Impact of Built Environment on Carbon Emissions from Cross-District Mobility: A Social Network Analysis Based on Private Vehicle Trajectory Big Data

Abstract

The realization of the “double carbon” goals and the development of green transportation require a focused approach to reducing carbon emissions from private cars. Starting from the perspective of social network analysis, this paper constructs the carbon emission network of private car cross-district mobility based on vehicle trajectory big data in Guangzhou and Foshan and analyzes its spatial network characteristics. Next, the MRQAP model is constructed to examine the impact of built environment factors on carbon emissions from private cars. Furthermore, the paper explores the moderating effect of private car mobility in the central urban area. The results indicate the following: (1) Private vehicle cross-district mobility in the Guangzhou and Foshan region are closely interconnected and exhibit a phenomenon of central clustering. (2) Both population density and the number of road intersections have a positive relationship with private car carbon emissions, and after a series of robustness tests, the results are still valid. (3) Private vehicle mobility in central urban areas contributes to an increase in carbon emissions, and the positive impact is reinforced by population density, while road intersections and private car mobility in central urban areas have a substitutive effect on private car carbon emissions.

1. Introduction

Addressing the rapidly growing carbon emissions from road transportation has become a pressing challenge to achieve the global carbon peak and carbon neutrality goals. The development of strategic emerging industries, particularly the promotion of new energy vehicles, has emerged as a crucial measure for effectively mitigating energy and environmental pressures. New energy vehicles, which refer to automobiles that utilize unconventional fuels as a power source and incorporate advanced technologies for power control and propulsion, offer a viable solution to reduce the auto industry’s dependence on petroleum and minimize pollutant emissions [1]. However, by the end of 2022, the number of new energy vehicles in China was only 13.1 million, while the number of conventional fuel-powered vehicles reached 319 million [2], still dominating the road transportation sector and representing a significant source of energy consumption in urban road traffic. The continuous growth in private vehicle ownership has reshaped urban transportation networks and altered residents’ travel patterns [3]. Addressing road congestion and improving urban functionality through vehicle data utilization, road networks planning, and public facilities supporting has become an important breakthrough to solve the emission problem [4]. However, challenges exist in effectively extracting mobility information between the origin and destination points due to spatial discrepancies and insufficient precision [5]. The development of geographic information systems (GIS) and big data technology makes it possible to provide planning for optimal route delivery services, introduce the concept of shared bicycle systems in urban logistics, and integrate data collected from users, public and private mobility service providers, and infrastructure into Mobility-as-a-Service (MaaS) platforms to offer integrated services. This support contributes to solving urban transportation problems and advancing the sustainability of urban transportation systems [6,7,8,9]. Meanwhile, it also offers opportunities to extract travel behavior and spatial-temporal characteristics from private car trajectories, enabling the analysis of complex intersections, the study of car aggregation effects, and the assessment of urban attractiveness for human travel behavior and city planning. Furthermore, scholars have also utilized vehicle trajectory big data in the fields of intelligent transportation and smart city planning, thereby providing valuable insights for private car route selection, urban traffic network construction, and traffic flow prediction [10,11,12]. Particularly, by understanding private car travel behavior and capturing the spatiotemporal evolution of urban hotspots, these data-driven approaches offer new perspectives for addressing urban challenges, mitigating traffic congestion, and improving transportation services [13,14]. Additionally, due to the lack of official statistical data on transportation carbon emissions in China, existing studies often rely on the “top-down” and “bottom-up” approaches outlined by the Intergovernmental Panel on Climate Change (IPCC) to estimate transportation carbon emissions [15,16] or develop and apply simulation-based econometric models to estimate carbon emissions [17,18]. However, different modeling types and measurement methods have resulted in significant differences in the estimation of transportation carbon emissions [17,19]. Leveraging vehicle trajectory data enables the precise estimation of carbon emissions from private cars at a micro-level, providing a new perspective for carbon emission reduction in road transportation and the analysis of transportation network characteristics.

In addition, private transportation is emission-intensive and behavior-driven [20]. The agglomeration and purposefulness of private car usage make the carbon emissions of private cars mainly influenced directly by individual characteristics of private cars and residents’ travel preferences, as well as indirectly by urban spatial structure, socioeconomic attributes of households, and government regulations [21,22]. Different types of vehicles and driving speeds significantly affect the fuel consumption and carbon emission factors per unit distance traveled [23], but residents’ preferences for private car travel weaken these differences. Residents’ preferences for low-carbon travel modes such as walking and public transportation are influenced by environmental awareness and income levels [24,25]. Urban built environment factors, such as density, land use mix, design, proximity to public transportation as well as accessibility, also influence residents’ preference for private car usage [26]. However, due to different research perspectives and data sources, scholars have reached divergent conclusions regarding the impact of various built environment factors on transportation carbon emissions [27,28]. High-density and compact urban spatial forms can improve transportation accessibility and reduce reliance on private cars, thereby decreasing private car carbon emissions. However, higher population density in cities can also lead to concentrated use of private cars, resulting in traffic congestion and increased carbon emissions from private cars [29,30]. Proper design of road intersections can enhance network connectivity and reduce traffic congestion. However, an increase in the number of road intersections can reduce the travel efficiency and fuel efficiency of private cars, leading to increased carbon emissions [31,32,33]. Diversified land use mix can achieve a balance between residential and employment areas, thereby reducing the distance traveled by private car. However, it may also increase the frequency of private car travel among residents, thereby increasing carbon emissions [34,35]. The shorter the distance between residents and public transportation, the more likely residents are to use public transportation for their travel. However, research suggests that living near a bus stop does not significantly alter residents’ preference for private car travel [36,37]. Improved destination accessibility can shorten commuting distances and reduce the intensity of private car use among residents. However, these findings are based on specific research scenarios and contexts [38,39,40]. Additionally, the level of urban traffic congestion and the completeness of the public transportation system, as well as geographical factors such as topography and urban layout, have a significant impact on residents’ choice of travel mode [41,42].

