## 3 Methodology and Data
### Network Mixing Patterns
#### 3.1.3 Significance Testing for Assortativity Coefficients  
Based on [PERSON]'s paper [17], the method for testing the statistical significance of the assortativity coefficient \(r\) is the jackknife method, which treats each edge as an independent measurement and calculates the standard deviation \(\sigma_{r}\) using Equation (4).  
\[\sigma_{r}=\sum_{i=1}^{M}(r_{i}-r)^{2} \tag{4}\]  
where \(r_{i}\) represents the \(r\) value with the \(i_{th}\) edge removed, and \(M\) represents the number of edges in the network. However, while this method is theoretically sound, it becomes computationally intensive for large networks due to the need to recalculate the coefficient multiple times by removing each edge sequentially. To evaluate the statistical significance of the network assortativity coefficient, this study employed the bootstrap resampling method, which is well suited for large-scale datasets. The networks analyzed in this study primarily contain over 1000 edges, making the Jackknife method used by [PERSON]'s paper [17]. Computationally expensive due to its reliance on repeated calculations. Initially, this study calculated the original assortativity coefficient \(r_{0}\) for each urban network. This study then conducted 1000 bootstrap resampling iterations. In each iteration, this study randomly selected, with replacement, several edges equal to the size of the original network's edge set. Using the degree distribution, this study reconstructed the network and calculated its assortativity coefficient \((r_{i},i=1,2,\ldots,1000)\). From these 1000 resampled coefficients, this study computed the standard deviation of the assortativity coefficient \(\sigma_{r}\).  
To determine the statistical significance of the assortativity coefficient, this study assumed that the resampled coefficients follow a normal distribution and conducted a Z-test. The Z-value was calculated as \(Z=r/\sigma_{r}\), where \(r\) is the original network's assortativity coefficient and \(\sigma_{r}\) is the standard deviation derived from the Bootstrap method. At a 95 percent confidence level, the null hypothesis (that the network exhibits no significant assortativity or disassortativity) was rejected if \(|\)\(Z\)\(|\)\(>\) 1.96. A Z-value greater than 1.96 indicates significant assortativity, while a Z-value less than \(-\)1.96 suggests significant disassortativity. If \(|\)\(Z\)\(|\)\(\leqslant\) 1.96, the assortativity coefficient is deemed statistically insignificant.  
It is worth noting that although the bootstrap method is primarily designed to assess degree assortativity, it does not account for node attributes during resampling. Despite this limitation, this study extended the method to evaluate assortativity coefficients based on node attributes. While this adaptation may overlook certain attribute-specific considerations, it offers a preliminary statistical reference for analyzing assortativity patterns involving node attributes.  
Additionally, this study examines the distribution of assortativity coefficients across different network types. Based on distribution fitting results on the empirical network, a universal indicator for mixing patterns in urban agglomerations is established. By recognizing how assortativitytativity coefficients are distributed across different network types, we can better understand the generality of different mixing patterns in urban agglomeration development.