Evaluation on the Rationality of Spatial Layout of Social Facilities in Inland Coastal Cross-River Cities Based on POI Data: A Case Study of Nanjing, China

Abstract

Social facilities play a crucial role in urban development. However, there are currently few studies on the rationality of the spatial layout of social facilities in inland coastal cross-river cities. In view of this, we choose Nanjing City, China as an example, based on the point of interest (POI) data of social facility, and use the techniques including kernel density analysis, standard error ellipses, and spatial correlation analysis to systematically investigate the spatial distribution characteristics and patterns of social facilities in Nanjing. The research results show that there are significant differences in the spatial distribution of different types of social facilities in Nanjing, and the overall layout presents a pattern of denser distribution in the central urban area and more dispersed distribution in the peripheral areas. Shopping and transportation facilities are mostly concentrated in the core area of the main urban district, medical facilities are relatively concentrated, and cultural and educational facilities are located in all regions. The expert weighting analysis based on the Delphi method indicates that the influence weights of shopping consumption and transportation facilities on urban facilities are relatively greater than those of other factors. Overall, the social service facilities in the central urban area of Nanjing are well developed and well arranged, whereas the construction of facilities in several new districts and suburbs still needs to be further strengthened. The findings offer a scientific foundation for improving the layout of social facilities and urban planning in Nanjing, while also serving as a valuable reference for the development of other inland coastal cities spanning rivers.

1. Introduction

With the continuous advancement of global urbanization, the evolution of urban spatial structure has become increasingly complex. This complexity brings new challenges to the rationality of public resource allocation, which has become a key concern in urban geography [1,2], urban planning [3,4,5], and sustainable development research [3,5]. In the context of this study, the rationality of social facility distribution primarily refers to its fairness, emphasizing whether residents in different areas enjoy equitable access to essential public services. Social facilities, including those related to education, healthcare, cultural activities, and commerce, play a fundamental role in shaping the quality of life for residents, promoting social equity, and enhancing the comprehensive competitiveness of cities [6,7,8]. A rational spatial layout, understood in terms of fairness, seeks to ensure that resources are organized not only with efficiency in mind but also with an emphasis on equitable distribution, thereby narrowing spatial disparities and fostering livable urban environments [9,10,11]. In this research, the fairness dimension of rationality is defined through several interrelated considerations. We examine whether social facilities provide adequate service coverage within reasonable travel distances, ensuring that residents, regardless of their location, can conveniently access essential services such as schools, hospitals, and shopping centers [10]. We also evaluate the degree of spatial correspondence between facility distribution and population density, aiming to ensure that areas with greater population concentrations receive a proportional and sufficient allocation of resources, while avoiding redundancy in sparsely populated zones. In addition, we consider the overall balance of facility allocation across different parts of the city, including central districts, emerging urban centers, and peripheral or transitional urban–rural areas, such that public service provision achieves a spatially equitable pattern. These considerations collectively form the foundation for assessing the fairness-oriented rationality of social facility distribution in this research.

Nanjing, as a provincial capital and megacity in eastern China, offers a typical case for such investigation. Located in the lower reaches of the Yangtze River, Nanjing plays an important role in the national Yangtze River Delta integration strategy and the Yangtze River Economic Belt development [12,13,14]. The city spans both sides of the river, with the southern area serving as the traditional urban core and the northern Jiangbei New District emerging as a new center of industrial and residential development [13,15]. The western part of the city, adjacent to Anhui Province, remains in the early stages of urbanization and shows weak infrastructure support [16,17]. This spatial pattern, which includes cross-river development, polycentric expansion, and urban fringe integration, has led to significant disparities in the distribution of social facilities [13], urgently requiring systematic assessment and optimization research.

In recent years, a growing number of studies have examined the spatial distribution, accessibility, and equity of social facilities in urban areas [18,19]. Many of these studies have relied on traditional data sources such as census data or statistical yearbooks. Although these sources provide valuable information, they often suffer from long update cycles, low spatial resolution, and limited categorical detail [20,21]. These shortcomings make it difficult to capture the dynamic evolution of urban functional spaces and the rapid changes in facility distribution, especially in cities experiencing significant population movement and spatial restructuring [12,15,18]. To address these limitations, researchers have increasingly turned to high-resolution spatial data and advanced analytical methods. Point of interest(POI) data have gained particular attention due to their strong timeliness, high spatial precision, rich categorical content, and frequent updates [22,23]. POI data provide detailed information about individual facilities, including their names, locations, categories, and functional attributes. These features enable more accurate identification of spatial patterns, such as facility clustering, functional zoning, and urban vitality distribution [24,25]. Compared with conventional data, POI data allow for more flexible and detailed analysis of micro-level spatial differences, which is especially valuable in cities with complex spatial structures and uneven development [25,26,27].