Due to data limitations, existing studies on carbon emissions from road transportation exhibit significant deviations and often rely on macro-level perspectives. Moreover, the investigation of the impact of built environment on private car carbon emissions mainly relies on questionnaire survey data, which cannot exclude the influences of individual characteristics of private car owners, external macroeconomic factors, and individual preferences of residents. This paper utilizes vehicle trajectory big data to eliminate external factors and uncover the spatial correlation of private car mobility at the micro-level. Meanwhile, by utilizing vehicle trajectory big data and adopting a social network analysis perspective, this study aims to explore the impact of the built environment on carbon emissions from private car mobility, leading to a deeper understanding of the spatial distribution and flow patterns of emissions, and providing valuable insights for urban low-carbon transportation planning. Therefore, based on the Guangzhou and Foshan (hereafter referred to as Guangfo) vehicle trajectory big data, this paper employs a social network analysis method to reveal the spatial network characteristics of carbon emission from private car cross-district mobility. Furthermore, focusing on the urban built environment, the multiple regression quadratic assignment procedure model (MRQAP) is constructed to analyze the impact of factors such as population density, road intersections, and accessibility of public service facilities on private cars’ carbon emissions. The regulating effect of private car travel in central urban areas is further studied. This paper aims to offer valuable insights for urban low-carbon transportation planning and the realization of a “double carbon” goal in the transportation sector. The remaining sections are organized as follows: Section 2 provides a theoretical analysis of the relationships between various built environment factors and carbon emissions from private cars. Section 3 introduces the data sources and research methods used in this paper. Section 4 utilizes social network analysis to reveal the spatial network characteristics of carbon emissions from private cars in cross-district mobility in the Guangfo area. Section 5 constructs the MRQAP model to investigate the impacts and mechanisms of built environment factors (population density, road intersections, and accessibility to public service facilities) on carbon emissions from private car cross-district mobility. Further, this paper analyzes the moderating effects of private car mobility in the central urban area. Section 6 presents the conclusions and provides proposals.

2. Theoretical Background and Research Hypotheses

As of the end of 2022, the number of private cars in China reached 2778.73 million, with an average annual growth rate of 245.17% over the past decade [43]. The rapid growth of private cars has made road transportation one of the fastest-growing sources of carbon emissions globally. In 2022, carbon emissions from the transportation sector in China accounted for approximately 10.4% of the country’s total terminal carbon emissions, and within the transportation sector, road transportation accounted for around 90% of carbon emissions [44]. Therefore, in the current context of private cars being the primary energy consumer in China’s road transportation sector, rational urban spatial planning and built environment design are crucial for reducing fuel consumption of private cars and promoting green mobility, addressing environmental concerns, and fostering sustainable development. The built environment serves as the environmental carrier for urban living and is closely related to residents’ travel behavior, exerting a significant influence on their travel choices [45]. However, issues such as urban sprawl and disorderly development severely hinder residents’ low-carbon travel. Cervero was the first to propose the “3D” elements of density, land use mix, and design to characterize the urban built environment [46]. Subsequently, the introduction of accessibility and proximity to public transit formed the “5D” system of the built environment [47]. Based on the concepts of smart growth and new urbanism, many scholars argue that high density and land use mix can reduce commuting distances, decrease preferences for private car usage, and lower carbon emissions [48]. However, excessively high urban density can lead to traffic concentration and congestion, prolong commuting time, and increase energy consumption [49]. Meanwhile, some scholars suggest that the relationship between residents’ private car travel and density is not significant and is instead related to their travel attitudes and lifestyles [50]. This effect can be explained by the “self-selection effect,” where residents choose a built environment suitable for private car travel, rather than the built environment promoting residents’ private car travel behavior [51]. Therefore, there are significant differences in the mechanisms through which the built environment influences carbon emissions from private cars.

In summary, to effectively investigate the impact of the built environment on carbon emissions from private cars, the focus should primarily address two questions. First, do different built environment factors have an impact on carbon emissions from private cars, and if so, what kind of impact do they have? Second, how can we eliminate individual-scale differences and socioeconomic environmental factors of the research subjects and instead focus on the spatial characteristics of the urban built environment to reveal the impact of the built environment on carbon emissions from private cars at a micro-level. In existing studies, individual micro-level differences in residents’ cognitive preferences and travel mode choices, as well as socioeconomic factors, can weaken and bias the impact of the built environment. In previous studies, disparities in residents’ cognitive preferences and socio-economic factors have been identified as potential factors that weaken and bias the impact of the built environment. By utilizing available vehicle trajectory data, this paper aims to investigate the influence of the built environment on carbon emissions from private cars and provide valuable insights and reliable data support. Additionally, drawing upon the “3D” and “5D” system categorization of built environment factors [52], this paper attempts to explore the impact of density, design, and accessibility on carbon emissions from private cars. However, it is important to note that due to significant data deficiencies and limited availability at the urban level, this paper solely explores the effects of built environment factors such as population density, road intersections, and accessibility to public service facilities on carbon emissions from private cars.

2.1. Population Density and Carbon Emission from Private Car

According to the theory of urban agglomeration economics, the concentration of population and various economic activities in cities affects the overall resource consumption through the concentration of resource elements, and this phenomenon generally exhibits two effects: the first is the scale effect. Population agglomeration involves “Marshallian externalities,” which can promote the development of economies of scale and technology sharing [53], expand the labor market scale, drive technological progress, improve production efficiency, and thus achieve the effect of large-scale pollution control. The second is crowding effect [54]. Due to factors such as rising input costs and limited environmental carrying capacity, population agglomeration can lead to the emergency of diseconomies of scale, increase the production factors input, decrease economic efficiency, and intensify energy consumption and environmental externalities [55]. Specifically, in areas with high population density, the compact spatial structure and well-developed transportation infrastructure can effectively shorten residents’ travel distances, reduce operational costs of regional facilities, decrease reliance on private car usage, and thus reduce carbon emissions. However, high urban population density can also lead to inadequate sharing of transportation infrastructure and the decline in the efficiency of public transportation accessibility, exacerbating energy consumption. This article argues that high-density areas have more employment opportunities and commuting needs, resulting in increased demand for transportation, causing traffic congestion and a higher concentration of vehicles, which leads to increased carbon emissions from private cars. Based on this, the following hypothesis is proposed:

H1: 

An increase in population density will lead to increased demand for transportation, resulting in traffic congestion and increased carbon emissions from private cars.

