Spatial Dynamic Interaction Effects and Formation Mechanisms of Air Pollution in the Central Plains Urban Agglomeration in China

Abstract

Accurately identifying the dynamic interaction effects and network structure characteristics of air pollution is essential for effective collaborative governance. This study investigates the spatial dynamic interactions of air pollution among 30 cities in the Central Plains Urban Agglomeration using convergent cross mapping. Social network analysis is applied to assess the overall and node characteristics of the spatial interaction network, while key driving factors are analyzed using an exponential random graph model. The findings reveal that air pollution levels in the Central Plains Urban Agglomeration initially increase before they decrease, with heavily polluted cities transitioning from centralized to sporadic distribution. Among the interactions, Heze’s air pollution impact on Kaifeng was the strongest, while Xinxiang’s impact on Changzhi was the weakest. The emission and receiving effects peaked during 2010–2012. The air pollution interactions among cities exhibit significant network characteristics, with block model results indicating that emitting and receiving relationships are primarily concentrated in the bidirectional spillover plate. Natural factors such as temperature and precipitation significantly influence the spatial interaction network. Economic and social factors like economic level and industrial sector proportion also have a significant impact. However, population density does not influence the spatial interaction network. This study contributes to understanding the spatial network of air pollution, thereby enhancing strategies for optimizing regional collaborative governance efforts to address air pollution.

1. Introduction

Since the Industrial Revolution, air pollution has paralleled human development [1]. China, as a rapidly developing nation, has made significant strides in economic growth. However, this progress has come with severe air pollution challenges due to insufficient environmental protections amidst rapid urbanization [2,3]. According to China Environment News, PM_2.5 contributes to 60% of all polluted days and China is among the countries experiencing significant increases in PM_2.5 concentrations worldwide [4]. To improve air quality and reduce PM_2.5 pollution, the Chinese government has enacted various air pollution control measures and initiated numerous research projects to investigate the factors driving air pollution [5]. Despite China’s success in managing PM_2.5 levels, the number of fine days far exceeds that of India, which has a similar population size. But there is still a significant gap between China’s overall air quality and that of developed countries.

The formation of suspended particles in the air mainly comes from two major sources: indoor human activities and outdoor industrial activities [6]. Influenced by natural and socio-economic factors, air pollution has interactive effects at certain spatial and temporal scales [7,8]. When studying the spatial interactions of air pollution, scholars usually approach it from two different perspectives: physical transport and information transfer. Specifically, some scholars have constructed air pollution transport models to simulate the pollutant transport process, which provides insights into the mechanism of air pollution trans-regional transport from a physical transport perspective [9,10,11]. From an information transfer perspective, academics believe that air pollution data contain comprehensive information about pollution levels and their drivers [12]. Earlier studies preferred to use correlation analysis, including correlation coefficients and spatial correlation coefficients, to explore spatial correlations and dependencies among air pollutants [13]. However, correlation does not directly imply causality [14], so this method cannot accurately measure the causality of air pollution and its direction in different regions. As a result, scholars have begun to employ causal reasoning to reveal the effects of spatial interactions so as to address this limitation. In this context, scholars have attempted to explore the spatial interactions of air pollution using Granger causality tests [15,16]. This method is suitable for analyzing closely related variables. However, with the expansion of the study scope and geographical distance, the correlation between the polluted areas decreases, making the results of the Granger causality test distorted. To overcome this shortcoming, Sugihara et al. [17] introduced convergent cross mapping (CCM), a data-driven approach grounded in embedding theory and state–space reconstruction techniques within the framework of non-linear dynamics. This innovation offers a more accurate and scientifically robust approach to discerning spatial correlations of air pollution within urban environments.

From the spatial scale, studies targeting PM_2.5 pollution characteristics initially focused on individual cities [18,19,20,21]. However, the spatial distribution pattern of PM_2.5 in different regions varies greatly due to the complex formation and spatial heterogeneity of PM_2.5 concentrations and the study of a single city alone ignores the spatial interaction characteristics of air pollution [22]. In terms of research methodology, existing studies have used ordinary least squares [23], geographically weighted regression models [24], standard deviation ellipse models [25], and spatial statistical methods [26] to test the spatial aggregation characteristics and overflow effects of PM_2.5. However, studies addressing the spatial correlation of PM_2.5 have notable limitations. Most current research relies on pollution attribute data rather than relationship data, hindering the accurate representation of spatial interaction characteristics. In contrast, relational data can offer more valuable insights by better reflecting the performance of attribute data [27]. Current research does not fully elucidate the spatial interaction characteristics and dynamic effects of PM_2.5. Traditional measurement techniques are restricted to assessing quantitative impacts, often overlooking spatial interactions. Recently, social network analysis (SNA) has emerged as an innovative approach to studying spatial relationships between variables, with applications across various fields such as economics, management, and sociology [28,29]. SNA is a multidisciplinary method used to examine the collective, individual, and structural attributes of spatial relational networks. This approach not only reveals association patterns within networks using attribute data but also provides valuable insights into the interconnections among network nodes through relational data [30]. In the context of air pollution analysis, an increasing number of scholars are utilizing SNA to explore the complex network relationships of regional environmental pollution from a relational data perspective [31].

