Research on Weighted Network Model Construction and Layout Structure of New Energy Vehicle Charging Station

Featured Application

At present, there are few studies on the layout of new energy vehicle charging stations in the academic world. This paper provides an idea for the construction and development of new energy vehicle charging stations by constructing the network structure of new energy vehicle charging stations, designing network indicators, and analyzing their spatial layout characteristics.

Abstract

(1) Background: Spatial layout is the key to the construction and development of new energy vehicle charging stations; (2) Methods: A network analysis method is used to build the new energy vehicle charging station network, design network indicators, analyze the structural characteristics of new energy vehicle charging stations based on the local nodes and the overall structure of the network, and identify the key nodes and important parts of the network; (3) Results: Taking the new energy vehicle charging station in Jinan City of Shandong Province as an example, the empirical analysis is carried out. The empirical results show that the new energy vehicle charging station network constructed in this paper and the network indicators designed can effectively describe the layout of new energy vehicle charging stations, identifying key stations and important parts of the network; (4) Conclusions: This provides a theoretical basis for further improving the utilization rate of charging stations and the reasonable planning of new energy vehicle charging stations. It provides an idea and method for the research on the layout of charging stations for new energy vehicles.

1. Introduction

Accelerating the construction of new energy vehicle charging/changing power stations and improving the coverage of fast charging/changing power stations in highway service areas and public parking spaces is one of the important measures for the country to successfully develop smart cities [1]. As the carrier of electric vehicle charging and replacement services, the charging station is an important transportation and energy integration infrastructure. In 2023, The General Office of the State Council issued the Guiding Opinions on Further Building a High-quality Charging Station System, planning to basically build a high-quality charging station system with wide coverage, moderate scale, reasonable structure, and perfect functions by 2030, and effectively support the development of the new energy vehicle industry, consequently meeting people’s travel charging needs [2].

With the investment of public resources in the construction of charging stations, their development has been greatly improved, but there are still some problems restricting it. Zhang Houming believes that China’s charging pile industry is still facing serious construction lag, unbalanced development, low utilization rate, unreasonable layout, and other outstanding problems, the main reasons for which are the high cost of construction and operation of charging piles, the fact that the standard is not uniform, the layout planning is unreasonable, there are hidden dangers, etc. On the basis of the above factors, it is proposed to optimize the relevant support policies, promoting the sustainable and healthy development of the charging pile industry [3]. Taking 101 communities in Beijing as an example, Wu et al. estimated the impact of the availability of public charging piles on the sales of electric vehicles by using panel regression analysis and investigated the obstacles in the construction and operation of public charging piles. The results showed that the lack of public charging piles would seriously limit the sales of electric vehicles [4]. Tao et al. described the current research status of the method of determining charging demand points at home and abroad according to the different planning methods of charging facilities for new energy vehicles, and they found that the spatial distribution of charging demand points extracted by the current location method is somewhat deviated from the actual situation [5]. Wang Xiaohong also pointed out that the current convenience of charging is the main factor affecting the promotion of new energy vehicles. At this stage, the regional construction of new energy vehicle charging stations has not yet been completed, hindering the large-scale promotion and development of new energy vehicles [6]. It can be seen that the difficulty of charging restricts the construction and development of charging stations. Many scholars identify the factors that affect the construction and development of charging stations through empirical research which ought to be optimized. From the perspective of complex networks, Wang et al. analyzed the distribution characteristics of new energy vehicle charging piles and the temporal and spatial changes between provinces from May 2016 to April 2019, and then analyzed the time distribution of new energy vehicle charging piles in combination with national policies and new energy vehicles, so as to promote the sustainable development of electric vehicles and the green energy industry [7]. By combining visual analysis with complex networks, Hu et al. deeply analyzed the reform policies of the power system in the United States, so as to improve the activity and competitiveness of various entities in the power market, and further promote the supply and efficiency of carbon energy and the use of other renewable energy sources, so as to further reduce carbon dioxide emissions and promote the sustainable development of the American economy [8].

The key to improving the efficiency of a charging station is to optimize the allocation of resources and establish a sound charging network. As an engineering system, the charging station network involves many elements, and some scholars have also conducted related research on the network itself. Using complex network theory, Wang Wentao and Xu Xianyuan first constructed the charging station network structure of Shanghai under ideal conditions, and then constructed the electric vehicle charging station network of Shanghai, Xi’an, Hefei, and Dalian under actual conditions. Thus, it is verified that the network structure of the EV charging station has a significant impact on its utilization rate and stability [9]. Liu Qiwei et al. defined the network connection strategy of the new charging station from two dimensions of network centrality and the number of charging piles at network nodes, built a dynamic simulation model of charging network, simulated the promotion of charging station construction under different strategies, and revealed the evolution law of urban charging network structure characteristics and usage efficiency [10]. Based on the “input-output” critical infrastructure interdependence analysis method, Jin Chenghao et al., taking energy, communication, water supply, and transportation systems as objects, combined with the hierarchical structure of each system, built an interdependent network model, and found that energy nodes have the highest influence [11]. Wang et al. analyzed the distribution characteristics of new energy vehicle charging piles from May 2016 to April 2019 and the temporal and spatial changes among provinces from the perspective of complex networks, and then analyzed the time distribution of new energy vehicle charging piles in combination with national policies and new energy vehicles, so as to promote the sustainable development of electric vehicles and green energy industry [7]. Based on the perspective of policy incentives and consumers’ preference for electric vehicles, Fang et al. used complex networks to build an evolutionary game model and proved that balanced dynamic subsidies and tax policies have advantages for the promotion of charging stations [12].