2.2. Road Intersections and Carbon Emission from Private Cars

Road intersections are key to developing low-carbon transportation and optimizing traffic organization. The interactions, diversions, and mergers of traffic flows at intersections establish a close relationship between the operational conditions of intersections and the overall urban traffic flow [56]. Existing research has identified two impacts of road intersections on transportation carbon emissions: first, road intersections contribute to emission reduction by facilitating traffic flow. The greater the number of road intersections in an area, the stronger the accessibility, providing residents with more options and diverse routes, making it easier to choose low-carbon transportation modes such as walking and public transit. This finding aligns with the research conducted by Cynthia, Hong, and others [57,58], who concluded that there is a negative correlation between road intersection density and transportation carbon emissions. A lower number of road intersections leads to poor street connectivity, which hampers low-carbon travel. Second, road intersections contribute to increased emissions due to congestion. In urban road networks, intersections often experience mixed traffic conditions, resulting in reduced vehicle speeds, frequent acceleration and braking, and increased start-stop events, which in turn decrease traffic efficiency, cause congestion, lower fuel efficiency, and increase carbon emissions [59]. This article suggests that while an increase in the number of road intersections tends to enhance the connectivity of road networks, it inevitably leads to lower vehicle speed and increased stopping and starting frequencies. This, in turn, reduces fuel efficiency and travel efficiency, ultimately resulting in increased carbon emissions from private cars. Based on this, the following hypothesis is proposed:

H2: 

An increase in the number of road intersections has a congestion-inducing effect, tending to increase private car carbon emissions.

2.3. Accessibility of Public Service Facilities

Accessibility to public service facilities refers to the ease with which residents can access public services within a certain geographical area, which depends on the quantity and quality of such facilities [60]. Scholars have proposed that a high degree of spatial matching between compact urban spatial forms and public service facilities is beneficial for shortening residents’ commuting distances, reducing their transportation demands and private car usage intensity, thereby reducing urban transportation carbon emissions [61]. However, the irrational spatial layout of urban public service facilities can result in additional energy consumption for residents living in proximity to these facilities, creating additional environmental costs without economic benefits [62]. This paper argues that an increase in the number of public service facilities within a region is conducive to shortening residents’ commuting distances, reducing urban traffic congestion, improving traffic mobility efficiency, and tending to reduce private car carbon emissions. Based on this, the following hypothesis is proposed:

H3: 

The increase in the number of public service facilities is conducive to shortening residents’ travel distances, improving traffic mobility efficiency, and tends to reduce private car carbon emissions.

3. Research Design

3.1. Data Sources

The research data were obtained using low-cost GNSS-OBD devices in real-world working scenarios. The data collection period was from 12:00 a.m. to 11:59 p.m. on 1 July 2018, with a sampling frequency of 1 Hz, a time resolution of 0.01 s, and a position resolution of 0.1 m. The average positional error could be controlled within 10 m [63,64]. The data mainly include vehicle information ID, trip start time, trip end time, start point latitude and longitude (unit: degree), end point latitude and longitude (unit: degree), driving distance (unit: meter), travel time (unit: second), and fuel consumption (unit: milliliter), as shown in

Table 1. Recorded trip sample dataset.

Vehicle ID	Trip Start Time	Start Point Longitude	Start Point Latitude	Trip End Time	End Point Longitude	End Point Latitude	Driving Distance	Fuel Consumption	Travel Time
135848	2018/7/1 0:11	113.2694	23.23151	2018/7/1 0:58	113.3077	23.1412	20,308	2498	2864

[65]. The geographical location of each trajectory point was determined using reverse geocoding based on latitude and longitude, providing precise addresses at the city (district) and road level. Considering the availability of big data of vehicle trajectory and the consistency and completeness within the collection time range, the research object of this paper is finally selected as 16 urban districts of Guangzhou and Foshan in Guangdong Province, China, with a total of 3370 private car trajectory data.

3.2. Specification of Variables

Existing research on the factors influencing private car carbon emissions focuses primarily on individual factors, urban built environment, and macroeconomic elements. However, this paper utilizes short-term OD (Origin-Destination) spatiotemporal data from private car trajectories, which does not need to consider the influence of individual preference of residents in using private cars. Additionally, macroeconomic factors primarily have long-term effects and have minimal impact on instantaneous private car carbon emissions. Therefore, this paper primarily focuses on examining the impact of the built environment on private car carbon emissions.