The growing use of POI data has led to a wide range of applications in urban studies. These include identifying facility agglomeration areas using kernel density analysis [27], assessing accessibility through the construction of service coverage indicators such as the 15-minute living circle [28], and delineating urban functional zones by integrating POI with population, transportation, and remote sensing data [29]. In addition, POI data have been applied in commercial vitality assessment, land use classification, and spatial equity evaluation [30,31,32]. The integration of POI data with advanced spatial analysis techniques, such as spatial autocorrelation [33,34], hotspot detection [35,36], and geo-statistical modeling, reflects a clear trend in the field toward data-driven and fine-scale urban research. This trend highlights the evolving characteristics of urban spatial analysis, including an emphasis on spatial heterogeneity, real-time data, and the integration of multiple data sources. Despite these advances, most existing studies tend to focus on single types of facilities or specific administrative units [20,21]. Few have conducted comprehensive assessments of multiple types of social facilities across an entire city, especially in large and structurally diverse cities. In addition, there is a lack of research that systematically examines the spatial imbalances of facilities in relation to population distribution and geographic conditions. These gaps are particularly evident in megacities with cross-river layouts, multiple centers, and transitional urban–rural areas [13].

This study selects Nanjing as a representative case of a coastal megacity and uses POI data from April 2025 to conduct a comprehensive analysis of urban social facilities. The analysis focuses on six categories of facilities, including shopping and consumption (SC), livelihood services (LFs), transportation infrastructure (TF), science and education culture (ESC), medical healthcare (MH), and tourist attractions (TAs). A series of spatial analysis methods are applied, including kernel density estimation [37,38], average nearest neighbor index [35,36], hotspot analysis [35,36,39], spatial autocorrelation [33,34], and the Delphi method [40,41]. Geographic information such as population density, transportation networks [42], and topography is also integrated. Using these methods, the study constructs a spatial convenience index of social facilities and visualizes the results through geographic information system technology. The combination of kernel density analysis [33], hotspot analysis [35], spatial correlation analysis [38], and the Delphi method [40] was deliberately chosen to address the multi-dimensional nature of the research problem and to maximize the analytical potential of POI data. Kernel density analysis enables the visualization and quantification of spatial concentration patterns of different facility types, providing an intuitive representation of service intensity across the urban landscape [36]. Hotspot analysis complements this by statistically identifying areas of significant clustering or scarcity, allowing the detection of spatial anomalies that might not be apparent from density patterns alone [36]. Spatial correlation analysis further advances the understanding of interrelationships between facility categories, revealing synergistic or competitive spatial arrangements that are essential for assessing integrated urban service systems [39]. The Delphi method, grounded in expert knowledge, introduces a structured means to determine the relative importance of different facility types, enabling the rationality assessment to account for functional priorities rather than relying solely on uniform weighting [41]. This methodological integration transcends the limitations of traditional statistical approaches, which often treat spatial data in an aggregated and aspatial manner. By preserving the granularity of POI data and incorporating both quantitative spatial statistics and qualitative expert judgment, the approach yields deeper insights into the equity, efficiency, and functional coordination of social facility distribution. Such a framework not only facilitates a more comprehensive assessment of spatial rationality but also supports evidence-based recommendations for urban planning and policy formulation. We place particular emphasis on the spatial disparities between the northern and southern parts of Nanjing, as well as between central urban areas and peripheral districts. It evaluates the degree of spatial matching between population distribution and public service facilities and assesses the fairness of social service allocation. The aim is to provide both theoretical foundations and practical guidance for optimizing facility distribution and promoting spatial equity in urban development.

We pay special attention to the following key issues. First, whether social facilities illustrate the spatial agglomeration characteristics of strong in the main city, weak in the new district. Second, whether the rapidly developing Jiangbei New District has obvious lag in the infrastructure support. Third, whether there are structural shortcomings in the configuration of facilities in the urban fringe areas (such as Gaochun and Lishui Districts). Fourth, whether the transportation network and population distribution have an impact and restriction on the accessibility of facility services. Our study enriches the methodological system of POI data in the research of social facility layout, expand the data foundation and technical path of urban spatial analysis, and propose targeted optimization strategies to serve the spatial development goals of cross-river integration and functional improvement in Nanjing, and provide scientific support for the construction of a fair, inclusive, flexible and resilient urban public service system. At the same time, the research results can also provide a replicable analytical framework and empirical experience for other megacities with complex geographical patterns and multiple development gradients.