The potential contributions of this study are manifold. Firstly, we introduce an innovative approach to analyzing the spatial dynamic interaction effects of air pollution among cities. Utilizing the CCM technique, we identify the causal links of air pollution in non-linear spatial interactions and construct a causality matrix. Through SNA, we analyze the overall and node characteristics of the air pollution network, uncovering the spatial dynamic interaction effects of air pollution and the linkage patterns of each city, thus providing a novel analytical perspective for existing research. Secondly, we identify the key influencing factors of the spatial interaction network of air pollution in the Central Plains Urban Agglomeration by the exponential random graph model (ERGM). This provides empirical insights for accurately enhancing the efficiency of regional air pollution management. Thirdly, this study extends the theoretical framework of spatial networks concerning regional collaborative governance of air pollution. By integrating collaborative development theory, the CCM technique, SNA, and ERGM, we construct a comprehensive research framework for regional cooperation in air pollution governance in the Central Plains Urban Agglomeration. This interdisciplinary approach not only broadens the theoretical understanding but also offers practical implications for policymakers aiming to improve regional air quality management strategies.

This article aims to address the following questions: What is the spatiotemporal change process of air pollution in the Central Plains Urban Agglomeration? What are the dynamic interactions between cities, and how do they change over time? What are the structural characteristics of the air pollution spatial interaction network in the Central Plains Urban Agglomeration? What are the key influencing factors of the network?

The remaining chapters are organized as follows: Section 2 describes the research methodology and data sources. Section 3 presents the results and discussion. Section 4 contains the conclusions and recommendations.

2. Materials and Methods

2.1. Study Area

This study focuses on the Central Plains Urban Agglomeration, situated in the central–eastern region of China, primarily encompassing Henan Province and 30 prefectural-level cities under the governance of Henan, Shanxi, Hebei, Shandong, and Anhui provinces. Spanning a total area of 287,000 square kilometers and housing approximately 170 million residents, this agglomeration is recognized as one of the seven prominent urban clusters nationwide [32]. The geographical positioning of the research area and its constituent cities are illustrated in Figure 1.

2.2. Research Methods

2.2.1. Convergent Cross Mapping

CCM is a method based on dynamical systems theory for identifying and verifying causal relationships between variables in a system. This method, which is theoretically based on the embedding theorem and causal inference, was proposed by Sugihara et al. [17] in 2012, aiming to address the limitations of traditional statistical methods when dealing with non-linear, non-stationary time series data. For two time series variables, X and Y, the CCM makes a judgement on whether X is the cause of Y by determining the extent to which historical information about Y can reliably estimate X’s state from X. Specifically, suppose that M_Y is a shadow manifold constructed using the lagged coordinates of the time series Y and M_X is a shadow manifold constructed using the lagged coordinates of the time series X. If nearby points on M_Y can be used to identify nearby points on M_X, then Y can be used to estimate X; i.e., X is the cause of Y.

Considering two time series X and Y with period length L, shadow manifolds M_X and M_Y are constructed by generating lagged coordinate vectors.

$$M_X:x\left(t\right)=\left\{X\left(t\right),X\left(t-\tau \right),X\left(t-2\tau \right),\dots ,X\left(t-(E-1)\tau \right)\right\}$$

$$M_Y:x\left(t\right)=\left\{Y\left(t\right),X\left(t-\tau \right),Y\left(t-2\tau \right),\dots ,Y\left(t-(E-1)\tau \right)\right\}$$

where $t$ is in the range of ($1+\left(E+1\right)\tau ,L)$, $\mathrm{E}$ is the embedding dimension, and $\tau$ is a time lag phase. The lagged coordinate vector $x\left(t\right)$ and its nearest $E+1$ points at $M_X$ can be selected at the same time, and these points are used to generate weights ${\omega }_i$ and the actual values of $Y$ are locally weighted and averaged by these weights, thus forming a cross-mapping estimate $\widehat{Y}\left(t\right)\mid M_X$ of $Y\left(t\right)$.

$$\widehat{Y}\left(t\right)\mid M_X=\sum {\omega }_{i}Y\left(t_i\right) i=1,2,\dots ,E+1$$

where ${\omega }_i$ denotes the relative distance between $x\left(t\right)$ and its $i$-th neighbour on $M_X$, and $Y\left(t_i\right)$ is the true value of the time series $Y\left(t\right)$ at the $i$-th observation.

In the CCM method, if there are $L$ sequence points on the shadow manifold $M_X$ that can predict $L$ estimates of the original time series $Y$, the degree to which these estimates match the actual values determines the efficacy of the variable $X$ in predicting $Y$. This predictive efficacy can be assessed by calculating the correlation between the actual and estimated values, which is known as the CCM correlation coefficient. The magnitude of the CCM correlation coefficient indicates the extent to which the dependent variable influences the independent variable, and the CCM correlation coefficient is calculated as follows:

$${\rho CCM}_{Y\widehat{Y_t}}=\rho \left[Y\left(t\right),\widehat{Y}\left(t\right)\mid M_X\right]$$

CCM correlation coefficients are affected by the length of time. As the value of $L$ grows, the amount of data increases, allowing the attractor manifold to be filled more completely, and the distance between the observation and the $E+1$ nearest neighbors on the shadow manifold decreases progressively. This means that if $Y$ is the cause of $X$, then the cross-mapped predicted value $\widehat{Y}\left(t\right)\mid M_X$ based on $M_X$ will gradually approach the actual value; i.e., the predictive power $\rho {CCM}_{Y\widehat{Y_t}}$ will keep increasing until it converges to 1.