• Dependent variable: carbon emissions network matrix from private car cross-district mobility between Guangzhou and Foshan. First, using the latitude and longitude of the start and end points from the vehicle trajectory big data, the specific regional locations of the start and end points of private cars are determined through reverse geocoding, establishing the connections of private cars from cross-district mobility between Guangfo. Secondly, employing the IPCC’s “bottom-up” approach, the carbon emissions of each private car’s trajectory data are calculated, and then divided by the distance traveled to obtain the carbon emissions per kilometer for each private car. Considering the individual differences in private car vehicle types, a weighted average is applied to the carbon emissions per kilometer for cross-district mobility between the same start and end points, resulting in the average carbon emissions per kilometer for different private car cross-district mobility between the same start and end points. Finally, the constructed subnetworks of private car cross-district mobility are overlaid by districts to obtain a 16 × 16 directed carbon emissions network matrix for private car cross-district mobility between Guangzhou and Foshan. Meanwhile, due to the bidirectional nature of macro factors between districts, in the MRQAP analysis, the private car cross-district mobility between the same start point–end point districts and end point–start point districts are combined in both directions, resulting in a 16 × 16 undirected carbon emissions network matrix for private car cross-district mobility between Guangzhou and Foshan.
• Independent variable. (1) Population density. Population density is measured by the ratio of the population quantity to the area of each district. (2) Accessibility to public service facilities. The accessibility of public service facilities incorporates four indicators: the number of primary and secondary schools, hospitals, tourist attractions, and museums in each district. The comprehensive index is calculated using the entropy method to measure the destination accessibility. (3) Road intersection. To measure road intersections, the road network data extracted in the previous steps are used in ArcGIS software to create a network dataset and construct a turning model for calculating the quantity of road intersections. To construct the independent variable network matrix, this paper borrows the idea from gravity models. The product of the built environment elements at the origin and destination of cross-district mobility from private cars represents the spatial connectivity between different districts. The average distance of cross-district mobility from private cars is used to represent the distances between different districts. The spatial connectivity network matrix of different districts in terms of population density, road intersections, and accessibility is obtained. The basic expression is shown in Equation (1).

  $$G_{ij}=k\frac{c_i{c}_j}{d_{ij}^2}$$

  (1)

  Among them, $G_{ij}$ represents the degree of connectivity of built environment factors between district i and district j. k is a constant, and $d_{ij}^2$ represents the average distance traveled by private cars between district i and district j. $c_i$ and $c_j$ represent the built environment factors of district i and district j, respectively.

3.

Control variables: (1) Terrain fluctuation. The terrain fluctuation is obtained by calculating the difference in altitude between the highest and lowest points in each district using ArcGIS. (2) Private car speed. The private car speed network matrix is measured by the average unit travel distance from the start district to the end district for each private car. (3) Road length. The road length is measured by the length of roads in each district. The data sources for the variables in this paper are shown in

Table 2. Variable data sources.

	Variable	Data Sources
Dependent variable	Carbon emissions from private cars cross-district mobility	Vehicle trajectory big data from Guangzhou and Foshan
Independent variable	Population density	Statistical Yearbook of Guangzhou and Foshan for the year 2018
	Road intersections	Road network data extracted from OpenStreetMap for the year 2018
	Accessibility of public service facilities	Statistical Yearbook of Guangzhou and Foshan for the year 2018 A-level tourist attractions list of Guangdong Province (as of 29 August 2018) The museum directory of Guangzhou released by the Guangzhou Bureau of Culture and Tourism on 20 November 2018
Control variable	Terrain fluctuation	GDEMV2 30 m resolution digital elevation data from the geographic spatial data cloud database
	Private car speed	Vehicle trajectory big data from Guangzhou and Foshan
	Road length	Road network data extracted from OpenStreetMap for the year 2018

.

3.3. Research Methods

3.3.1. Social Network Analysis Method

As an important emerging spatiotemporal data source, private car trajectory data holds profound significance and value when thoroughly explored and analyzed. Building upon existing scholarly research, this paper intends to employ social network analysis methods to provide a fresh perspective on revealing the spatial correlation and distribution characteristics of carbon emissions from private car cross-district mobility in the Guangfo region. Specifically, social network analysis methods will be employed to describe the network density and reciprocity of the overall network, as well as individual networks such as eigenvector centrality, degree centrality, betweenness centrality, and closeness centrality [66].

• Network density (des). Measure the closeness of the connections between nodes. The calculation formula is shown in Equation (2), where n is the theoretical maximum number of nodes and m is the number of network edges.

$$des=\frac{2m}{n(n-1)}$$

(2)

2.

Reciprocity (rec). Measure the degree of interconnection between two nodes in a directed network. The calculation formula is shown in Equation (3), where y is the number of nodes with bidirectional connections, and s is the number of total connected lines in the network.

$$rec=\frac{y}{s}$$

(3)

3.

Feature vector centrality (eig). Measure the importance of a node versus its neighbors. The calculation formula is shown in Equation (4), where B is the adjacency matrix of the network. If node i is connected to j, $B_{ij}$ is 1; otherwise, it is 0; b is the maximum eigenvector of matrix B.

$${eig}_i=b^{-1}\sum _j{B}_{ij}{eig}_j$$

(4)

4.

Degree center degree (deg). Indicates the number of nodes that are directly connected to other nodes. When i is directly connected to j, ${\delta }_j^i$ is 1, otherwise it is 0. The directed network can be divided into ideg and odeg. The calculation formula is shown in Equation (5).

$${deg}_i=\sum {\delta }_j^i$$

(5)

5.

Proximity to center (clo). Represents the sum of the shortest paths between a node and other nodes. $d_{ij}$ represents the shortest path distance between nodes i and j. In the directed network, it can be divided into in-degree (iclo) and out-degree (oclo). The calculation formula is shown in Equation (6).

$${clo}_i=\frac{1}{{\sum }_{j=1}^n{d}_{ij}}$$

(6)

6.