2. Materials and Methods

2.1. Study Area

This study selected Nanjing as a typical case (Figure 1a–c) to systematically analyze the spatial distribution pattern and regional difference characteristics of social facilities in inland coastal cross-river core cities. Nanjing is located in the western part of Jiangsu Province, in the middle and lower reaches of the Yangtze River, which is an important central city in the country and a connecting hub between the eastern coastal economic zone and the central and western regions [12]. Its unique geographical location, historical and cultural heritage, and comprehensive transportation advantages are highly representative in the Yangtze River Delta urban agglomeration [18]. The city has a land area of 6587.0 square kilometers, spanning both sides of the Yangtze River, showing a development pattern of equal emphasis on the south and north of the Yangtze River, and a rich spatial structure [16,18]. By the end of 2025, Nanjing’s permanent population is estimated to exceed 9.5 million, whose economic aggregate ranks among the top in Jiangsu Province, with per capita GDP ranking among the top among sub-provincial cities in China [16]. The city has 11 administrative districts, including the main urban area (such as Gulou District, Xuanwu District, Qinhuai District), emerging development areas (such as Jiangbei New District, Yuhuatai District) and suburban county-type areas (such as Lishui District and Gaochun District). Different regions have significant differences in population density, economic foundation, and social resource supply. The urban spatial structure extends along the Yangtze River in an east–west direction, forming a pattern of cross-river development [12]. The old urban area in the south of the Yangtze River gathers a large number of high-level social service facilities, while the social facilities layout of the Jiangbei New District, as a key development area in recent years, is still being improved, and the overall distribution shows a trend of being strong in the south and weak in the north [18]. Nanjing’s distinctive cross-river spatial structure, strong functional zoning, and evolving population distribution characteristics provide an ideal empirical platform for studying the configuration of social facilities in inland coastal cross-river large cities.

2.2. POI Data

Based on the Gaode Map (i.e., Amap) API, we derived the social facility point of interest (POI) data for Nanjing City in April 2025 (https://www.amap.com/, accessed on 23 May 2025), involving six major service functions of shopping and consumption (SC), livelihood services (LFs), transportation facilities (TF), science and education culture (ESC), medical healthcare (MH), and tourist attractions (TAs). These classifications comprehensively cover the main spatial carriers of urban social activities and have good representativeness and practical reference value. We processed the POI data from Gaode Map through a multi-step cleaning procedure to ensure reliability and representativeness. Duplicate entries with identical names, coordinates, and facility types were removed, facility classifications were cross-checked and corrected according to official category codes, and records outside Nanjing’s administrative boundaries or lacking essential information were excluded. Abnormal coordinates were verified and corrected using spatial visualization and official map references, and facilities confirmed to be out of service were eliminated. This process ensured an accurate and representative dataset for the subsequent spatial analyses. Eventually, a total of 291,971 valid records were retained, and these data have clear latitude and longitude coordinates, category information, and name information, laying a foundation for conducting spatial visualization, density analysis, and regional difference research. Although the Jiangbei New Area was officially approved by the State Council in June 2015, most of its large-scale infrastructure projects remained under construction as of August 2025, with only some public service facilities completed and operational in advance. A comparative analysis of POI datasets from April 2024 and April 2025 revealed only marginal variations across the six facility categories (Supplementary Table S1), indicating that short-term fluctuations induced by recent policy measures were limited. Therefore, the adoption of the April 2025 POI dataset ensures both the reliability and representativeness of the data while capturing the most up-to-date spatial configuration of social facilities in Nanjing. The spatial distribution and statistical information of the six categories of POI data are shown in Figure 2 and

Table 1. Statistical information of specific types of POI data.

Category	Subcategory	POI Count	Proportion (%)
SC	Markets, convenience stores, supermarkets, commercial streets, fairs, shopping malls, etc.	128,514	44.02
LS	Sports and fitness, leisure and entertainment, daily service facilities, etc.	72,223	24.74
TF	Bus stops, subway stations, bus stations, service areas, parking lots, etc.	43,224	14.80
ESC	Higher education, news media, libraries, training institutions, etc.	29,807	10.21
MH	Medical centers, medical clinics, pharmaceutical sales, elderly care institutions, etc.	16,011	5.48
TA	Parks, squares, museums, gardens, etc.	2192	0.75

, respectively.

2.3. Basic Geographic Data

The basic geographic data used in this study include Nanjing’s administrative boundary data, urban road network, population spatial distribution data, and digital elevation model (DEM). Among them, the administrative boundary, urban road data, and DEM data are derived from the open source geographic information platform of OpenStreetMap (https://www.openstreetmap.org, accessed on 24 May 2025), where the complete street-level information and spatial structure framework with high geographic timeliness and spatial accuracy are accessible. By screening and processing the data on this platform, the multi-scale road hierarchy structure (such as main roads, secondary roads, branch roads, etc.), complete administrative division vector boundaries, and urban elevation information within Nanjing are obtained, providing support for the spatial matching analysis of POIs and urban functional areas and the analysis of the potential impact of terrain undulation on the layout of social facilities. The population data are derived from the WorldPop project (https://hub.worldpop.org, accessed on 26 May 2025), which provides the population spatial distribution data expressed in raster form with a spatial resolution of 100 m. We utilized the 2025 version of the population raster data to spatially perform the population density in different areas of Nanjing, whereby evaluating the spatial service capacity of social facilities and their matching degree with population distribution.