The steps involved in creating a delayed version of a time series for state–space reconstruction in CCM are as follows: Determine the time lag. Determine the embedding dimension E. Build the embedding vector. The nearest neighbor of the embedded vector is used to make the prediction, and the correlation between the predicted value and the actual value is calculated. First, determine embedding parameters. Determine embedding dimension E and time lag τ. Second, state–space reconstruction. Construct embedding vectors of time series X(t) and Y(t). Third, cross-mapping prediction. Use the nearest neighbor of X(t) to predict Y(t) value. Fourth, test convergence. As the amount of data increases, verify the convergence of the prediction ability. Fifth, evaluate causality. Evaluate the strength of causality through correlation analysis.

2.2.2. Social Network Analysis

Compared with complex network analysis, SNA focuses more on the study of the relatively stable relationship system formed by the interaction among network members, emphasizing how the interaction and connection between nodes affect social behavior. The overall association network characteristics are assessed based on four key metrics: network density, connectedness, hierarchy, and efficiency [33]. The network density indicates the connectivity strength of the air pollution spatial network, which represents the proportion of connections that are actually present among the possible connections. Network connectedness measures the extent to which a network is dependent on a particular city. The network hierarchy measures the asymmetry of city accessibility in the network, which shows the hierarchical structure and hierarchy among cities. Network efficiency reflects the efficiency of interconnections among cities in the air pollution network. High efficiency means that information and resources can be transferred quickly, facilitating efficient collaboration and response.

Degree centrality, betweenness centrality, and closeness centrality are the three main network centrality metrics when analyzing the characteristics of each node [34,35]. Degree centrality measures the activity of a city in the air pollution network and is equal to the number of other nodes that a node is directly connected to. Higher degree centrality indicates that the city is directly connected to more cities in the network and has stronger influence and information dissemination capacity. Betweenness centrality describes a city’s importance as a bridge to other cities in the network, and the intermediate centrality of a node is equal to the frequency at which the node appears in the shortest path between all pairs of nodes in the network. Cities with high betweenness centrality serve as key intermediaries in the transmission of information and resources. Their actions and decisions significantly impact the overall efficiency and stability of the network. Closeness centrality measures the average distance of a city from all other cities in the network and can be measured by calculating the inverse of the sum of shortest path distances from one node to all other nodes. Cities with high closeness centrality are nearer to all other cities, enabling them to influence and respond to network changes more rapidly. This makes them core nodes within the network, vital for maintaining network cohesion and functionality.

In this study, each city in the original urban agglomeration is taken as a network node. The interactive impact of air pollution among cities is considered as the network relationship. The study focuses on the spatial interactive impact and network structure characteristics of air pollution among these cities.

2.2.3. Block Model Analysis

In SNA, block model analysis is different from other clustering methods in that it focuses on revealing the structural pattern of the network and understanding the macro structure of the network by grouping nodes, especially focusing on the relationship and interaction among groups. Block model analysis reveals the structural characteristics of urban air pollution networks, elucidating the roles and influence of cities (nodes) within various segments. This analysis offers insights into the dynamic overflow effects between different sections of the network. In this paper, the CONCOR algorithm was used to divide 30 cities into 4 plates with a maximum segmentation depth of 2 and concentration of 0.2. This classification considers the total number of relationships each node receives and emits, along with the expected and actual proportions. In addition, different blocks are constructed according to the role and function of each node in order to minimize the limitations of block model analysis. The plates, based on their dynamic interactions, can be categorized into four types: main outflow plate, bidirectional spillover plate, main inflow plate, and agent plate [36].

2.2.4. Exponential Random Graph Models

ERGM is a statistical model used to analyze the structural features of network data. By decomposing the global structural features of a network into a probabilistic model of local configurations, it is able to simultaneously take into account the interactions and dependencies between nodes in the network [37]. It has strong flexibility and wide applicability and can simulate and infer complex dependency structures present in real-world networks. The basic mathematical expression for ERGM is

$$P_{\theta }\left(X=Y\right)=\left({\displaystyle \frac{1}{k}}\right)exp\left\{\sum _n{\theta }_n{g}_{\theta }\left(y\right)\right\}$$

where $g\left(y\right)$ is the network statistic associated with the spatial interaction matrix $y$, $\theta$ is the coefficient of the statistic, and $g_{\theta }\left(y\right)$ is the network statistic value corresponding to $\theta$. When $\theta$ occurs in $y$, then $g_{\theta }\left(y\right)=1$; otherwise, $g_{\theta }\left(y\right)=0$; $k$ is a normalization constant that counts and calculates all probabilities to take values.

In the process of constructing ERGM model, it is necessary to assume that the statistics contained in the model are sufficient statistics to describe the network structure and the nodes and edges have commutative properties. In this paper, the model was selected by cross-validation and information criteria to avoid excessive statistics and maintain the sufficiency and simplicity of the model. The attributes of nodes and edges are introduced into the model, and heterogeneity statistics are used to capture the differences and ensure the exchangeability of nodes and edges.