Intermediation centrality (bet). Represents the ability of one node to control other nodes. $p_{ij}$ is the number of shortest paths between nodes i and j. $p_{ij}\left(x\right)$ is the number of shortest paths of nodes i and j through node x. The calculation formula is shown in Equation (7).

$${bet}_i=\sum \sum \frac{p_{ij}\left(x\right)}{p_{ij}} i\ne j\ne x,i<j$$

(7)

3.3.2. MRQAP

Since most of the influencing factors of carbon emissions from private cars are relational data, the traditional measurement method may have a high degree of collinearity. However, MRQAP is considered as a non-parametric estimation method, which does not need to assume the mutual independence of variables and can include multiple independent variables into the model test, which can solve the autocorrelation and multicollinearity problems of the measurement model of relational data and is more robust for the test of results [67,68]. At the same time, this model is more inclusive for the number and type of variables, which can not only consider the influence of endogenous network structure and exogenous dynamics, but also include categorical variables without violating the distribution hypothesis. Therefore, based on the previous research hypothesis and data processing, this paper endeavors to incorporate population density, road intersections, and accessibility to public service facilities and carbon emissions of private cars into a unified research framework. By examining the influence of various built environment factors on carbon emissions from private cars, it aims to provide valuable insights for urban road spatial planning and carbon emission reduction from private vehicles. The model is formulated as follows:

$$car={\alpha }_0+{\alpha }_{1}pop+{\alpha }_{2}inter+{\alpha }_{3}acc+{\alpha }_{i}Control+\epsilon$$

(8)

where pop is the population density network matrix. inter is the road intersection network matrix. acc is the accessibility network matrix of public service facilities. ${\alpha }_0$ is a constant term. ${\alpha }_1-{\alpha }_3$ are the coefficients of each variable. Control is the control variable. $\epsilon$ is the error term.

4. Analysis of Carbon Emission Network from Private Car Cross-District Mobility

4.1. Spatial Feature Analysis

In order to reveal the spatial characteristics of the carbon emission network from private car cross-district mobility in Guangfo, ArcGIS software was used in this paper to draw the visualization diagram, as shown in Figure 1. From the perspective of spatial characteristics, Baiyun District, Tianhe District, Panyu District, Zhuhai District, Liwan District, and Yuexiu District in the main urban area (refer to Appendix A for details) of Guangzhou and Nanhai District, Chancheng District, and Shunde District in the central urban area of Foshan have a large number of private car trajectory points and are closely connected, showing a regional agglomeration flow. Compared with the outer urban area, the cross-district mobility of private cars in the central urban area presents a closer trend, and the rich club effect is obvious. In addition, in Foshan City, the areas with high carbon emissions from private car cross-district mobility are pyramidal with Nanhai District as the center and are concentrated between adjacent urban areas, while the areas with low carbon emissions from private car cross-district mobility are concentrated between non-adjacent urban areas in the periphery, forming a spatial pattern of high carbon emissions in the central area and low carbon emissions from private car cross-district mobility in the peripheral area. From the perspective of Guangzhou, the carbon emission of private cars in cross-district mobility tends to decline from the main urban area to the outer urban area. The cross-district mobility of private cars in the main urban area has high carbon emission, and the cross-district mobility of private cars from the main urban area to the outer urban area gradually decreases, and the areas with high carbon emission of private cars are also concentrated in the central urban area.

4.2. Analysis of Network Density and Centrality

The carbon emission network density of private cars in Guangfo is 0.79, which is relatively high, consistent with the previous analysis results of spatial characteristics. The cross-district mobility from private cars in Guangfo is closely related, and the mobility of private cars in different urban areas is significant. In order to further analyze the bidirectional degree of private car flow in Guangfo, the reciprocity degree of the network is calculated as 0.85 considering the directivity of private car flow in Guangfo, which indicates that the bidirectional carbon emission network of private car cross-district mobility in Guangfo is closely connected.

In addition, in order to explore the status and role of each urban area in the carbon emission network of private car cross-district mobility in Guangfo, this paper uses Ucinet software to calculate four central indicators of urban nodes. As shown in

Table 3. Centrality characteristic analysis.

City	District	odeg	ideg	oclo	iclo	bet
Guangzhou city	Baiyun District	14	13	16	17	3.23
	Conghua District	11	10	19	20	0.17
	Panyu District	13	14	17	16	3.32
	Haizhu District	15	14	15	16	7.76
	Huadu District	12	13	18	17	2.70
	Huangpu District	11	13	19	17	3.92
	Tianhe District	13	12	17	18	1.68
	Yuexiu District	13	11	17	19	1.91
	Zengcheng District	12	11	18	19	1.14
	Liwan District	12	14	18	16	2.41
	Nansha District	8	8	22	22	0.27
Foshan city	Sanshui District	9	9	21	21	2.10
	Shunde District	12	13	18	17	5.24
	Chancheng District	13	14	17	16	6.35
	Gaoming District	6	5	24	25	0.11

. Nodes in different urban areas show different point entry degree and point exit degree, among which the point entry degree and point exit degree in Nanhai District are the largest and equal, which indicates that Nanhai District node occupies the core position in the carbon emission network of private car cross-district mobility in Guangfo, and the connection degree of private cars flowing into Nanhai District and out of Nanhai District is relatively balanced. On the whole, the main urban area of Guangzhou and the central urban area of Foshan city are at the forefront of the point-in and point-out degrees, which have obvious influence on the network. The visualization diagram of feature vector centrality of each city node is shown in Figure 2. In this paper, it is divided into four levels by natural discontinuity method. The highest level of feature vector centrality is Nanhai District, Chancheng District, Baiyun District, Liwan District, Haizhu District, and Panyu District. These urban areas are the central urban areas of Guangfo. There is a core-edge decreasing trend.

Gaoming District, Nansha District, Sanshui District, and Conghua District, which are the outer urban areas of Guangfo city, are at the front of the entrance degree and exit degree near the central point. At the end are Haizhu District and Nanhai District and other central areas of Guangfo city. This indicates that the outer urban area is less restricted in the cross-district flow of private cars, and the inflow and outflow are smooth, while the central urban area is on the contrary. The reasons are as follows: firstly, the redundant urban space structure and the excessive number of private cars in the downtown in Guangfo are easy to cause traffic jams, resulting in the “crowding effect”, which leads to the increase of carbon emissions from private cars. Second, the outer urban area of Guangfo city is large, and private cars can choose many routes to flow, which can avoid the small urban road area, and the road is very likely to be blocked so as to improve travel efficiency and reduce carbon emissions. The intermediary centrality of each urban node is significantly different, with the highest values in Nanhai District and the second highest values in Haizhu District reaching 8.68 and 7.76, respectively. Private cars are mostly via routes in the cross-district mobility, which has the advantage of intermediary control in the whole network. However, the intermediary centrality of Gaoming District and Conghua District are only 0.11 and 0.17, indicating that private car flow in the peripheral urban areas has little influence on the overall network and has a weak position.