2.4. Kernel Density Estimation

Kernel density estimation (KDE) [33,34] is a commonly used non-parametric spatial statistical analysis method, which is mainly used to continuously express the spatial distribution characteristics of discrete point data. This method regards each observation point as an independent probability density center and constructs a smooth kernel function (i.e., density surface) around it. The density value reaches the maximum value at the observation point and gradually decreases with the increase in distance, and finally tends to zero outside the set bandwidth. By superimposing the kernel functions of all sample points, a continuous spatial density distribution map can be formed, which effectively reveals the clustering trend and hot spots of samples in geographic space. The core advantage of KDE lies in its independence from specific distribution assumptions, allowing it to flexibly adapt to the analysis requirements of various types of spatial point data. At the same time, the choice of kernel function and the setting of bandwidth parameters directly affect the smoothness and recognition accuracy of the estimation results: a smaller bandwidth will result in a steeper density surface, which is conducive to identifying local clustering but may introduce noise; meanwhile, a larger bandwidth will lead to excessive smoothing, masking local structures but being more suitable for macroscopic analysis. In this study, KDE was applied to quantitatively analyze the spatial distribution pattern of social facility POI data in Nanjing. By constructing a kernel density surface based on the POI data of six types of social facilities (SC, LS, TF, ESC, NH, TA) obtained from the Gaode Map, the high-density areas and potential functional agglomeration zones of the city’s internal facility distribution were identified, thereby revealing the heterogeneity and regional differences in the spatial layout of facilities. The mathematical expression is as follows [33,34]:

$$f\left(x\right)={\displaystyle \frac{1}{n{h}^d}}{{\displaystyle \sum }}_{n=1}^{n}K\left({\displaystyle \frac{\left|x-x_i\right|}{h}}\right)$$

(1)

where f(x) represents the kernel density estimate at position x, n is the total number of samples, and h is the bandwidth parameter, which determines the influence range of the kernel function. d indicates the dimension of the spatial data (two-dimensional in this study, i.e., d = 2). K(⋅) represents the kernel function, whose common forms include Gaussian kernel, Epanechnikov kernel, etc. (Gaussian kernel used in this study). $\left|x-x_i\right|$ represents the Euclidean distance between the estimated point x and the i-th sample point of the POI. The kernel density map generated by this method can not only intuitively reflect the spatial clustering situation of different types of social facilities, but can also be superimposed with basic geographic data such as population density and road network for analysis, thereby evaluating the spatial accessibility and configuration rationality of facility resources, and providing important technical support for the optimization of urban spatial structure and the balance of public service supply.

2.5. Spatial Correlation Analysis

To further explore the spatial co-distribution characteristics of different types of social facilities in Nanjing, we used the Band Collection Statistics tool to construct a multi-band raster dataset with the kernel density estimation layer of social facilities as input, and conducted multivariate statistical analysis [43]. This method can effectively identify the spatial correlation and co-agglomeration trend of different categories of POI data and provide support for the study of urban functional coupling relationships. Specifically, the tool quantifies the numerical relationship between various types of social facility density layers by calculating the covariance matrix and correlation matrix between raster-stacked layers [44]. The covariance matrix reflects the degree of joint variation in pixel values between different layers, while the correlation matrix measures the linear correlation strength between layers. The calculation formula is as follows:

$$Co{v}_{ij}={\displaystyle \frac{{{\displaystyle \sum }}_{k=1}^N\left(Z_{ik}-{\mu }_i\right)\left(Z_{jk}-{\mu }_j\right)}{N-1}}$$

(2)

$$Cor{r}_{ij}={\displaystyle \frac{Co{v}_{ij}}{{\delta }_i{\delta }_j}}$$

(3)

where $Co{v}_{ij}$ represents the covariance between the i-th and j-th raster layers, and their correlation coefficient is expressed as $Cor{r}_{ij}$. Z_ik represents the value of the k-th pixel in the i-th layer, and μ_i and μ_j indicate the average values of the i-th and j-th layers, respectively. δ_i and δ_j are the standard deviations of the corresponding layers, N is the total number of pixels, and k is the pixel index. The correlation coefficient matrix generated by this method is a symmetric matrix, with the diagonal elements always being 1, indicating the complete correlation of the layer itself. The values of the off-diagonal elements are used to judge the spatial relationship between different types of social facilities: the closer the value is to 1, the stronger the positive correlation is, indicating that such facilities often co-occur in the same spatial area; the closer it is to 0, the stronger the spatial distribution independence is. Through the above analysis, the collaborative agglomeration characteristics of different types of social service facilities in Nanjing can be fully identified in the urban space, thereby providing a quantitative basis for revealing the coupling mechanism of urban composite functions and optimizing the functional layout of urban space [45].

