. Notably, this influencing factor demonstrates a significant negative correlation with UAs in the mature stage of development, signifying that such mature UAs prominently feature a central city that assumes a leading role within the UA network. The greater the divergence in economic development levels, the more conspicuous the radiative influence of the central city, contributing to the stabilization of the network structure. Simultaneously, under the impact of COVID-19, this influencing factor exerts a negative impact on mature UAs. Furthermore, COVID-19 intensifies the adverse effects of this influencing factor on these UAs. Scholars have substantiated that COVID-19 disproportionately affects the central city of UAs, consequently diminishing the hierarchical structure of the UA network. For UAs in the growth stage of development, the correlation is notably positive, with little change observed before and after COVID-19. This pattern is attributed to the less prominent role of the central city in these UAs, making greater differences in urban economic development detrimental to network structure. Additionally, COVID-19 has a more extensive influence on these UAs, resulting in minimal hierarchical changes in the network structure. Consequently, the impact of this influencing factor remains relatively stable before and after COVID-19. Furthermore, the impact of the level of medical facilities, transportation facilities, and innovation accessibility on the network structure varies significantly for each UA before and after COVID-19. Before COVID-19, the level of medical facilities was not the primary factor influencing network structure. However, during the normalization stage of COVID-19, the level of medical facilities emerged as the principal factor affecting the UA network structures, with a greater impact than observed before COVID-19.