2.3. Data Description

Noise and missing values will affect the convergence of CCM. In this paper, PM_2.5 concentration is selected as the proxy variable of air pollution and there are no missing and abnormal values in the data. In Central Plains Urban Agglomeration, 30 cities were grouped into two categories, medium and high, according to the annual average concentration of PM_2.5 in each city. The extent of spatial interaction of air pollution among cities was examined in terms of main effects and convergence effects. In the selection of nodal covariates, this study considers both natural and economic and social factors and chose five influencing factors, temperature (Average annual temperature of the city) [38], precipitation (Average annual precipitation of the city) [39,40], economic development degree (GDP per capita) [41,42], population density (Number of people per unit area) [43,44], and the level of industrial development (The proportion of secondary industry in regional GDP) [45]. The above factors are introduced into the ERGM model, and the role they play in the formation of spatial interaction network of air pollution is explored. The above data are derived from the China City Statistical Yearbook and the statistical yearbooks from the provinces within the Central Plains Urban Agglomeration.

3. Results and Discussion

3.1. Spatial Distribution Patterns

In this study, the average annual PM_2.5 concentration data (μg/m³) of 30 cities in the Central Plains urban agglomeration from 2000 to 2020 are summarized according to the Monthly Report of National Urban Air Quality released annually by the China Environmental Monitoring Station. The spatial visualization analysis was carried out by ArcGIS 10.8 software, and the natural breakpoint method was used to divide 30 cities into five categories according to the pollution degree (Figure 2).

Between 2000 and 2020, the level of air pollution in the Central Plains Urban Agglomeration showed a trend of first aggravation and then alleviation, and the air pollution situation was significantly improved in 2020. In terms of spatial distribution, Kaifeng, Xingtai, Puyang, Liaocheng, and Hebi that are located in the central and northern areas are severely polluted, while Sanmenxia, Nanyang, Changzhi, Jincheng, Suzhou, and Bengbu that are located in the peripheral areas of the urban agglomerations have always been at a lower level of pollution. The cities with the highest pollution levels changed from the central and south Henan regions in 2000 to Xuchang, Luohe, Jiaozuo, Xinxiang, and Hebi in 2005, shifting to six cities in central and northeastern Henan in 2010, to the northern part of the Central Plains Urban Agglomeration in 2015, and showing a sporadic dot distribution in 2020, with a major concentration in Handan, Yuncheng, and Pingdingshan. Comparing the pollution levels of the five provinces in the Central Plains Urban Agglomeration, it can be found that the Henan and Hebei provinces are heavily polluted, while the Shanxi, Shandong, and Anhui provinces are less polluted. The air pollution in the Central Plains Urban Agglomeration shows a distribution characteristic of “high in the center and low in the surroundings”.

3.2. Spatial Dynamic Interactions of Air Pollution

3.2.1. CCM Causality Identification

As China’s main grain-producing cities, the cities within the Central Plains Urban Agglomeration are tasked with ensuring food security, which are dominated by the plains, leading to the diffusion and spread of air pollutants among the cities. This feature makes the traditional causal inference technique represented by the Granger causality test method no longer applicable. For this reason, the CCM method is adopted in this study to test the causal relationship of air pollution among cities in the Central Plains Urban Agglomeration.

Embedding dimensions in CCM greatly affects the results. In order to improve the accuracy of the CCM results, it is necessary to determine the optimal embedding dimension of the CCM test. In general, the optimal embedding dimension will affect the degree of prediction accuracy. Univariate predictive power indicates the correlation coefficient between the true and predicted values, which will peak at the optimal embedding dimension [46]. The false nearest neighbors method is used to determine the embedding dimension, and the autocorrelation and information criterion is used to determine the lag period. The results show that the optimal embedding dimension of 30 cities in the Central Plains Urban Agglomeration is concentrated between 2 and 5.

In CCM, the significance of convergence is to verify the causal effect of the dependent variable on the outcome variable. By observing the convergence of the predictive power, we can effectively infer a causal relationship between two variables and ensure that the relationship is stable and credible. It is necessary to observe whether the predictive power of the cross mapping converges to a certain peak when identifying the causal relationship between the variables using the CCM method. When the cross-map lag L reaches its maximum value, the cross-map skill ρ can measure the intensity of air pollution interaction between city A and city B. Due to the space limitation, the two groups of cities with the largest CCM coefficients are selected in this thesis as representatives, and the results are shown in Figure 3. The CCM correlation coefficients of air pollution between Fuyang and Bozhou are at a high level, and the CCM curves converged to a higher level with the expansion of the prediction intervals, which indicates a close interaction of air pollution between them. The CCM curves between Heze and Kaifeng are also at a high level, but there is a gap between the two CCM curves, indicating that the changes in air pollution in Heze are more predictive of the level of air pollution changes in Kaifeng.

3.2.2. Overall Spatial Dynamics Interaction Effects

Longer data series in CCM help to reconstruct the state–space more accurately and improve the accuracy and reliability of the prediction. Choosing a data series with 50 times the optimal embedding dimension is a reasonable choice. In this study, 252 sets of monthly air pollution data of 30 cities in Central China Urban Agglomeration during 2000–2020 were used to explore the interaction effect of air pollution between cities. Origin 2021 software is used to visually explore the causal relationships between these cities, as illustrated in Figure 4.

The intensity of air pollution causality between the two cities is measured by correlation coefficient. The higher the correlation coefficient, the stronger the causation. As the length of the time series increases, the prediction correlation should become stable and converge. If the predicted correlation increases with the increase in the data length and eventually converges, it indicates that there is a stable causal relationship between the air pollution between the two cities. The analysis reveals 527 interaction effects with correlation coefficients ranging from 0.9396, representing Heze’s impact on Kaifeng, to 0.0001, indicating Xinxiang’s influence on Changzhi. The findings indicate that Heze’s air pollution is most strongly correlated with that of other cities, whereas Yuncheng shows the weakest correlation. Additionally, air pollution in Luohe is most influenced by other cities, while Changzhi is the least affected. The likelihood of causal interactions in air pollution is higher among cities located centrally within the urban agglomeration and lower among those on the outskirts, highlighting the importance of geographic distance in these interactions.