2.6. Average Nearest Neighbor Analysis

Average nearest neighbor analysis is a spatial point pattern analysis method that is widely used in geospatial statistics and urban spatial structure research [35,36], which quantitatively analyzes the spatial distribution pattern by measuring the spatial relationships between point elements to determine whether they tend to be clustered, random, or uniformly distributed [36]. The core idea is to calculate the distance between each point and its nearest neighbor and compare it with the expected value under the theoretical model to identify the degree of deviation between the actual distribution pattern and the complete spatial randomness (CSR) model. The actual average nearest neighbor distance Do represents the average distance from all points in the study area to their nearest neighbors, and its calculation formula is as follows:

$$D_O={\displaystyle \frac{{{\displaystyle \sum }}_i^n{d}_i}{n}}$$

(4)

where d_i is the distance from the i-th point to its nearest neighbor, and n is the total number of points. Under the complete spatial randomness (CSR) assumption, the expected nearest neighbor distance D_E of a point can be expressed as half of the inverse of the point density, whose calculation formula is as follows:

$$D_E={\displaystyle \frac{\sqrt{A}}{2\sqrt{n}}}$$

(5)

where A represents the total area of the study area. Based on the above two distance indicators, the nearest neighbor ratio of R can be further calculated:

$$R={\displaystyle \frac{D_O}{D_E}}$$

(6)

when R = 1, it indicates that the spatial distribution of the points is consistent with the random distribution; when R < 1, it shows that the distances between the points are relatively close, indicating a significant clustering; when R > 1, it represents that the points are distributed relatively far from each other, presenting a uniform distribution characteristic. To evaluate the statistical significance of the R value, the standard error (SE) and the standardized Z-value statistic are used to test the deviation between the observed values and the expected values [44]. The calculation formula is as follows:

$$Z={\displaystyle \frac{D_O-D_E}{\mathrm{SE}}}$$

(7)

$$SE=\sqrt{{\displaystyle \frac{\left(4-\mathrm{\pi }\right)\mathrm{A}}{4{\mathrm{\pi }\mathrm{n}}^2}}}$$

(8)

The larger the Z value, the more uniform the distribution; the smaller the Z value, the more concentrated the distribution. When the p value is less than 0.05 and R < 1, Z < 0, it indicates that the sample has significant spatial aggregation characteristics; when R > 1, Z > 0, p < 0.05, it shows that the points show significant spatial discreteness; if p > 0.05, it is referred to as the point pattern does not deviate significantly from the random distribution [46]. This method is widely applied in the study of urban social facilities, business districts, accident distribution, and disease transmission, and can be used as a preliminary test method for identifying spatial agglomeration characteristics. In this study, we used the average nearest neighbor analysis to identify the distribution pattern of POI data of different categories of social facilities in Nanjing, evaluate whether there is significant spatial agglomeration, and provide basic support for the subsequent optimization of facility layout and resource allocation.

2.7. Standard Deviational Ellipse

We use the standard deviational ellipse [44,47] to characterize the overall distribution trend, degree of dispersion, and dominant direction of POI spatial point data, which constructs a statistically significant ellipse in two-dimensional space by calculating the spatial covariance matrix and azimuth of various types of spatial points. In the standard error ellipse, the major axis direction represents the main distribution direction of the data, indicating the main extension trend of the point data in space; the minor axis direction reflects the secondary distribution trend of the data. The azimuth corresponding to the major axis can be used as the core parameter to characterize the directionality of spatial distribution, indicating the orientation characteristics of the spatial structure of the facility. The flattening of the ellipse represents the strength of the directional trend. The larger the flattening rate, the thinner the elliptical shape, indicating a clear directional aggregation trend of spatial points; the smaller the flattening rate, the more circular the ellipse tends to be, indicating a more uniform data distribution and less obvious directionality feature. Additionally, the area of the ellipse reflects the spatial dispersion of the point data. The larger the area of the ellipse, the wider the distribution range of the spatial points and the stronger the dispersion; the smaller the area, the more concentrated the point data is, showing a stronger aggregation feature. Therefore, the ellipse can not only be used to analyze the spatial structure of a single type of facility, but also to compare multiple types of facilities and identify the similarities and differences in their distribution patterns and spatial characteristics. The calculation formula is as follows [44,47]:

$$\begin{array}{l}\tan \theta ={\displaystyle \frac{{\displaystyle \sum _{i=1}^n{\left(x_i-\overline{x}\right)}^2}-{\displaystyle \sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}}{2{\displaystyle \sum _{i=1}^n\left[{\displaystyle \sum _{i=1}^n{\left(x_i-\overline{x}\right)}^2}-{\displaystyle \sum _{i=1}^n\left(y_i-\overline{y}\right)}\right]}}}+\\ {\displaystyle \frac{\sqrt{{\left[{\displaystyle \sum _{i=1}^n{\left(x_i-\overline{x}\right)}^2}-{\displaystyle \sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}\right]}^2+4{\left[{\displaystyle \sum _{i=1}^n{\left(x_i-\overline{x}\right)}^2}-{\displaystyle \sum _{i=1}^n\left(y_i-\overline{y}\right)}\right]}^2}}{2{\displaystyle \sum _{i=1}^n\left[{\displaystyle \sum _{i=1}^n{\left(x_i-\overline{x}\right)}^2}-{\displaystyle \sum _{i=1}^n\left(y_i-\overline{y}\right)}\right]}}}\end{array}$$

(9)

$${\sigma }_x=\sqrt{{\displaystyle \sum _{i=1}^n{\left[\left(x_i-\overline{x}\right)\cos \theta -\left(y_i-\overline{y}\right)\sin \theta \right]}^2}/n}$$

(10)

$${\sigma }_y=\sqrt{{\displaystyle \sum _{i=1}^n{\left[\left(x_i-\overline{x}\right)\sin \theta -\left(y_i-\overline{y}\right)\cos \theta \right]}^2}/n}$$

(11)

where (x_i, y_i) represent the coordinates of each point, while $\overline{x}$ and $\overline{y}$ are the average values of all x and y coordinates, respectively. The parameter θ indicates the rotation angle, and ${\sigma }_x$ and ${\sigma }_y$ refer to the standard deviations along the x-and y-axes.

2.8. Delphi Method

The Delphi method is a systematic prediction and evaluation method that relies on the wisdom of expert groups [40,41], which is commonly used in the research scenarios such as multi-criteria decision analysis, weight determination, and future trend judgment. In this study, we employed the Delphi method to determine and assess the importance weights of various types of social facilities in the urban spatial layout. In the Delphi survey, a panel of 40 authoritative experts was initially selected from disciplines including physical geography, ecological environment, and urban planning, with their geographical distribution encompassing the entire administrative region of Nanjing and representing both urban and suburban areas. A questionnaire on the weight evaluation of social facilities, including the research theme and evaluation indicators, was distributed via email. These experts were invited to evaluate the roles and priorities of different types of social facilities in the urban space. After data cleaning and preprocessing, 20 valid responses and feedback were obtained. To assess the consistency and coordination of group opinions, we calculated measures of central tendency and dispersion for the expert responses. For indicators with large discrepancies, we compiled anonymized feedback summarizing the statistical results and key points of disagreement, and sent it back to the experts, asking them to adjust their opinions based on the overall trend. This iterative process was conducted for 3–4 rounds until a predefined convergence criterion of the coefficient of variation (CV) ≤ 15% was met, resulting in an integrated consensus among experts. The CV of expert group opinions is an important metric for assessing the relative dispersion or consistency within an expert group, which quantifies the degree of variability or convergence of group opinions, allowing for comparisons of consensus across different expert groups or evaluation items. In general, a smaller CV indicates greater coordination among group evaluations. It is calculated as σ/u, where σ represents the standard deviation of expert evaluations and u represents the arithmetic mean of the expert opinions. The detailed background information on the experts, including their disciplinary fields and geographical distribution, are shown in Supplementary Table S2. Subsequently, based on the expert scoring results, we further utilized the weighted overlay analysis method to comprehensively assess the spatial distribution priorities of various social facilities [40]. By incorporating the weights determined by experts into the spatial density map layers of facilities, we quantitatively expressed the supporting role of each facility type in urban functions, whereby identifying the key areas, optimization directions, and functional blind spots of social facility layout in Nanjing. We conducted a sensitivity analysis by varying the proportion of suburban experts and found that the resulting changes in the calculated weights were not pronounced, which further confirm the reliability of our study.