By summarizing and analyzing the previous literature on the layout of charging stations for new energy vehicles, it is found that there are few studies on the spatial layout of charging stations by the network analysis method in the academic circle. The main purpose of this paper is to build a new energy vehicle charging station network to analyze its structural characteristics, so as to provide an idea and reference for the construction and development of new energy vehicle charging stations.

2. Model Method

Urban charging stations fit the description of network complexity, so network analysis can be used to investigate them in depth. Network analysis is a quantitative and visual research method for analyzing the relationship between a group of actors, which is developed by combining mathematical methods and graph theory. An important index of social network analysis is the centrality index (point centrality, middle centrality, proximity centrality), which is mainly used to reveal the relationship between individual nodes and the relationship between individuals and the whole network [13]. Point degree centrality refers to the number of nodes directly connected to a node, and point degree centrality also includes in-degree and out-degree; in-degree is the number of other nodes pointing to the node, and out-degree is expressed by the number of nodes pointing to other nodes [14]. Intermediate centrality is the ability of a node to control the communication of other nodes measured according to the closeness or distance between nodes in the network, which can reflect the status and bridge role of the node. On the contrary, the degree of proximity to the center measures the degree of “independence” of a node that is not controlled by other nodes. The greater the degree of proximity to the center, the weaker the independence of the node [15].

2.1. 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:

$$\begin{array}{l}{B}_1^1{B}_2^1,w_{12}^{11}=1\\ B_1^1{B}_2^2,w_{12}^{12}=0\\ B_1^2{B}_2^1,w_{12}^{21}=0\\ B_1^2{B}_2^2,w_{12}^{21}=1\\ w_{12}=w_{12}^{11}+w_{12}^{12}+w_{12}^{21}+w_{12}^{21}=2\end{array}$$

2.2. Model Step

To sum up, the network analysis method is selected as the modeling method in this paper. The network analysis method model can reflect the relationship between non-adjacent nodes in the new energy vehicle charging station network, and can also reflect the degree of correlation between some distant nodes. In this paper, on the assumption that the up-going and down-going lines of bus routes overlap, the nodes of charging stations are connected to each other. This paper studies the charging station network based on the network analysis method, so as to analyze its layout significance more objectively.

Define the charging station network as $G=(V,E,W)$. The specific steps are as follows:

Step 1: Determine the node set of the new energy vehicle charging station network.

To build the charging station network model, we first need to determine the node set. Determine the research area R, capture all the new energy vehicle charging stations in the area R on the open platform of AmAP, abstract the charging station as nodes in the network, and the relationship between charging stations as the edges in the website; the set formed by all nodes in the region is $V$, the set formed by all edges is $E$, and the weight of the edge is $W$. Build a charging station network model, which can be expressed as follows:

$$G=(V,E,W)\left\{\begin{array}{l}V=\left\{v_1,v_2,v_3,\cdots v_i,\cdots ,v_j\right\}\\ E=\left\{e_1,e_2,e_3,\cdots e_i,\cdots ,e_j\right\}\\ W=\left\{w_{e1},w_{e2},w_{e3},\cdots w_{ei},\cdots ,w_{ej}\right\}\end{array}\right.$$

Obtain the specific location information (expressed by latitude and longitude) of all new energy vehicle charging stations in Lixia District, Shizhong District, Liccheng District, Tianqiao District, and Huaiyin District of Jinan City through the open platform of AmAP, and then select the location information of all bus routes and stations according to the official website of Jinan Public Transport. Considering from the charging station to the adjacent bus lines, setting 100 m as the limit in this paper, set a node i; if the node i and the area-adjacent bus line distance is less than 100 m, and the bus line passes through the node i, select the node i and repeat the above steps, selecting all the nodes.

Step 2: Calculate the correlation coefficient matrix of the new energy vehicle charging station network.

The collection of bus stops corresponding to charging stations $v_i$ and $v_j$ is $B_i$ and $B_j$, $B_i=\left\{B_i^1,B_i^2,B_i^3\cdots B_i^S\right\}$, $B_j=\left\{B_j^1,B_j^2,B_j^3\cdots B_j^T\right\}$.

$w_{ij}^{pq}=1$ represents when $B_i^p$ and $B_j^q$ are on the same bus route; $w_{ij}^{pq}=0$ represents when $B_i^p$ and $B_j^q$ are not on the same bus route.

The edge weight of charging stations $v_i$ and $v_j$ is $w_{ij}={\displaystyle \sum _{p=1}^S{\displaystyle \sum _{q=1}^T{w}_{ij}^{pq}}}$.