3.2.3. Spatial Dynamics Interaction by Period

In this study, the rolling window technique is combined with the CCM to construct the rolling window technique-based convergent cross-mapping method (RW-CCM) to identify the spatial dynamic interaction effects of air pollution among cities in the Central Plains Urban Agglomeration by periods. The length of windows is three years, and the window interval is one year, totaling 19 windows. Emitting effect measures the extent to which a city’s air pollution affects other cities’ air pollution, and receiving effect measures the extent to which a city’s air pollution is affected by other cities’ air pollution. The CCM coefficients between each city and the other 29 cities were summed to obtain the intensity of the emission and receiving effects. Due to space limitations, this study selects the five cities with the largest intensity of emission and receiving effects for demonstration purposes, and the results are shown in

Table 1. Dynamic interaction coefficients.

Window Phase	Emission Effect Intensity					Receiving Effect Intensity
	Heze	Kaifeng	Liaocheng	Zhoukou	Puyang	Luohe	Xuchang	Xinxiang	Kaifeng	Anyang
00–02	20.206	20.214	19.506	19.334	19.309	20.289	20.264	20.194	20.203	20.049
01–03	20.209	20.179	19.439	19.349	19.227	20.349	20.307	20.254	20.220	20.143
02–04	20.255	20.250	19.589	19.488	19.413	20.597	20.513	20.428	20.379	20.224
03–05	20.282	20.209	19.622	19.523	19.428	20.667	20.653	20.483	20.419	20.403
04–06	20.316	20.297	19.627	19.610	19.567	20.761	20.769	20.537	20.467	20.557
05–07	20.441	20.388	19.834	19.731	19.613	20.998	20.800	20.764	20.616	20.609
06–08	20.471	20.419	19.642	19.687	19.813	20.943	21.016	20.671	20.584	20.694
07–09	20.523	20.375	19.751	19.734	19.711	21.386	21.285	21.022	20.961	20.686
08–10	20.491	20.461	19.169	19.910	20.019	21.546	21.642	20.492	21.164	20.641
09–11	20.621	20.698	20.049	20.416	20.049	21.849	21.489	21.067	20.894	20.889
10–12	20.792	20.641	20.541	19.843	20.112	22.064	21.249	21.649	21.349	20.984
11–13	20.471	20.556	20.040	19.671	19.876	21.649	21.164	21.421	20.876	20.661
12–14	20.667	20.417	20.331	20.001	20.134	21.669	21.541	21.341	21.034	20.871
13–15	20.613	20.399	20.201	20.164	19.864	21.541	21.473	20.864	20.671	20.314
14–16	20.743	20.541	20.246	20.019	20.164	21.550	21.400	20.946	20.764	20.513
15–17	20.640	20.216	20.349	19.671	19.943	21.506	21.246	20.716	20.664	20.530
16–18	20.513	20.016	19.973	19.780	19.641	21.300	21.149	20.846	20.604	20.431
17–19	20.556	20.164	20.049	19.704	19.430	21.294	21.204	20.877	20.159	20.300
18–20	20.319	20.013	19.870	19.647	19.216	21.001	20.846	20.613	20.443	20.304

.

In Table 1, the dynamic interaction effect of air pollution shows a trend of first strengthening and then weakening, and reaches its maximum in the window period of 2010–2012, which is consistent with the characteristics of the temporal evolution of air pollution. The five cities with the highest intensity of emitting effects are Heze, Kaifeng, Liaocheng, Zhoukou, and Puyang, of which Heze and Liaocheng show the highest intensity of emitting effects during the window period of 2010–2012, and Kaifeng and Zhoukou show the highest intensity of emitting effects during the window period of 2009–2011, and Puyang shows the highest intensity of emitting effects during the window period of 2014–2016. These cities are mainly distributed in the northeast of the Central Plains Urban Agglomeration, and the fluctuations in air pollution levels within their cities are prone to forming spatial interaction relationships with air pollution in other cities, making them the main source cities for the formation of spatial interaction relationships of air pollution within the urban agglomeration. The five cities with the greatest intensity of receiving effects are Luohe, Xuchang, Xinxiang, Kaifeng, and Anyang, of which Luohe, Xinxiang, Kaifeng, and Anyang have the greatest intensity of receiving effects in the window period 2010–2012, and Xuchang has the greatest intensity of receiving effects in the window period 2008–2010. These cities are mainly located in the central part of the urban agglomeration, with convenient transport and close economic contacts with the remaining cities, making it difficult to plate the diffusion of air pollutants.

3.3. Social Network Analysis

3.3.1. Overall Characteristic Analysis

This paper constructs a 30 × 30 matrix for SNA, based on the interaction coefficients’ size and significance regarding air pollution among 30 cities. The maximum possible number of spatial interactions among 30 cities is 870 (30 × 29), while the total number of tested significant causality is 527 (Figure 5). The overall network density of the air pollution correlation network among 18 cities is 0.606 (527/870) and indicates that air pollution among 30 cities shows significant network relationships during the sample study period. The air pollution linkages among cities account for 61 per cent of the total linkages, and the spatial interactions are not only limited to the neighboring cities, but also show a multi-threaded, multi-city, and cross-region network distribution within the urban agglomerations. The correlation coefficient of the air pollution network among cities is 1, indicating a strong interconnected relationship among all cities. The Central Plains Urban Agglomeration exhibits an air pollution network efficiency of 0.345, suggesting that over 65% of the connections are redundant. Additionally, a superposition phenomenon is observed in the correlation of air pollution between various cities within the agglomeration, indicating a strong network stability. A network hierarchy of 0.186 reveals a lack of clear hierarchy among cities, indicating that the status and role of each city are similar. This underscores the need for collaborative efforts from all cities to effectively manage air pollution in the urban agglomeration.

