## 2 Materials and Methods
### Methodology
#### 2.3.1 Social Network Analysis (SNA)  
(1) Calculation of the strength of network connectedness  
Network connectedness refers to the degree or closeness of interconnection between nodes within the network, reflecting the linkage strength between cities in the UA network structure. In this paper, the preliminarily acquired Baidu migration big data are calculated and processed by Equations (1)-(3), and the data of in-migration intensity andout-migration intensity between cities are summed up to obtain the network connectedness of the UAs. \[D_{ab,in}=d_{ab,in}*F_{a} \tag{1}\]  
\[D_{ab,out}=d_{ab,out}*F_{a} \tag{2}\]  
\[Q_{ab}=D_{ab,in}+D_{ab,out} \tag{3}\]  
where \(D_{ab,in}\) is the migration intensity of city a to city b on the same day, and \(d_{ab,in}\) is the percentage of the migration intensity from city a to city b on the same day. \(D_{ab,out}\) is the migration intensity of city b to city a on the same day, and \(d_{ab,out}\) is the percentage of the migration intensity from city b to city a on the same day. \(F_{a}\) is the index of the scale of city a's migration on the same day, and \(Q_{ab}\) is the strength of the network connectedness of the UA. Network density refers to the degree of connection between the nodes in a network, reflecting the degree of closeness of the node cities in the UA network, and is usually used to characterize the connectedness of the network structure. Network density is generally characterized by the ratio of the number of line elements actually constituting the connection to the number of theoretically existing line elements in the network structure. The calculation formulas are simplified and expressed in Equation (4). \[P_{a}=2L/[n(n-1)] \tag{4}\]  
where \(P_{a}\) is the density of the network of UA a, \(L\) is the number of links that are actually connected in the network, and \(n\) is the number of nodes in the network. Centrality serves as a fundamental statistical metric within the domain of complex networks, offering insights into the hierarchical aspects of network structure. This metric encompasses point-out degree, point-in degree, and centrality, each of which plays a distinct role. The point-out degree gauges the number and extent of nodes connecting to other nodes, signifying a node's capacity to propagate information throughout the network. Conversely, the point-in degree reflects the number and magnitude of nodes linked to the node in question, signifying its attractiveness to neighboring nodes within the network. The point centrality degree, which is the summation of the point-out and point-in degrees, encapsulates the influence yielded by each node within the network. This centrality metric characterizes the position and role of cities within the UA network, where higher node centrality corresponds to greater importance and a more elevated status within the network structure. The calculation formulas are Equations (5)-(7):  
\[IB(a)=\sum_{b=1}^{n}D_{ab,in}\ (a\
eq b) \tag{5}\]  
\[OB(a)=\sum_{b=1}^{n}D_{ab,out}\ (a\
eq b) \tag{6}\]  
\[B_{a}=IB(a)+OB(a) \tag{7}\]  
where \(IB(a)\) represents the point-in degree of city a; \(OB(a)\) represents the point-out degree of city a; and \(B_{a}\) represents the point-centeredness of city a. (4) Calculation of network connectivity  
Network connectivity characterizes the degree of connectivity of a network by selecting the number of existing connections in the network, the strength of network connections, and the density of the network. The higher the network connectivity, the more stable the network structure of the UAs is. The calculation formula is Equation (8). \[S=\frac{\sum Q_{a}*P_{a}*M}{\max(M)} \tag{8}\]  
where \(S\) denotes the connectivity of the UA network, \(Q_{a}\) denotes the strength of city connections within the UAs, \(P_{a}\) denotes the density of the UA network, \(M\) denotes the number of redundant connections in the network, and \(\max(M)\) denotes the maximum number of possible redundant connections in the network.