Then, the charging station correlation coefficient matrix is as follows:

$$w=\left(\begin{array}{cccccc}{w}_{11}& w_{12}& \cdots & w_{1t}& \cdots & w_{1n}\\ w_{21}& w_{22}& \cdots & w_{2t}& \cdots & w_{2n}\\ ⋮& ⋮& \ddots & ⋮& \ddots & ⋮\\ w_{s1}& w_{s2}& \cdots & w_{st}& \cdots & w_{sn}\\ ⋮& ⋮& \ddots & ⋮& \ddots & ⋮\\ w_{n1}& w_{n2}& \cdots & w_{nn}& \cdots & w_{nm}\end{array}\right)$$

Step 3: Determine the strong correlation coefficient matrix of the charging station.

Starting from the column direction of the charging station correlation coefficient matrix $w$, the W-T index is calculated to determine the critical value, and then the charging station’s strong correlation coefficient matrix is calculated. The steps are as follows:

①

Arrange each column $E(1,j),E(2,j)\cdots ,E(i,j),\cdots E(n,j)(i,j=1,2,\cdots ,n)$ of the correlation coefficient matrix between charging stations in order from largest to smallest to obtain the adjusted matrix $F(i,j)(i,j=1,2,\cdots n)$, and set the matrix $IndexE(i,j)$ as the corresponding relation between the positions of the elements of matrix $E(i,j)$ and matrix $F(i,j)$.

②

Calculate the W-T exponential matrix $w(i,j)$ corresponding to matrix $F(i,j)$:

$$w(i,j)={\displaystyle \sum _{i=1}^n{\left[s(k,i)-100\times \frac{F(k,j)}{{\displaystyle \sum _{l=1}^{n}F(l,j)}}\right]}^2}$$

Let vector $\alpha =\min \left\{w(1,j),w(2,j),\cdots ,w(n,j)\right\}$ be the minimum W-T exponent for each column in the W-T exponential matrix $w(i,j)$. Vector $\beta$ marks the position of each element in the vector in the W-T exponential matrix.

③

Construct a 0–1 matrix $\beta$ from vector $B$. The construction principle is that, for the $j$ column and $i$ row of the $B$ matrix, if $i\le \beta (1,j)$, then $B(i,j)=1(i=1,2,\cdots ,n)$.

④

According to matrix $IndexE(i,j)$, adjust the positions of elements in matrix $B$; that is, the charging station relationship is restored, and the charging station network 0–1 matrix $C$ is obtained.

⑤

The charging pile’s strong correlation coefficient matrix $W=w\ast C$ is calculated.

$$W=w\ast C=\left(\begin{array}{cccccc}{W}_{11}& W_{12}& \cdots & W_{1t}& \cdots & W_{1n}\\ W_{21}& W_{22}& \cdots & W_{2t}& \cdots & W_{2n}\\ ⋮& ⋮& \ddots & ⋮& \ddots & ⋮\\ W_{s1}& W_{s2}& \cdots & W_{st}& \cdots & W_{sn}\\ ⋮& ⋮& \ddots & ⋮& \ddots & ⋮\\ W_{n1}& W_{n2}& \cdots & W_{nn}& \cdots & W_{nm}\end{array}\right)$$

Step 4: Build a network of charging stations.

In the strong correlation coefficient matrix of charging station $W$, $W_{ij}>0$ indicates that there is an edge between city $i$ and city $j$. Conversely, there is no edge between city $i$ and city $j$; based on this, the charging station network model is established.

For example, charging station $v_1$ corresponds to bus stop $B_1=\left\{B_1^1,B_1^2\right\}$, charging station $v_2$ corresponds to bus stop $B_2=\left\{B_2^1,B_2^2\right\}$, charging station $v_3$ corresponds to bus stop $B_3=\left\{B_3^1\right\}$, and charging station $v_4$ corresponds to bus stop $B_4=\left\{B_4^1\right\}$.

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 $B_3^1$ passes through bus routes 3 and 5, and bus station $B_4^1$ passes through bus routes 1, 2, 4, and 5.

Then, the correlation coefficient matrix of the charging station is calculated as follows:

$$w=\left(\begin{array}{cccc}0& 2& 0& 4\\ 2& 0& 2& 3\\ 0& 2& 0& 1\\ 4& 3& 1& 0\end{array}\right)$$

The strong correlation coefficient matrix of the charging station is calculated as follows:

$$w=\left(\begin{array}{cccc}0& 2& 0& 4\\ 2& 0& 2& 3\\ 0& 2& 0& 0\\ 4& 3& 0& 0\end{array}\right)$$

3. Design of Structural Metrics

In the network structure of the charging station, degree and centrality indices are selected for local node analysis, network density is selected for overall network analysis, and core–edge structure and cohesive subgroups are constructed for network cohesion analysis.

3.1. Degree

Degree is used to measure the number of edges around a node. A node with a higher degree of node has better [18] connectivity in the network. In a charging station network, this means that there are more charging facilities close to the charging station and convenient transportation. When an undirected network has no self-loops and no double edges, the degree of a node is numerically equal to the number of other nodes that are directly connected to the node by an edge. The degree of a node is numerically equal to the number of other nodes that are directly edged to the node. Let the adjacency matrix of an undirected network with a given node be $A={(a_{ij})}_{n\times n}$; then, we have

$$k_i={\displaystyle \sum _{j=1}^n{a}_{ij}}={\displaystyle \sum _{i=1}^n{a}_{ji}}$$

(1)

where $i$ is a node, $k_i$ is the degree value of the node, $n$ is the number of nodes, and $a_{ij}$ is the adjacency matrix built based on nodes.

