## 4 Methods  
### Transportation Integration Evaluation Index System of Yangtze River Delta Urban Agglomeration  
We combined existing research results with the characteristics of different transportation modes in the Yangtze River Delta urban agglomeration (e.g., highways and railways), the transport capacity of the network characteristics and role, and the influence of factors like data availability and computability. Then, we chose corresponding indicators. See the following Table 1.  
Figure 2: Spatial distribution map of expressway mileage in the Yangtze River Delta urban agglomeration in 2020. Specific indicators are described as follows:  
1. In-degree centrality and out-degree centrality are measured by degree centrality. The formula is \(C_{D}(i)=k_{i}\), where \(k_{i}\) is the degree of city \(i\), and generally refers to the number of city \(i\) with direct rail connections in this study. Degree centrality refers to the number of points directly connected to a point and measures the central position of a node in the network. The higher the degree centrality is, the more nodes are directly connected to the point and the point is in the center. When the connection has direction, degree centrality can be divided into in-degree centrality and out-degree centrality [30]. 2. The formula of eigenvector centrality is \(C_{E_{i}}=k_{i}=c\sum\limits_{j=1}^{S}a_{ij}k_{j}\), where \(k_{i}\) is the degree of city \(i\)[30]. 3. The formula of betweenness centrality is \(C_{B_{i}}=\sum\limits_{j=1}^{N}\sum\limits_{k=1}^{j-1}\frac{\varphi_{k}(i)}{ \varphi_{jk}};j\
eq k\
eq i,j<k\), where \(\varphi_{jk}\) is the number of shortest paths between cities, \(\varphi_{jk}(i)\) is the number of shortest paths through city \(i\) between city \(j\) and city \(k\), and \(\frac{\varphi_{jk}(i)}{\varphi_{jk}}\) is the mediations of city \(i\) relative to city \(j\) and city \(k\)[30]. 4. The formula of closeness centrality is \(C_{C_{i}}=\sum\limits_{j=1}^{N}\frac{1}{4j_{i}}\), where \(d_{ij}\) is the shortest path length between city \(i\) and city \(j\)[30]. 5. Highway passenger capacity and highway freight volume can be obtained according to the Statistical Yearbook of Chinese Cities (2012-2021) and the Statistical Yearbook of Provinces and Cities. 6. The formula of effective average travel time [31] is \(A_{i}=\sum\limits_{j=1}^{n}\big{(}T_{ij}*M_{j}\big{)}/\sum\limits_{j=1}^{n}M_ {j}\), where \(T_{ij}\) is the shortest travel time between two cities based on the land transport network, and \(M_{j}\) is the economic quality of city \(j\), which is measured by the square root of the product of the city's GDP and population. 7. The formula of economic potential is \(P_{i}=\sum\limits_{j=1}^{n}\frac{M_{j}}{T_{ij}}\), where \(T_{ij}\) is the shortest travel time between two cities based on the land transport network, and \(M_{j}\) is the economic quality of city \(j\), which is measured by the square root of the product of the city's GDP and population. According to the actual situation of this study and the entropy weight method, the calculation steps of the transportation integration index of the Yangtze River Delta urban agglomeration are as follows:  
1. First, all indicators need to be de-dimensionalized;
2. Use the entropy weight method to assign weights to the traffic network structure index and the traffic network function index, and calculate the traffic network structure index and the traffic network function index; \begin{table}
\begin{tabular}{c c c} \hline \hline
**The Target Layer** & **Rule Layer** & **Index Layer** \\ \hline \hline \multirow{8}{*}{Urban agglomeration transportation integration evaluation index} & A11 In-degree Centrality & A12 Out-degree Centrality \\  & A1 Transportation network structure & A13 Eigenvector centrality \\  & A14 Betweenness centrality \\  & A15 Closeness centrality \\  & A21 Highway passenger capacity \\  & A22 Highway freight volume \\  & A23 Effective average travel time \\  & A24 Economic Potential \\ \hline \hline \end{tabular}
\end{table}