3. Results

3.1. Spatial Distribution Characteristics of Social Facilities in Nanjing

The results of the spatial kernel density analysis of social facilities in Nanjing are shown in Figure 3a–f, revealing the significant differences in the distribution of different types of facilities in urban space, reflecting the reality of the imbalanced urban functional structure and spatial development. Shopping and consumption (44.02%) and livelihood service (24.74%) facilities, respectively, exhibit a highly concentrated spatial distribution feature, with high-density cores mainly concentrated in Qinhuai District, Gulou District, and Xuanwu District in the central urban area, and radially extending to the periphery along urban trunk roads such as Zhongshan Road, Central Road, and Longpan Middle Road. The spatial distribution of transportation facilities (14.8%) is more function-oriented, concentrated in urban transportation hub nodes, such as Nanjing Lukou International Airport, Nanjing Port, Nanjing South Railway Station, and the intersection of various trunk roads and expressways. This distribution feature is highly consistent with Nanjing’s positioning as a regional comprehensive transportation hub, reflecting the networking and node agglomeration characteristics of facility layout. Science, education, and culture facilities (10.21%) are mainly concentrated in a belt-like manner along both sides of the Yangtze River in space, especially in Jiangbei New District, Jiangnan Main Urban District, and other areas, forming obvious hotspots, covering Nanjing colleges and universities as well as science and education parks. Medical and healthcare facilities (5.48%) are concentrated in old urban areas such as Gulou and Qinhuai, forming a core of medical resource concentration. However, in new urban areas such as Pukou, Jiangning, and Lishui, as well as peripheral areas, the density of facilities is relatively insufficient, showing a spatial imbalance of medical service resources. Tourist attraction facilities (0.75%) are more dispersed in spatial distribution than other types and are widely distributed throughout the city. Although this part accounts for a small proportion overall, its balanced distribution characteristics help to enhance the city’s overall tourism carrying capacity and spatial radiation effect and promote regional coordinated development. Overall, the spatial agglomeration and directionality of social facilities in Nanjing are relatively significant, and the central urban area is fully functional, while the development of facilities in the peripheral areas is relatively lagging behind.

3.2. Spatial Imbalance of Social Facilities and Their Impact Weights

The research results show that the main urban area of Nanjing City has a significant advantage in terms of resource concentration in social service facilities, with a relatively complete supporting system and a high density of facilities, whereas the facility configuration in the peripheral areas of the city still lacks certain deficiencies. From the regional distribution statistics of Figure 4 and

Table 2. Statistics on social facilities and population distribution in Nanjing.

District	Area (km2)	Proportion (%)	POI Count	Proportion (%)	Population	Proportion (%)	Density
Qinghuai	49.11	0.75	32,980	11.30	740,809	8.19	671.55
Xuanwu	75.46	1.15	20,077	6.88	537,825	5.95	266.06
Yuhuatai	132.39	2.01	20,508	7.02	608,780	6.73	154.91
Qixia	395.44	6.00	23,469	8.04	987,835	10.92	59.35
Jianye	81.75	1.24	21,207	7.26	534,257	5.91	259.41
Pukou	913.75	13.87	31,841	10.91	1,171,603	12.96	34.847
Liuhe	1470.99	22.33	27,569	9.44	946,563	10.47	18.74
Lishui	1063.57	16.15	15,362	5.26	491,336	5.43	14.44
Gaochun	790.22	12.00	13,578	4.65	429,173	4.74	17.18
Jiangning	1563.33	23.73	52,803	18.08	1,926,117	21.30	33.78
Gulou	51.48	0.78	32,577	11.16	669,090	7.40	632.81
Nanjing	6587.49	100	291,971	100.00	9,043,388	100.00	44.32

, Jiangning district, as the largest administrative area in Nanjing City (with an area of 1563.33 km², accounting for 23.73% of the total area of the city) and the one with the largest population, has a total of 52,803 social facilities, accounting for 18.08% of the total POI in the city, which ranks first in terms of absolute quantity. However, its POI density per unit area is only 33.78 per km², significantly lower than the average level of the city, indicating that although it has a strong population carrying capacity, the spatial configuration density of its facility resources is still relatively low, and there is a certain problem of mismatch between supply and demand. In contrast, Qinhuai and Gulou districts, although their areas only account for 0.75% (49.11 km²) and 0.78% (51.48 km²) of the total area of the city, respectively, have gathered a large amount of social service resources. The unit area POI density of these two districts is as high as 671.55 and 632.81 per km² respectively, far higher than that of other areas in the city, presenting a highly concentrated characteristic. This not only reflects the high comprehensive nature of social functions in the old urban area and the historical accumulation effect but also indicates that its facility services have a strong cross-regional radiation capacity. Additionally, other larger peripheral areas, such as Pukou, Liuhe, Lishui and Gaochun districts, although their facility totals have increased, the unit area density is generally low. These findings further indicate that the spatial layout of urban social facilities in Nanjing City presents a typical gradient structure from the center to the periphery and an uneven spatial distribution characteristic. We further used the Delphi method weight analysis to estimate the impact weights of the six types of POIs on the overall social facilities in Nanjing, which are shown in Figure 5. The results illustrate that transportation facilities (24.46%) and shopping and consumption facilities (23.07%) have the largest impact weights, while those of science and education culture (10.34%) and tourist attractions (7.90%) are the lowest. This reflects the consensus of the expert group on the importance of various social facility functions, providing a quantitative basis for subsequent spatial optimization configuration and resource allocation, and also demonstrating the heterogeneity of the influence of different social facilities in urban construction.