3.2. Degree Centrality

Point centrality [19] refers to the ratio of the number of sites connected to site i or the number of edges to the maximum possible number, which intuitively reflects the size of the direct connection between the site and other sites in the network. In simple terms, degree centrality refers to the number of nodes that are directly connected to other nodes. The larger the value, the more important the site is. In a network containing n nodes, the maximum value of the node degree is n − 1. The normalized degree centrality of a point i with a degree value of is defined as follows:

$$D{C}_i={\displaystyle \frac{k_i}{N-1}}$$

(2)

where $D{C}_i$ is degree centrality, $k_i$ is the degree value of the node, and $N$ indicates the number of nodes.

3.3. Closeness Centrality

Closeness centrality [20] represents the ratio of the sum of the number of lines from one site to other sites, to the number of sites in the remaining network, reflecting the proximity of the site to all other sites in the network or the degree of convenience. More generally, proximity centrality reflects the efficiency with which a person or point in a social network obtains information or influences others. The larger the value, the greater the degree of portability of the site, the more important the site is. The proximity centrality of node i is defined as follows:

$$C{C}_i={\displaystyle \frac{1}{d_i}}={\displaystyle \frac{n}{{\displaystyle \sum _{j=1}^n{d}_{ij}}}}$$

(3)

where $n$ represents the number of nodes in the network, represents the average of the shortest distance from node $i$ to all other nodes in the network, and represents the shortest distance from node $i$ to node $j$ in the network.

3.4. Betweenness Centrality

Betweenness centrality [21] is the ratio of the number of shortest paths passing through the site in the network to the sum of the shortest paths in the network [22]. In layman’s terms, intermediate centrality reflects how many shortest paths a person or node has through the network. The larger the value, the greater the importance of the site, which depicts the ability of a site in the network to control the other sites, and removing these sites increases the shortest distances between the majority of the other sites in the network, and also increases the impact on the transmission of the network. The median centrality of node i refers to the number of shortest paths through node i to portray node i importance. The median centrality of node i is defined as follows:

$$B{C}_i={\displaystyle \sum _{s\ne i\ne t}\frac{G{N}_{st}^i}{G{N}_{st}}}$$

(4)

where $G{N}_{st}$ represents the number of shortest paths from node s to node t and $G{N}_{st}^i$ is the number of shortest paths passing through the node.

3.5. Network Density

As one of the criteria to evaluate the cohesiveness and structural stability of the network, the network density value is calculated by comparing the actual number of relationships between the participants in the network with the total number of relationships in the network. After analyzing the obtained value, if the value is higher, it shows that the network structure has higher stability and cohesion degree, lower looseness degree, and higher coordination in the overall development. The specific formula is as follows:

$$D={\displaystyle {\sum }_{i=1}^l{r}_{ij}/n(n-1)}$$

(5)

where $D$ is the network density, $r_{ij}$ is the number of edges between two nodes, and $n$ is the number of nodes.

4. Empirical Analysis

4.1. Data Source and Processing

This paper takes Lixia District, Liccheng District, Huaiyin District, Tianqiao District, and Shizhong District of Jinan City as the research scope, and discusses the charging stations of new energy vehicles within the scope as the research object.

When analyzing the charging station network in the five districts of Jinan City, the data sources are divided into two categories, namely the geographical location information of the charging station and the location information of the bus lines. In order to avoid errors caused by subjective factors in the analysis of the layout of the charging stations, this paper captured the geographical location information of the charging stations in Lixia District, Shizhong District, Licheng District, Tianqiao District, and Huaiyin District of Jinan City through the open platform of AmAP, as well as the data information of all bus lines in these five districts, so as to lay a foundation for the subsequent visualization analysis by ArcGIS.

First of all, Tuba bus, bus network, 8684, local network, and other websites are used to obtain the relevant information of bus routes and route stations. Such websites provide bus line names divided by numbers and letters, and use Python programming to climb all the bus line information in the required research area. Then, the AmAP open platform is used to provide API services and information such as line name, route site, and site location, which is then verified. In the same way, the open platform of AmAP is used to obtain the relevant information of new energy vehicle charging stations in the required areas, and the data of the charging stations are crawled by Python programming language. Finally, Python programming is used to parse the data, and the extracted data are preliminarily cleaned and organized, stored as csv files, and imported into Excel for the next stage of data processing and analysis.

The data of bus lines and new energy vehicle charging stations obtained initially need to be further structured and arranged to facilitate the establishment of the subsequent network adjacency matrix, and then generate complex network models. There are duplicate stations passed by the original bus line, and the name description of the same station may be different for different bus lines. In this case, the corresponding location coordinates of the stations are used for further consolidation processing. For charging stations and bus line stations, the charging station and bus line stop rarely overlap directly. In this paper, the nearby charging station is extracted according to the bus line, and the distance of 100 m is taken as the limit. If the vertical distance of the selected bus line at the charging station is less than or equal to 200 m, the charging station is selected. Finally, a total of 1274 bus lines and 75 new energy vehicle charging stations were obtained.