4.3. Analysis of Condensed Subgroups

The carbon emission network from private cars cross-district in Guangfo can be divided into four subgroups, as shown in

Table 4. Carbon emission network pattern of private cars in Guangzhou and Foshan.

Subgroup	Urban Area
I	Baiyun District, Haizhu District, Conghua District, Panyu District, Tianhe District, Zengcheng District
II	Liwan District, Huadu District, Nansha District, Huangpu District, Yuexiu District
III	Chancheng District, Nanhai District
IV	Gaoming District, Shunde District, and Sanshui District

. The network connection density of subgroup I was 1, which included Haizhu District, Tianhe District, Baiyun District, and Panyu district in the downtown area of Guangzhou and Conghua District and Zengcheng District in the peripheral area of Guangzhou, showing an agglomeration trend of close connection between adjacent urban areas. The network connection density of subgroup II was 0.65, which was sparse compared with that of subgroup I, which contained Liwan District and Yuexiu District in the central urban area of Guangzhou and Huadu District, Nansha District, and Huangpu District in the peripheral urban area, showing a trend of dislocation distribution. The network connection density of subgroup III and subgroup IV was 1 and showed a trend of clustered connections in the central urban area and dispersed connections in the peripheral urban area. On the whole, the carbon emission network from private car cross-district mobility subgroups of private cars in Guangfo showed a fragmented distribution trend with Guangzhou or Foshan as the core. The carbon emission network subgroups of private cars cross-district with Guangzhou as the core showed a spatial pattern of neighbor agglomeration connection and dislocation distribution connection. With Foshan as the core, the carbon emission network subgroups of private car cross-district mobility showed a spatial pattern of centralized connections and peripheral dispersed connections.

5. Result Analysis

5.1. Correlation Analysis of Quadratic Assignment Procedure

The quadratic assignment procedure (QAP) is a combinatorial optimization algorithm for solving the quadratic assignment problem. The international literature identifies the quadratic assignment problem as the problem of finding a minimum cost allocation of facilities into locations, taking the costs as the sum of all possible distance-flow products [69]. QAP correlation analysis can be used to judge whether there is correlation between two relational matrices [70]. In this paper, Ucinet software is used to perform 5000 random permutations of the matrix, and QAP correlation analysis results of the relationship between the carbon emission network matrix of private car cross-district mobility and the built environment are obtained, as shown in

Table 5. Results of QAP correlation analysis.

	road	ter	pop	inter	acc	spe
car	0.938 ***	0.609 ***	0.795 ***	0.954 ***	0.743 ***	0.969 ***
road	1
ter	0.666 ***	1
pop	0.802 ***	0.768 ***	1
inter	0.940 ***	0.774 ***	0.874 ***	1
acc	0.776 ***	0.839 ***	0.942 ***	0.867 ***	1
spe	0.894 ***	0.438 ***	0.672 ***	0.875 ***	0.601 ***	1

Note: *** stand for 1% significance level test.

. It can be seen that the correlation coefficients between population density, road intersections, and accessibility of public service facilities, road mileage, terrain fluctuation, and private car speed and carbon emissions of private cars are significantly positive. In addition, the independent variable and the control variable showed a positive correlation. This indicates that all factors have an important impact on the carbon emissions of private cars moving across the region, and there is a high possibility of multicollinearity among all factors.

5.2. MRQAP Analysis

MRQAP analysis is used to study the regression relationship between multiple matrices and one matrix [71].

Table 6. MRQAP analysis results.

	Variable	(1)	(2)	(3)
Independent variable	pop	0.126 ***	0.071 **	0.097 **
		(0.022)	(0.020)	(0.027)
	inter		0.291 ***	0.316 ***
			(0.045)	(0.048)
	acc			−0.042
				(0.050)
Control	road	0.039	−0.006	−0.003
		(0.037)	(0.035)	(0.037)
	ter	0.141 ***	0.048 *	0.051 *
		(0.060)	(0.049)	(0.053)
	spe	0.787 ***	0.651 ***	0.635 ***
		(0.244)	(0.151)	(0.168)
	intercept	0.033 ***	0.020 ***	0.017 ***

Note: ***, ** and * stand for 1%, 5% and 10% significance level test; data in parentheses are standard error.

presents the results of MRQAP regression analysis between various built environment factors and carbon emissions from private car cross-district mobility. In Model (3), population density and road intersections both have a significant positive impact on carbon emissions from private car cross-district mobility, validating hypotheses H1 and H2. This suggests that an increase in population density leads to a tighter urban spatial environment, excessive pressure on urban transportation infrastructure, and a decrease in transportation accessibility efficiency. Additionally, the increase in road intersections hinders smooth traffic flow, reduces road traffic speed, prolongs waiting time for residents’ private car travel, contributes to traffic congestion, intensifies energy consumption in road transportation, and consequently increases carbon emissions from private cars. The accessibility of public service facilities has a negative impact on carbon emissions from private car cross-district mobility, but it does not pass the significance test and is not statistically significant. When population density, road intersections, and the accessibility of public service facilities are sequentially included in Models (1) to (3), it is found that the regression coefficients and significance levels of population density, road intersections, and the accessibility of public service facilities are generally consistent, indicating a certain level of robustness. In terms of control variables, private car speed and topography have a significant positive impact on carbon emissions of private cars moving across districts, while road length does not have a significant influence. This differs from previous research findings [24,34], providing a reference for further exploring the influencing factors of carbon emissions from private car cross-district mobility.