3.3.2. Individual Node Characteristics Analysis

Table 2. Network characteristics of node cities.

City	Outdegree	Indegree	Degree	Betweenness	Closeness
Handan	15	11	26	0.000	4.947
Xingtai	18	20	38	2.363	5.375
Changzhi	4	2	6	54.000	1.807
Jincheng	2	2	4	0.000	0.867
Yuncheng	2	2	4	0.000	0.867
Bengbu	21	16	37	3.859	5.441
Huaibei	21	16	37	62.456	5.446
Fuyang	16	17	33	3.014	5.300
Suzhou	21	10	31	1.787	5.441
Bozhou	18	16	34	2.832	5.300
Liaocheng	23	22	45	8.325	5.672
Heze	23	24	47	53.387	5.723
Zhengzhou	20	21	41	5.343	5.505
Kaifeng	23	24	47	8.909	5.619
Luoyang	14	2	16	1.313	4.829
Pingdingshan	18	24	42	4.911	5.620
Anyang	22	24	46	9.412	5.724
Hebi	20	25	45	9.853	5.724
Xinxiang	21	25	46	39.307	5.871
Jiaozuo	20	20	40	7.650	5.508
Puyang	20	22	42	4.185	5.564
Xuchang	22	26	48	11.918	5.724
Luohe	21	25	46	7.023	5.672
Sanmenxia	7	2	9	0.000	3.613
Nanyang	20	24	44	5.116	5.620
Shangqiu	20	21	41	3.824	5.504
Xinyang	14	22	36	5.373	5.504
Zhoukou	23	23	46	8.729	5.563
Zhumadian	23	25	48	11.532	5.672
Jiyuan	15	14	29	1.576	4.942

presents the centrality analysis of the air pollution correlation network among cities, encompassing degree centrality, betweenness centrality, and closeness centrality metrics.

The average degree centrality is 35.133, with 20 cities exceeding this average. Notably, Heze and Kaifeng exhibit the highest degree centrality at 47, each having 23 emitting and 24 receiving relationships. This indicates that Heze and Kaifeng are highly connected within the network, meaning that changes in their air pollution levels significantly impact other cities. In contrast, cities with lower degree centrality are predominantly located in the northern part of the Central Plains Urban Agglomeration, suggesting that geographic distribution affects the air pollution correlation network.

The mean betweenness centrality of 11.267 highlights that certain cities act as key connectors within the network, managing the linkage relationships. Specifically, five cities exceed the average betweenness centrality, serving as essential “bridges” and “intermediaries.” On the other hand, peripheral cities in the Central Plains Urban Agglomeration display lower betweenness centrality, indicating a reduced influence on the network.

The average closeness centrality in the air pollution correlation network is 4.999, reflecting a significant level of interconnectedness among cities. Xinxiang, with the highest closeness centrality of 5.871, emerges as the central node of the network. Among the 30 cities analyzed, 23 have closeness centrality values above the average, highlighting their proximity to the network’s core and their influential roles. Conversely, Jincheng, Yuncheng, and Changzhi exhibit much lower closeness centrality, placing them at the edge of the agglomeration in Shanxi Province. Consequently, these cities experience less impact from air pollution fluctuations and occupy a “follower” position within the network.

3.3.3. Spatial Clustering Analysis

To further elucidate the roles and functions of different cities within the air pollution correlation network, we employed the CONCOR method. The specific results are detailed in

Table 3. Spillover effect of the spatially related plate.

Plate	Relations Received		Relations Sent		Expected Internal Relations	Actual Internal Relations
	Inside	Outside	Inside	Outside
I	205	115	205	116	51.724%	63.863%
II	78	119	78	99	27.586%	44.068%
III	6	0	6	2	6.897%	75.000%
IV	2	12	2	19	3.448%	9.524%

. Among them, Plate I includes 16 cities, which are Handan, Xingtai, Liaocheng, Zhengzhou, Kaifeng, Pingdingshan, Anyang, Hebi, Xinxiang, Jiaozuo, Puyang, Xuchang, Luohe, Nanyang, Zhumadian, and Jiyuan. Plate II consists of nine cities, namely, Bengbu, Huaibei, Fuyang, Suzhou, Bozhou, Heze, Shangqiu, Xinyang, and Zhoukou. Plate III is comprised of Changzhi, Jincheng, and Yuncheng. Plate IV includes Luoyang and Sanmenxia.

In the air pollution correlation network, there are 291 inside relations and 236 outside relations, accounting for 55.218% and 44.782% of the total relationships, respectively. Plate I has 116 received relationships and 115 sent relationships, with a ratio of 51.724% for expected internal relationships and 63.863% for actual internal relationships. It is high for both emitting and receiving relationships and belongs to the bidirectional spillover plate. Plate II has 99 sent and 119 received relations, so fewer sent relations than received relations and is the main inflow plate. Plate III is the main inflow plate, which only emits relations in the correlation network and does not receive relations from other cities. Plate IV belongs to the agent plate, with 19 sent relations and 12 received relations, with an expected internal relationship ratio of 3.448% and actual internal relationship ratio of 9.524%.