4.2. Research Area

Using ArcGIS geographic information analysis software (v.10.8.2), this paper first established a spatial database and took Lixia District, Shizhong District, Liccheng District, Tianqiao District, and Huaiyin District as the research areas by referring to the official administrative division definition of National Basic Information Geographic Center—Administrative Division of Jinan Municipal Government in 2023. The bus route information of the five districts of Jinan City obtained in this paper was imported into ArcGIS software for spatial correction and then output into a .shp file in different layers to obtain the bus route map of the five districts of Jinan City, as shown in Figure 1.

As places with dense bus lines have more developed traffic, the charging stations near the bus lines in the five districts of Jinan City are extracted, and the location data of remote infrastructure are excluded with the distance of 100 m. Finally, 75 effective charging stations are obtained. The charging stations are numbered as 1, 2, 3…

The five districts of Jinan City are imported into the ArcGIS layer to obtain the regional map of the five districts of Jinan City. Vector data of bus lines and bus stations in the five districts of Jinan City are captured through the open platform of AmAP and imported into ArcGIS, and then 75 charging stations near the bus lines are imported together, as shown in Figure 2. As can be seen from the figure, the charging stations are more distributed in areas with more developed traffic. The charging stations are distributed in all five regions, among which Lixia District, Shizhong District, Tianqiao District, and Pagoda Shady District, and their junctions and bus line interchanges are most distributed.

5. Analysis of Empirical Results

5.1. Construction of Charging Station Network Model in Five Districts of Jinan City

The charging station network model established in this paper is a weighted undirected network based on the network analysis method. Gephi software (v.0.10.1) is used to import the above adjacency matrix to obtain its network structure topology, as shown in Figure 3.

This paper is based on the layout of Fruchterman Reingold in Gephi software, which follows the principle that nodes are close to each other and unconnected nodes are mutually exclusive; according to the node degree, a network model containing 75 nodes and 1724 connected edges is constructed. The number of edges between two nodes is the weight between the two nodes. The network structure diagram is divided into modules according to the importance of the node degree. Those with the same or similar degree values are grouped together. The darker the node color, the greater the degree value. As can be seen from Figure 3, nodes 10, 11, 12, 13, 39, 41, 42, 43, 44, 47, and 71 have a high degree value, indicating that they have a high degree of importance and can be regarded as key nodes, playing a crucial role in the whole network. Due to the large weight of the connecting edges between the above nodes, it can be seen that they have a close relationship. These nodes not only connect their own regions, but also are the core nodes of the connection between regions.

5.2. Analysis of Network Characteristics of Charging Stations in Five Districts of Jinan City

5.2.1. Network Index Analysis Based on Node Local Structure

According to the charging station network model and the calculation formula of degree value index obtained in Figure 3, a series of indicators are calculated with the help of ucinet software (v.6.0). The calculation results are shown in the following table.

1.

Degree

In terms of importance,

Table 1. Top 10 sites with node degree.

Ranking	Station Number	Site Name	Area
1	12	Special call car charging station (Jiayi Harmony Yidian, Ginza, Jinan)	Huaiyin District
2	13	Epp Public charging station	Huaiyin District
3	11	Eway Energy car charging station	Huaiyin District
4	42	Special call public charging stations	Lixia District
5	43	Special call public charging stations	Lixia District
6	44	Special call car charging station (Shandong News Building Electric Vehicle)	Lixia District
7	51	Eway Energy Car charging station	Lixia District
8	52	Eway Energy Vehicle public charging station	Lixia District
9	53	Eway Energy Vehicle public charging station	Lixia District
10	39	Unitech Car Charging Station (Watt Road)	Lixia District

lists only the top ten sites in terms of degree value, which are analyzed at the midpoint. The same is true of the following analyses. They are 12, 13, 11, 42, 43, 44, 51, 52, 53, and 59, which, respectively, correspond to the special call car charging station (Jinan Ginza Jiayi Harmony Yidian), Apu Public charging station, Iwei Energy vehicle charging station, special call public charging station, special call public charging station, special call public charging station, special call public charging station, special call public charging station, special call public charging station, and special call public charging station. Special electric charging station (Shandong News Building electric vehicle), Yiwei Energy car charging station, Yiwei Energy car public charging station, Yiwei Energy car public charging station, Youke Technology car charging station (Watt Road), and Special electric car charging station (Jinan Ginza Jiayi Harmony Yidian). Terai electric car charging station (Jinan Ginza Jiayi Harmony Yidian) and Aipu public charging station have the highest degree value and are the key core nodes in the network.

As can be seen from Table 1, the charging stations with higher degree values are concentrated in Huaiyin District and Lixia District, which generally reflects that these two areas have dense population and good economic development, so the demand for charging stations is higher. Therefore, infrastructure investment in these two areas can be increased to facilitate the travel convenience of users.

2.

Degree centrality

From the perspective of new energy vehicle charging stations, “degree centrality” represents the general coverage of infrastructure, which reflects the construction degree of charging stations and the distribution of charging points in a region.

