## 2 Model Method
### Modeling Principle  
The charging pile system is a complex system. It is of great significance to study the topological structure of the charging pile layout network to optimize the charging pile stations and improve the service range and service efficiency of the charging pile [16]. Network analysis is an important method to study its relationships and its structure. From the perspective of the network, the charging pile system can be understood as a network formed with charging piles as nodes and the connection relationship between charging piles as edges. Therefore, the focus of the construction of the charging pile network is as follows: first, to find all the charging piles in the research area and take the charging piles as network nodes; second, to find the appropriate connection between the charging piles and quantify it.  
When determining the connection relationship between charging piles, this paper takes the bus lines passing through charging piles as the basis of connecting edges, and the number of bus lines passing through as the basis of connecting weights of charging piles. The reason for this setting is that the layout of charging piles mainly considers the flow of people, the demand for electricity, the scope of service, and the surrounding environment, such as whether the total number and distribution of charging stations in the region are uniform, and whether they can cover important places such as urban areas, residential areas, commercial areas, transportation hubs, tourist attractions, and meet the charging needs of different regions and people [17]. Correspondingly, the design principle of bus stations and bus routes is also to efficiently meet the maximum passenger flow routes and cover the maximum passenger flow areas. At the same time, bus stops and bus routes can provide more data. This paper is based on the bus line that passes the charging pile, which has strong feasibility.  
When determining the nodes of the charging pile network, the method adopted in this paper is to capture the geographical location data of the charging pile in the study area according to the Autonavi map, and the charging pile is numbered \(v_{1},v_{2},v_{3}\cdots v_{n}\).  
When determining the connection relationship between charging piles, the method adopted in this paper is to first calculate the collection of bus stations within 100 m of the linear distance of each charging pile, the collection number of bus stops corresponding to the charging pile \(1,2,3\cdots n\) is \(B_{1},B_{2},B_{3}\cdots B_{n}\), and the charging pile \(i\) has \(m\) bus stops, \(B_{i}=\left\{B_{i}^{1},B_{i}^{2},B_{i}^{3}\cdots B_{i}^{m}\right\}\). Secondly, if the bus stations corresponding to the two charging piles are on the same bus line, the two charging piles are connected to the edge, and the bus running frequency between the two charging piles corresponding to all bus stations is the weight of the edge.  
For example, the bus stop corresponding to charging pile 1 is \(B_{1}=\left\{B_{1}^{1},B_{1}^{2}\right\}\), the collection of bus stops corresponding to charging pile 2 is \(B_{2}=\left\{B_{2}^{1},B_{2}^{2}\right\}\). Bus station \(B_{1}^{1}\) passes through bus routes 1 and 2, bus station \(B_{1}^{2}\) passes through bus routes 2 and 4, bus station \(B_{2}^{1}\) passes through bus routes 1 and 3, bus station \(B_{2}^{2}\) passes through bus routes 4 and 5. Since the bus stations corresponding to charging pile 1 and charging pile 2 have the same bus routes 1 and 2, charging pile 1 and charging pile 2 are connected, and the weight of the connecting edge is calculated as 2 according to the bus running frequency. The specific calculation is as follows:  
\[B_{1}^{1}B_{2}^{1},w_{12}^{11} =1\] \[B_{1}^{1}B_{2}^{2},w_{12}^{12} =0\] \[B_{1}^{2}B_{2}^{1},w_{12}^{21} =0\] \[B_{1}^{2}B_{2}^{2},w_{12}^{21} =1\] \[w_{12}=w_{12}^{11}+w_{12}^{12}+w_{12}^{21}+w_{12}^{21}=2\]