The network density matrix for each plate was calculated based on the distribution of the air pollution correlation network among the plates, reflecting the relationships among the four major plates. The results shown in

Table 4. Density and image matrix of four plates.

Plate	Density Matrix				Image Matrix
	I	II	III	IV	I	II	III	IV
I	0.958	0.632	1	0	1	1	1	0
II	0.722	0.986	0	0.111	1	1	0	0
III	0.021	0.037	1	0	0	0	1	0
IV	0.531	0.611	0	1	0	1	0	1

indicate an overall network density of 0.606 for air pollution associations among the 30 cities. Plates with a network density above 0.606 are assigned a value of 1, while those below are assigned a value of 0. Consequently, the network density matrix of the plates is transformed into an image matrix. Plate I sends relations to Plate II and Plate IV and receives relations from Plate II. Plate II not only sends relations to Plate I but also receives relations from it. Plate III only receives relations from Plate I, and Plate IV only sent relations to Plate II.

3.4. Network Influence Factors Analysis

The ERGM can analyze the impact of multi-layer network structure variables on network construction by considering both endogenous network characteristics and external environmental factors. The ERGM type used in this paper is a comprehensive model that considers multiple levels of network structure variables, including self-organizing effects, node attribute effects, and exogenous network effects. This method can effectively simulate and infer the complex dependency structure in the real network and is suitable for analyzing the spatial dynamic interaction and driving factors of air pollution in the Central Plains Urban Agglomeration [47]. We utilized the TERGM package in the R environment to fit the ERGM model. The model parameters were estimated using the Markov Chain Monte Carlo maximum likelihood estimation method. The significance of parameter fitting was determined based on the ratio of absolute values to standard deviations [48]. The results are presented in

Table 5. ERGM model regression results.

	Base Model		Node Covariate	Network Covariate
	(1)	(2)	(3)	(4)
Network self-organization effect
Edges	−2.1567 (0.0196)	−1.9234 (0.0179)	−2.4691 (0.0579)	−2.8973 (0.0713)
Mutual	1.1784 (0.0271)	1.2620 (0.0304)	1.1648 (0.0288)	1.0094 (0.0416)
Individual attribute effect
Mid AP	0.2861 (0.0112)	0.1457 (0.0211)	0.1978 (0.0164)	0.1447 (0.0184)
High AP	0.5547 (0.0195)	0.5249 (0.0260)	0.3267 (0.0228)	0.2513 (0.0307)
Rain			−0.0237 (0.0118)	0.0201 (0.0123)
Temp			0.0328 (0.0579)	0.0319 (0.0649)
Rgdp			0.1597 (0.0249)	0.1794 (0.0230)
Pop			0.0198 (0.0106)	0.0202 (0.0109)
Ind			0.1312 (0.0306)	0.0165 (0.0284)
Exogenous network effect
Geographic location				1.1216 (0.3197)
Climate linkage				0.2449 (0.0497)
Economic linkage				0.3167 (0.0515)

.

Models (1) and (2) in Table 5 report the primary and convergent effects of air pollution concentration (AP), respectively, including the number of edges and the interaction characteristics among cities. The regression results indicate that the interaction characteristics of both effects are positive, with estimated coefficients of 1.1784 and 1.2620, respectively. This suggests that the spatial network of air pollution among cities exhibits bidirectional interaction, with mutual influence of air pollution phenomena among different cities. This finding aligns with the analysis of network characteristics. Both the primary and convergent effects of air pollution concentration were significant, indicating that heavily polluted cities are more likely to establish spatial air pollution linkages with other cities. Specifically, highly polluted cities are 1.46 times more likely to form spatial relationships with air pollution compared to cities with moderate pollution levels (=exp (0.5249–0.1457)). Additionally, similar levels of air pollution in cities promote spatial interactions. If both cities have moderate levels of air pollution, the likelihood of forming a spatial relationship for air pollution is 1.22 times higher (=exp (0.1978)). If both cities are severely polluted, the odds are 1.39 times higher (=exp (0.3267)).

Based on the baseline regression model (1), temperature (Temp), precipitation (Rain), economic development degree (Rgdp), population density (Pop), and industrial industry share (Ind) were incorporated into the ERGM model. The measurement results of model (3) indicate that both natural and socio-economic factors contribute to the formation of spatial interactions of air pollution among cities. Specifically, the effect of Temp on the spatial interaction of air pollution is significant, with a positive estimated coefficient, suggesting that higher temperatures promote the formation of spatial interactions of air pollution. In contrast, the estimated coefficient of Rain is negative, albeit relatively small, indicating that rainy weather reduces the spatial interactions of air pollution among cities. This attenuation likely occurs because rainwater captures air pollutants, causing them to settle on the ground, thereby reducing their spread and dispersion. Rgdp significantly influences the spatial interaction of air pollution. More economically developed regions, with higher frequencies of human and factor mobility, experience greater spatial interactions of air pollution. This may be due to ineffective mitigation measures within these integrated urban areas. Conversely, Pop does not play a significant role in forming spatial interactions of air pollution. Ind is the second most critical factor influencing the spatial interaction of air pollution. The greater the industrial similarity between two cities, the more likely they are to experience spatial interactions of air pollution. This underscores industrial pollution as a major source of air pollution within the urban agglomeration.