Table 2. Top 10 sites for degree centrality.

Ranking	Station Number	Site Name	Area
1	12	Special call car charging station (Jiayi Harmony Yidian, Ginza, Jinan)	Huaiyin District
2	13	Epp Public charging station	Huaiyin District
3	39	Unitech Car Charging Station (Watt Road)	Lixia District
4	41	Special call car charging station (Jinan Financial Supermarket)	Lixia District
5	71	Bus Honglou charging service station	Licheng District
6	42	Special call public charging stations	Lixia District
7	43	Special call public charging stations	Lixia District
8	44	Special call car charging station (Shandong News Building Electric Vehicle)	Lixia District
9	47	Ev Energy Car charging station	Lixia District
10	11	Eway Energy car charging station	Huaiyin District

lists the top 10 charging stations for degree centrality. They are 12, 13, 39, 41, 71, 42, 43, 44, 47, and 11, respectively, which correspond to special car charging stations (Jiayi Harmony Yidian in Jinan Ginza), Apu Public charging stations, Youke car charging stations (Watt Road), special car charging stations (Jinan Financial Supermarket), etc. Bus Honglou Charging service station, Special call public charging station, Special call public charging station, Special electric car charging station (Shandong News Building electric vehicle), Iwei Energy car charging station, and Iwei Energy car charging station. The largest degree of centrality is located in Huaiyin District special call car charging station (Jinan Ginza Jiayi Harmony Yidian), indicating that the station occupies an important position in the entire charging station network, as a key facility. It can also be seen that the connectivity is the best in the entire network, indicating that the nearby charging stations are more numerous, have closer contact, their charging is more convenient, and users benefit from rich charging resources. It further shows that road traffic is relatively developed.

It can be seen from Table 2 that the stations with high degree centrality are mainly distributed in Huaiyin District and Lixia District, indicating that the road conditions in these two areas are superior, the population density is larger, and the economy is better. Among them, the stations with the highest degree of centrality are the special electric car charging station (Jinan Ginza Jiayi Harmony Yidian) and the Aipu public charging station, indicating that it has a large number of charging stations connected within itself, covering a wide range, playing a key role in all charging station stations, and that its robustness is high. When other stations are damaged or affected, they can still maintain a high degree of independence.

3.

Closeness centrality

Proximity centrality is used to judge the spatial location of new energy vehicle charging station sites. If the distance between a site and multiple other sites is shorter, it indicates that the spatial location of the site is more important. The concept is similar to accessibility in traffic theory. Accessibility refers to the difficulty of reaching the charging station of new energy vehicle households from the charging demand point through many factors such as road congestion and demand point to the long distance of the charging station. Reflecting the accessibility of the charging station in space is an important basis for judging the matching degree of new energy vehicle charging station layout planning with new energy vehicles and the convenience of users. Among them, the top ten stations are 12, 13, 39, 41, 71, 42, 43, 44, 11, and 34, respectively, corresponding to special car charging stations (Jinan Ginza Jiayi Harmony Yidian), Apu Public public charging stations, Youke Technology car charging stations (Watt Road), special car charging stations (Jinan Financial supermarket), bus Honglu charging service stations, etc. Special call public charging station, special call public charging station, Special Electric vehicle charging station (Shandong News Building electric vehicle), Yiwei Energy vehicle charging station, and State Grid public charging station.

As can be seen from

Table 3. Top 10 sites in near centrality.

Ranking	Station Number	Station Number	Area
1	12	Special call car charging station (Jiayi Harmony Yidian, Ginza, Jinan)	Huaiyin District
2	13	Special call car charging station (Jiayi Harmony Yidian, Ginza, Jinan)	Huaiyin District
3	39	Unitech Car Charging Station (Watt Road)	Lixia District
4	41	Special electric car charging station (Jinan Financial Supermarket)	Lixia District
5	71	Bus Honglou charging service station	Licheng District
6	42	Special call public charging stations	Lixia District
7	43	Special call public charging stations	Lixia District
8	44	Special call car charging station (Shandong News Building Electric Vehicle)	Lixia District
9	11	Eway Energy car charging station	Huaiyin District
10	34	National Grid public charging stations	Central District

, the largest site is the special car charging station in Huaiyin District (Jinan Ginza Jiayi Harmony Yidian). Although this site is close to the center, its independence is weak. When it is fluctuating or damaged, it will weaken the connection with other charging stations, thus affecting the utilization rate of the surrounding or nearby charging stations. As can be seen from Table 3, the top ten stations are mainly concentrated in Huaiyin District and Lixia District, indicating that the traffic accessibility around the charging stations in these two areas is good and the convenience for users is high, but their independence is relatively weak.

4.

Betweenness centrality

Sometimes, when nodes are sorted according to their degree of centrality, for nodes with the same degree value, degree centrality cannot give a more detailed ranking. Therefore, the intermediate centrality is introduced to evaluate the charging station network. The intermediate centrality can reflect the importance of network nodes to some extent, and can effectively explore some important nodes with large “traffic” in the network. According to

Table 4. Top ten sites in terms of the centrality of the number of referrals.