5.3. Robustness Test

In order to test the robustness of the above results, this paper uses R language to conduct MRQAP analysis again [72], and the results are shown in

Table 7. Robustness test results.

	Variable	(4)	(5)	(6)
Independ variable	pop	0.066 ***	0.037 **	0.050 **
	inter		0.143 ***	0.156 ***
	acc			−0.039
Control variable	road	0.029	−0.005	−0.004
	ter	0.235 ***	0.080 *	0.084 *
	spe	1.193 ***	0.986 ***	0.961 ***
	intercept	0.033	0.020	0.017

Note: ***, **, and * stand for 1%, 5%, and 10% significance level test.

. Population density, road intersections, and accessibility of public service facilities are gradually added, and the significance of these factors is consistent with the above, which confirms the impact of each built environmental factor on the carbon emissions of private car cross-district mobility. Therefore, the conclusion of this paper is robust.

5.4. Analysis of Moderating Effect

As mentioned above, the carbon emission of private car cross-district mobility has the phenomenon of centralized flow in the central area. As the most concentrated area of population, traffic, business, and other functions in the city, more efforts to promote and optimize the development and resource allocation of the central urban area is the core engine of the economic and cultural development of the city and even the region. So, whether the cross-district mobility of private cars in the central urban area significantly exacerbates energy consumption and whether there is a significant interaction effect between private car mobility in the central urban area and built environment factors? In view of this, this paper attempts to construct dummy variables for private car mobility in central urban areas, and further explore the interaction effects of population density, road intersections, and private car mobility in central urban areas, which have significant influences on carbon emissions of private cars. It provides a reference for optimizing urban spatial layout reasonably and promoting the realization of “double carbon” in the private car sector. The adjustment effect model is set as follows:

$$car={\alpha }_0+{\alpha }_{\mathrm{i}}X+{\alpha }_{\mathrm{i}+1}cent\times pop+{\alpha }_{\mathrm{i}+2}cent\times inter+Control+\epsilon ,$$

(9)

where cent is the flow of private cars in the central urban area, and $cent\times inter$ is the crossing term between the flow of private cars in the central urban area and the road intersection. $cent\times pop$ is the intersection term between private car mobility in urban centers and population density. For the virtual variable private car flow in central urban area, if the start point and end point of private cars are both Guangzhou and Foshan central urban area, the value of the private car flow network matrix in the central urban area is 1, otherwise it is 0. In addition, all variables were centralized in the analysis of the moderating effect.

The analysis results of adjustment effect are shown in

Table 8. Moderating effect analysis.

Variable	(9)
pop	−1.396 ***
	(0.130)
inter	1.744 *
	(0.196)
acc	−0.045 ***
	(0.055)
road	−0.182 ***
	(0.157)
ter	−0.069
	(0.000)
spe	0.943 ***
	(0.113)
cent	0.500 ***
	(0.163)
pop × cent	1.239 ***
	(0.039)
Inter × cent	−0.458 ***
	(0.064)
intercept	−0.452 ***

Note: ***, and * stand for 1%, and 10% significance level test; data in parentheses are standard error.

. It can be seen that the regression coefficient of private car mobility in the central urban area is positive and passes the 1% significance test, indicating that private car mobility in the central urban area of Guangfo intensifies energy consumption and increases carbon emissions. This paper argues that this is because the central city realizes the regional comprehensive collection of commerce, entertainment, service, and other functions by gathering economic resources. Therefore, the daily life and work of residents tend to flow in the central city. Moreover, the convenience of private cars makes it a preferred tool for short-distance travel, which leads to the overflow of private cars and excessive pressure on transportation infrastructure in the main city. This further exacerbates the rise in private cars’ carbon emissions in the region. In addition, the interaction term between population density and private car mobility in central urban areas is significantly positive, indicating that population density strengthens the positive impact of private car mobility in central urban areas on carbon emissions. How can this effect be explained? This paper argues that with the continuous increase in the number of private cars, the traffic structure in the central urban area gradually shifts from non-motorized to motorized. Meanwhile, public resources such as education, medical treatment, and shopping malls are excessively concentrated in the core urban sections, and the degree of population agglomeration is too high and the sharing of transportation infrastructure is insufficient, which significantly enhances the “crowding effect” in the central urban area, causing traffic congestion and rising carbon emissions from private cars.

Therefore, a number of countries and regions have explicitly proposed to prohibit vehicles from entering the city center, adopt the sharing mode of the taxi and minibus, improve the energy efficiency of public transport, release the public space area of the central urban area, and alleviate traffic congestion. The regression coefficient of the interaction term between mobility in the central urban area and mobility in the central urban area is significantly negative, which indicates that the road intersection and mobility in the central urban area have a substitution effect on the positive impact of private car carbon emissions. Therefore, in the subsequent process of carbon reduction for private cars in Guangfo, reasonable layout and long-term planning of traffic intersections in the central urban area should be strengthened, and problems such as unreasonable distribution of lane functions at intersections and signal control disorder should be coordinated. It is necessary to comprehensively consider the question of road traffic relief, alleviate the typical congestion represented by traffic tide, improve the construction of urban road intersections, and form an efficient and smooth three-dimensional traffic network.

6. Conclusions and Discussion

6.1. Research Conclusions

This study aims to achieve three research objectives. The first objective is to analyze the spatial distribution characteristics and cross-district mobility patterns of private car carbon emissions in the Guangfo area. Based on vehicle trajectory big data, this paper explores the spatiotemporal characteristics of the carbon emission network of private car cross-district mobility in Guangfo from the perspective of social network analysis. The findings reveal that the cross-district mobility of private cars in Guangfo has the phenomenon of centralized flow in the central area, showing a core-edge decreasing trend from the central urban area to the peripheral urban area. The central urban areas such as Nanhai District and Haizhu District have the greatest influence on the carbon emission network of private car cross-district mobility in Guangfo, while the peripheral urban areas such as Gaoming District and Conghua District have little influence on the overall network and have a weak position. In the condensed subgroup, the carbon emission networks of private cars in Guangfo showed a fragmented distribution.