In Model (4), considering the role of network covariates, this study incorporated three factors into the ERGM model: geographic location, climate linkage, and economic linkage. The analysis results indicate that all three factors are significant, with positive estimated coefficients. Specifically, when a climatic link exists between two cities, the probability of forming a spatial link for air pollution increases by 1.28 times (=exp (0.2449)). Similarly, when an economic link exists, this probability increases by 1.37 times (=exp (0.3167)). Geospatial factors exert the greatest influence on the formation of spatial interactions of air pollution. The closer the geographic proximity of the cities, the higher the likelihood of forming spatial interactions of air pollution. This demonstrates that geographic location is a critical determinant in the spatial dynamics of air pollution among cities.

4. Conclusions and Policy Recommendations

4.1. Conclusions

Utilizing data on air pollution from 30 cities within the Central Plains Urban Agglomeration, this study employs CCM, SNA, and ERGM to construct and analyze a spatial network of air pollution interactions. The research investigates both the overall network characteristics and the specific attributes of individual nodes, as well as the primary factors influencing network dynamics. The main conclusions are as follows:

Firstly, air pollution levels in the Central Plains Urban Agglomeration showed a spatiotemporal trend of initially worsening and then improving, with highly polluted cities shifting from a centralized to a more dispersed distribution. Secondly, CCM confirmed the existence of 527 sets of spatial associations among 30 cities. The air pollution in Heze has the greatest impact on Kaifeng, while the impact of Xinxiang on Changzhi is the weakest. Between the different window periods, the peak periods for emission and reception effects across the cities occurred between 2010 and 2012. Thirdly, the SNA structure shows that the air pollution in the Central Plains Urban Agglomeration presents obvious network characteristics. The bidirectional spillover relationship of air pollution between cities is the most obvious relationships. Finally, ERGM analysis shows that Temp, Rain, Rgdp, and Ind significantly affect the spatial interaction network of air pollution, while Pop does not. Geographic proximity, climate linkages, and economic ties are crucial in shaping these spatial interactions.

Compared with existing studies. In terms of research objects, this study chose PM_2.5 concentration as the basic data to study the spatial correlation of pollution between cities, rather than pollution control technologies [31]. In terms of research area, this paper takes the Central Plains city cluster as the research object, not the Beijing–Tianjin–Hebei city cluster, the Yangtze River Delta city cluster, He nan province and the Pearl River Delta city cluster [49,50,51,52]. In terms of research methods, this paper uses the combination of CCM and SNA for the first time, and uses ERGM to explore the key drivers of the network. Compared with the QAP analysis method adopted by Zhang et al. [53] and Su and Yu [54], it can capture the complex dependencies and structural features in the network more flexibly.

4.2. Policy Recommendations

To address the interconnected effects of air pollution within the cities of the Central Plains Urban Agglomeration, it is imperative to enhance regional coordination. It is suggested that a collaborative framework for the prevention and control of air pollution throughout the urban agglomeration be established to promote information sharing, technology transfer, and resource consolidation among cities. This approach is expected to be efficacious in facilitating collaborative efforts to prevent and manage air pollution in the area through a range of strategies, such as policy direction, technical assistance, and financial resources. Furthermore, the promotion of sophisticated monitoring technologies and the utilization of big data analysis are recommended to enhance the capacity to mitigate pollution at its origin and promptly address alerts. Key nodal cities, characterized by high levels of pollutant emissions and significant transmission impacts within the region, should be prioritized for monitoring and governance efforts to enhance their role in regional air pollution prevention and control. This strategic approach not only facilitates resource allocation optimization and governance efficiency but also contributes to the reduction in air pollutant emissions and transmission on a broader scale, fostering a healthier and more sustainable ecological environment within the Central Plains Urban Agglomeration.

Moreover, policy innovation and public engagement play crucial roles in the realm of air pollution mitigation. Specifically, fostering innovation in environmental policies and regulations, including the utilization of economic incentives and market-based mechanisms, can incentivize businesses to decrease emissions and advance the adoption of sustainable, low-carbon technologies. Simultaneously, it is imperative to bolster public awareness and engagement in matters pertaining to air pollution. The implementation of an environmental education and publicity initiative aimed at fostering public involvement in air pollution monitoring and management endeavors has the potential to not only heighten community interest in environmental conservation matters but also cultivate a collaborative air pollution control framework involving governmental bodies, commercial enterprises, and the general public. This prevalent public participation model will contribute to the establishment of a collective air pollution prevention and control system, facilitate ongoing enhancements in air quality within the Central Plains Urban Agglomeration, and offer a robust environmental assurance for the region’s sustainable development.

4.3. Limitations

This study measures the interactive relationship of air pollution among cities in the Central Plains Urban Agglomeration. The network characteristics and influencing factors of an air pollution spatial interactive network are analyzed. The purpose of this paper is to explore the interactive model of air pollution between cities in Central Plains Urban Agglomeration and to provide new insights for regional collaborative control of air pollution.

Due to the limitation of data acquisition ability, we chose the data published by the China Environmental Monitoring Station and the National Meteorological Administration, rather than collecting data in the field for measurement. Future studies can analyze local PM_2.5 changes more accurately by collecting data in the field. This will help to achieve more accurate comparisons between cities and cities and cities and rural areas.