Ranking	Station Number	Station Number	Area
1	71	Bus Honglou charging service station	Licheng District
2	41	Special electric car charging station (Jinan Financial Supermarket)	Lixia District
3	24	Jinan Changyun Bus public charging station	Tianqiao District
4	25	Jinan long-distance bus transport Co., Ltd. bus public charging station	Tianqiao District
5	39	Unitech Car Charging Station (Watt Road)	Lixia District
6	12	Special call car charging station (Jiayi Harmony Yidian, Ginza, Jinan)	Huaiyin District
7	13	Epp Public charging station	Huaiyin District
8	11	Yiwei Energy car charging station	Huaiyin District
9	10	Special call charging station (Jinan Biya Di Gansheng electric Vehicle)	Huaiyin District
10	7	Eway Energy Vehicle public charging station	Huaiyin District

, the top ten stations in terms of intermediate number centrality are 71, 41, 24, 25, 39, 12, 13, 11, 10, and 7, corresponding to bus Honglu charging service station, special car charging station (Jinan Financial Supermarket), Jinan Changyun Bus public charging station, Jinan Long-distance Bus Transport Co., LTD. Youke Car charging Station (Watt Road), Special Electric car charging station (Jinan Ginza Jiayi Harmony Yidian), Aipu Public public charging station, Yiwei Energy car Charging Station, Special electric car charging station (Jinan Biya Diansheng Electric Vehicle), and Yiwei Energy car public charging station, respectively. As can be seen from Table 4, the bus Honglou charging service station in Licheng District has the largest number of interchangers, and this node has the greatest influence. It is also obvious from the network diagram that the node is the largest and the darkest. Therefore, this station is very important, occupying a core position in the entire charging station network and acting as a hub role, which has the greatest control over the traffic flow in the network.

Table 5. Ranking of each largest metric index.

Indicators	Site Name	Area
Degrees (214)	Special call car charging station (Jinan Ginza Jiayi Harmony Store)	Huaiyin District
Degree centrality (46.46464539)	Special call car charging station (Jiayi Harmony Yidian, Jinza)	Huaiyin District
Near centrality (3.804765463)	Special electric car charging station (Jiayi Harmony Yidian, Ginza, Jinan)	Huaiyin District
Intermediate centrality (3.877902269)	Bus Honglou charging service station	Licheng District

lists the stations with the largest metrics. It is found that the special call car charging station in Huaiyin District (Jiayi Harmony Yidian, Ginza, Jinan) has the highest degree, degree centrality, and proximity centrality, indicating that this station plays an important role in the network and is most closely connected with other stations. The nearby traffic convenience is high and the flow of people is large. The bus Honglou charging service station belonging to Licheng District has the largest centrality in terms of number of interchanges, indicating that this station has the greatest influence and an important position in the whole network.

5.2.2. Cohesion Analysis Based on the Overall Characteristics of the Network

1.

Network density analysis

The overall network density reflects the tightness of the traffic connection between the charging stations in the region, and the value range is [0, 1]; a value closer to 0 indicates a sparse network, and a value closer to 1 indicates a denser network. The higher the overall network density, the closer the traffic connection between the charging stations, and the higher the effect of the high-density network on each node. As shown in

Table 6. Network density characteristic.

Network Scale	Relation Total	Network Density
75	1724	0.613

, in this section, UCINET software is used to calculate the density value of the overall system network in five regions of Jinan City, and the result is 0.613, indicating that the charging station network constructed in this paper is relatively close, its nodes are closely connected, and the overall network connectivity is good, which further indicates that the road traffic flow is dense.

2.

Core–edge structure analysis

Based on the functions and characteristics of different charging stations in the whole network, core–edge structure can be divided into two types: core area facility point and edge area facility point. Through the analysis of core–edge structure, we can clearly know which charging station is covered in the core area and which charging station is involved in the edge area. In addition, we can also know the influence degree and correlation between each charging station and between two charging stations. Figure 4 shows the core-edge structure network diagram of charging stations drawn by UCINET software. Different colors in the diagram represent different nodes. Figure 4 shows the visual expression based on ARCGIS software.

As can be seen from Figure 4, the network forms a structure with the key node as the center and other nodes diverging to the periphery. Nodes 1, 2, 3, 5, 7, 8, 10, 11, and 12 are located in the core area of the network, with strong dominance and stable core position. However, the number of nodes in the core area is far less than that in the edge area, so it can be seen that the development of charging stations is relatively dispersed and evenly distributed in the surrounding area, which also shows that the traffic in the surrounding area is relatively convenient and the flow of people is relatively dense.

The degree values of 75 charging stations were imported into Arcgis, and core–edge structures were obtained throughout all regions, as shown in Figure 5. As can be seen from Figure 5, the charging station network in the five districts of Jinan City presents a dense core–edge structure in the northwest and sparse in the southeast. Among them, Huaiyin District, Shizhong District, Lixia District, and Licheng District have formed a small community structure and are in the core area. These areas have a dense charging station layout, convenient road traffic, and strong advantages in the network, which can improve user charging convenience to a certain extent. The charging station of Tianqiao District is in the edge area. Due to its remote location, the charging station in this area is not large and the traffic lines are sparse.