Regarding the second objective of this paper, the impact of built environment factors on private car carbon emissions is examined. The study further constructs an MRQAP model to investigate the effects of population density, the number of road intersections, and the accessibility of public service facilities on private car carbon emissions. The findings indicate that among the built environment factors, the increase of population density leads to a crowding effect, and the increase of the number of intersections leads to the decrease of vehicle traffic efficiency, both of which lead to the increase of private car carbon emissions, while the increase of the number of public service facilities has no significant impact on private car carbon emissions, which has no statistical significance.

The third objective of this paper is to explore the moderating effects of the flow of private cars in central urban areas. The paper constructs a moderation model to examine the interaction effects between the mobility of private cars in central urban areas and population density and the number of road intersections. The findings reveal that the mobility of private cars in the central urban area will aggravate energy consumption and lead to the increase of carbon emissions. Population density strengthens the positive impact of private car mobility on carbon emissions in central urban areas, while road intersections and private car mobility in central urban areas have a surrogate effect on carbon emissions.

In conclusion, the results related to the three objectives of this study provide answers to the overall research question and hold significant implications for optimizing urban built environments and formulating relevant environmental policies.

6.2. Discussion

Compared to scholars such as Xue and Hou who estimate private car carbon emissions using existing statistical data or questionnaire surveys [73,74], the data used in this paper were collected in real-world scenarios, focusing more on the micro-level analysis of individual behavior from private cars. Additionally, unlike hybrid lifecycle-based carbon footprint methods by Sun et al. and the use of traffic simulation methods by Plakolb et al. [75,76], this paper employs social network analysis to explore the spatial network characteristics of private car cross-district mobility in the Guangfo area, focusing more on analyzing the behavior of private car carbon emissions from the perspectives of group effects and propagation effect. Long et al. identified through clustering and spatial analysis that regions with high carbon emissions from private cars in Japan are concentrated in Hokkaido and the northeastern region, while regions with low carbon emissions are concentrated in the western region [30]. Pan utilized exploratory spatial data analysis methods to discover significant spatial variations in private car carbon emissions in Chinese prefectural cities [77]. This is consistent with the findings of this paper, indicating that private cars exhibit spatial clustering characteristics, primarily concentrated in economically developed areas. However, the difference lies in the more detailed focus of this paper on urban districts, where counties serve as the basic units of urban management and decision-making. Understanding carbon emissions of private cars at the county level has more direct significance for urban planning and policy making. Furthermore, this paper employs MRQAP to demonstrate the positive influence of population density and the number of road intersections on private cars carbon emissions. This is consistent with the conclusions of scholars Ashik and Madziel [47,78], further enriching the literature on how to improve urban built environments to promote carbon reduction in the private car sector. Moreover, the mobility of private cars in central urban areas intensifies energy consumption, which aligns with the findings of Li et al. [79]. According to Mihaela [80], addressing road traffic congestion in city centers requires preventing vehicle flow in city centers and improving connectivity between urban public transport and county public transport. This viewpoint aligns with the insights presented in this paper regarding the reduction of private car carbon emissions in the central urban areas.

6.3. Policy Implications

Based on the research findings, the policy implications of this paper are as follows:

(1) Optimize resource allocation between central and peripheral urban areas. Policies such as traffic restrictions and increased parking fees can be implemented to restrict and control private car flow in the central areas of Guangzhou and Foshan. Simultaneously, promote transit-oriented development (TOD) to enhance accessibility to neighboring urban areas. Encourage residents to prioritize public transportation for their daily commute, thereby reducing traffic congestion caused by private cars and promoting green and low-carbon travel. Furthermore, leverage the central role of Nansha and Haizhu districts in the carbon emission network of cross-district private cars in Guangzhou and Foshan—for example, improving the transportation infrastructure in these districts and enhancing the travel efficiency of residents’ private cars. It is necessary to construct dedicated transportation backbone networks and hubs between closely connected urban clusters to reduce the proportion of private car travel among residents.

(2) It is better to promote the rational allocation and expansion of urban resources, shift the center of urban development to the surrounding areas, encourage the migration of population to new urban areas and surrounding provinces and cities, and alleviate the population pressure in the central areas. Moreover, accelerate the improvement of urban road networks as a fundamental supporting measure. Optimize the layout of urban road intersections, with the goal of reducing the number of complex intersections, and adopt streamlined designs and optimize overpasses to create smooth traffic pattern and ensure continuous traffic flow through intersections [81].

(3) Consider comprehensive macro-control strategies and restrict private car access and usage in central urban areas. Relieve population density and resource pressures by diverting schools, hospitals, and other facilities from central areas to peripheral regions. In addition, improve the urban public transport system through optimizing the spatial configuration and scale structure of road network construction, so as to enhance the efficiency of private car travel, guide residents to switch from private car commuting to public transport and low-carbon travel.

The limitation of this study is that it only examined the impact of population density, number of road intersections, and accessibility of public service facilities on carbon emissions from private cars. With the supplementation of relevant data, future research can consider incorporating additional built environment factors such as land use mix and proximity to public transportation in the investigation of carbon emissions from private cars. Additionally, by collecting vehicle trajectory data from multiple time points, it becomes possible to analyze the changing trends and patterns of carbon emission networks. This analysis would contribute to identifying the impact of urban planning and policy measures on carbon emissions, providing a more reliable decision-making basis for future urban transportation planning and emission reduction strategies. In addition to studying the Guangfo region, this research method can be extended to other regions and cities to conduct comparative analyses of carbon emission networks associated with inter-district private car mobility in multiple regions and cities. Such comparative studies can reveal similarities and differences in carbon emission behavior between different cities, explore variations in carbon reduction strategies and urban planning approaches, and provide insights and inspiration for global cooperation in carbon reduction efforts.