# A Formation Mechanism of Spatial Distribution Pattern of Industrial Clusters under Flow Space
## 3 Materials and Methods
### Formation Mechanism Method of Spatial Distribution Pattern of Industrial Clusters under Flow Space
#### 3.2.2 Spatial Interaction Network Inference Methods  
* Traffic Interaction Intensity Network Construction;  
In geographic space, railway lines connect cities, and the interaction of various elements between cities relies on transportation networks, so the interaction of transportation networks of neighboring and non-areas plays an important role. The traditional method for building inter-regional accessibility is based on the Euclidean distance of railway lines, and it is difficult to express the inter-regional \"distance failure\" in geographic space. Since the amount of railroad stations is an essential measure of a city's accessibility intensity, this paper improves the inter-city accessibility measure by using the amount of urban railroad stations:  
\[O_{ij}=\max\left(\frac{1}{D_{ij}}*\left(T_{i}+T_{j}\right)\right)\,if(\text{ Direct rail line exists between i and j}) \tag{2}\]  
\[O_{ij}=\frac{1}{\min\left(\frac{1}{\Omega_{ik}}+\frac{1}{\Omega_{km}}+\ldots+ \frac{1}{\Omega_{mj}}\right)}\,if(\text{No direct rail line between i and j}) \tag{3}\]  
where \(O_{ij}\) represents the interaction strength of the transportation network between city \(i\) and city \(j\), \(Ti\) and \(T_{j}\) represent the number of stations within city \(i\) and the number of stations within city \(j\) on the railway line connecting city \(i\) and city \(j\), and \(D_{ij}\) represents the shortest Euclidean distance between city \(i\) and city \(j\) based on the railway line. \(k\) and \(m\) represents the cities through which the transportation link between city \(i\) and city \(j\) is to pass.  
* Human Resource Mobility Trends Network;  
Urban human resource mobility trends are an essential component of industrial agglomeration influencing factors. Since inter-city transportation accessibility is the basic conditions for population mobility trends, and consumption and income levels are the main drivers of human resource mobility, we use urban wage levels to represent basic urban income levels and use house price levels to represent living consumption levels, and construct the inter-city human resource mobility trend network based on transportation accessibility networks:  
\[POP_{\bar{\eta}}=\left(\frac{S_{j}-S_{i}}{S_{i}}-\frac{H_{j}-H_{i}}{H_{j}} \right)\times\left(O_{ij}\right)if\  
\[C_{i-}\_POP=\sum_{j=1}^{n}POP_{ji} \tag{7}\]  
where \(POP_{ij}\) is the intensity of the population movement trend from city \(i\) to city \(j\), \(S_{i}\) represents the wage level of city \(i\), \(H_{i}\) represents the house price level of city \(i\), \(C_{i+}\_POP\) represents the integrated human resource outflow trend of city \(i\), and \(C_{i-}\_POP\) represents the integrated human resource inflow trend of city \(i\).  
* Technological Innovation Flow Trend Network.  
The technology flow trend network is constructed based on the inter-regional human resource flow trend network and the level of technological innovation in the region indicates the intensity and direction of the technology flow trend among cities in the Yangtze River Delta region:  
\[TEC_{ij}=POP_{ij}\times\left(\frac{N_{i}-N_{j}}{N_{j}}\right) \tag{8}\]  
\[C_{i+-}TEC=\sum_{j=1}^{n}TEC_{ij} \tag{9}\]  
\[C_{i-}TEC=\sum_{j=1}^{n}TEC_{ji} \tag{10}\]  
where \(TEC_{ij}\) is the intensity of technological innovation knowledge spillover between city \(i\) and city \(j\), \(N_{i}\) represents the level of comprehensive innovation capability of region \(i\), \(C_{i+-}TEC\) represents the trend of comprehensive technological innovation outflow from city \(i\) to the surrounding region, and \(C_{i-}TEC\) represents the trend of comprehensive technological innovation inflow from city \(i\) to the surrounding region.