3.

Coacervation subgroup analysis

The degree of a single node can only represent the network correlation between the node and other nodes, but it cannot accurately describe the degree of cohesion or dispersion of all key nodes in the overall network. Therefore, it is necessary to further analyze the distribution and attributes of each sub-network in the complex network to judge the network cohesion. Coacervation subgroup analysis can quantitatively deal with the characteristics of the relationship between the members of the subgroup, the affinity between the members of the subgroup, and the relationship between the members of one subgroup and another subgroup, so as to describe the affinity and intimacy of the individual structure in the group scientifically and reasonably. In this section, Concor algorithm in UCINET software is used to conduct a cluster analysis of groups, reveal the actual or potential correlation degree of charging stations in five districts of Jinan City and the phenomenon of small group clustering, and explore the affinity and disaffinity of economic relations between different individuals or groups. As can be seen from Figure 6, the charging station structure in the five districts of Jinan City is divided into eight cohesive sub-groups.

Table 7. Condensed subgroup node distribution.

Subgroup	Node
1	1, 2, 3, 4, 5, 6, 7, 26, 9, 10, 11, 12, 13
2	32, 33, 34, 35, 27, 28, 29, 30, 31
3	18, 19, 16, 8, 22, 21, 20, 17
4	24, 14, 15, 25, 23
5	36, 37, 38, 43, 44, 41, 42, 47, 70, 45, 46, 69
6	40, 58, 59, 39, 57, 53, 54, 52, 60, 51
7	49, 55, 56, 50, 62, 63, 73, 48, 75, 67, 68, 74, 61, 71
8	72, 64, 65, 66

lists the echelon table of cohesive sub-groups of charging stations in the five districts of Jinan City, which is divided into eight gradients. The first gradient has 13 nodes, the second gradient has 9 nodes, the third gradient has 8 nodes, the fourth gradient has 5 nodes, the fifth gradient has 12 nodes, the sixth gradient has 10 nodes, the seventh gradient has 14 nodes, and the eighth gradient has 4 nodes. In general, the seventh gradient and the eighth gradient are the nodes with the most nodes and the least nodes, respectively, and their number of nodes is a large difference of 10, indicating that the number of nodes in each subgroup is unbalanced. Combined with the core–edge structure analysis mentioned above, the gravity of nodes located in the core region is stronger, while that of nodes located in the edge region is weaker. Moreover, road traffic conditions have a great impact on the distribution of charging stations, resulting in unreasonable charging station agglomeration in the five districts of Jinan City and poor network connectivity.

6. Conclusions and Recommendations

The development of charging stations has become an important means for the country to successfully promote new energy vehicles. This paper uses the method of network analysis to deeply explore the layout of the charging stations of new energy vehicles in the five districts of Jinan City. Firstly, the charging station network model is constructed by the network analysis method, and then the local characteristics of the nodes and the overall characteristics of the network are analyzed according to the network static statistical indicators designed above, and their importance is ranked. According to the node local analysis metrics, the degree, degree centrality, and proximity centrality of the key node special call vehicle charging station (Jinan Ginza Jiayi Harmony Yidian) are the largest, and have the greatest influence in the entire network. Therefore, more charging station points can be built near the station to ensure users’ charging services. Secondly, according to the overall structure of the charging station network in the five districts of Jinan City, the network structure is further divided into communities, and the in-depth analysis is carried out between each small group. It is found that the core area node has a strong dominant role, and it has a strong attraction to the edge area node. Therefore, the road traffic flow in the core area is large, and there are more traffic arteries, showing a trend of decentralization to the edge area. Huaiyin District, Lixia District, Shizhong District, and Licheng District in the research area are located in the core area, and the charging stations are more distributed, which further indicates that the traffic flow in this area is large and the economic development level is high.

Based on the above analysis, this paper hopes to provide certain theoretical and reference significance for investors and builders of new energy vehicle charging stations. Nodes with high node density should be maintained and operated to avoid damage that may affect user usage. However, the network structure of new energy vehicle charging stations often presents dynamic changes, showing different characteristics in different time and space, and with network analysis it is often difficult to capture and analyze this dynamic. Therefore, some dynamic indicators can be introduced to deeply explore the evolution law of the layout structure of new energy vehicle charging stations. To extend the modeling idea of this paper to other cities, the conditions of social economy, traffic factors, policies, and regulations should be considered comprehensively. For cities with similar conditions to this city, promotion can be considered, which will increase the depth of the study. However, some influencing factors unique to other cities should also be taken into account. Therefore, some references and ideas can be brought to other cities.

From the actual situation, Lixia District, as the most economically developed area in the five regions, is indeed consistent with the actual situation. As the number of vehicles in Huaiyin District gradually increases, the number of charging stations also increases, and the results are basically consistent with the actual user demand pattern or vehicle ownership distribution. For peak hours, there may be some obstacles to the use of charging stations. In this regard, the traffic management department can take some measures to make the necessary adjustments and disperse the crowd in the area more effectively to better alleviate the potential bottleneck problem during peak hours. In the future, we can delve into how traffic congestion and changing transportation patterns affect future network performance.