3.3. Spatial Correlation Analysis of Social Facilities

The results of the spatial correlation analysis of social facilities in Nanjing City are shown in Figure 6. The correlation coefficient between shopping and consumption facilities and medical care facilities is 0.91, indicating a highly consistent distribution trend in space and significant co-location, which reflects the complex needs of residents in terms of shopping and access to health services, as well as the formation of core area functional concentration and composite service spaces. The correlation between medical care facilities and educational and cultural facilities is strong (0.90), exhibiting the spatial synergy between educational and scientific research functions and health services, and to a certain extent, reflecting the functional coupling layout characteristics under the guidance of urban equity and sustainable development. The spatial dependence of livelihood service facilities and transportation facilities is also relatively strong (0.91), further verifying the high complexity of service functions in the urban core area. In contrast, the correlation coefficients of tourist attractions with medical care, educational and cultural, shopping and consumption facilities are relatively lower than those of other factors, indicating their more dispersed spatial layout characteristics. This objectively demonstrates the spatial differentiation of the facility distribution pattern driven by residents’ living needs in inland coastal cross-river areas. These results reveal the clustering and collaborative layout characteristics of different types of social facilities in the urban space, providing decision support for the urban planning and facility optimization configuration of Nanjing [12,13].

3.4. Nearest Neighbor Analysis of Social Facilities

The estimated results of the average nearest neighbor analysis for the six types of POI social facilities are presented in Figure 7 and

Table 3. Analysis of the proximity of social facilities in Nanjing City.

Facility Type	Average Observation Distance (m)	Expected Average Distance (m)	Nearest Neighbor Ratio (R Value, %)	Z-Score	p-Value	Pattern
SC	21.574	152.942	14.11	−589.07	<0.05	Clustered
LS	34.780	203.426	17.10	−426.22	<0.05	Clustered
TF	68.366	264.692	25.83	−295.01	<0.05	Clustered
ESC	52.784	312.970	16.87	−274.58	<0.05	Clustered
MH	76.641	421.222	18.20	−198.02	<0.05	Clustered
TAs	414.031	1151.794	35.95	−57.36	<0.05	Clustered

, where the spatial distribution of these six types of social facilities in Nanjing shows a highly significant clustering pattern. The actual observed average distances for all facility types are significantly lower than the theoretical expected distances under a completely random spatial distribution. The nearest neighbor ratio (R value) ranges from 14.11% to 35.95%, and the Z values are all negative and have large absolute values, with p values all less than 0.05. This indicates that the spatial distribution of each type of facility significantly deviates from the randomness assumption and is in a highly aggregated state. Specifically, the nearest neighbor ratio for shopping and consumption facilities (SC) is the lowest at 14.11%, with the Z value as high as −589.07, indicating that this type of facility has the strongest spatial clustering, possibly naturally forming dense commercial clusters due to its dependence on consumer flow and commercial atmosphere. Livelihood service facilities (LS) also exhibit strong clustering characteristics, with an R value of 17.10% and a Z value of −426.22, showing that they are concentrated in residential dense areas and the core of the living circle, meeting the needs of high-frequency and short-distance services. Transportation facilities (TF) and medical care facilities (MH) have the R values of 25.83% and 18.20%, respectively, indicating significant clustering at functional key points such as urban transportation nodes and hospital concentration areas, which conforms to their strong location dependence and relatively large service radius spatial logic. The aggregation degree of science and education culture facilities (ESC) is also relatively high (R = 16.87%, Z = −274.58), reflecting the spatial centralized distribution characteristic of educational and research resources in the central urban area. Tourist attraction facilities (TAs) have the highest R value (35.95%) and the weakest clustering, but still significantly deviate from random distribution (Z = −57.36), suggesting that although the spatial distribution of tourism resources is relatively scattered, there are still local hotspots of clustering in specific scenic area regions.

3.5. Analysis of Standard Deviational Ellipse of Social Facilities and Transportation Accessibility Analysis in Nanjing City

The standard deviational ellipse [48] analysis results of six types of social facilities in Nanjing are shown in Figure 8, from which it can be seen that the ellipse is generally distributed in the northwest–southeast direction. This is basically consistent with the direction of the city’s main roads and the spatial pattern of the Yangtze River passing through the city, reflecting the high degree of coordination between the spatial organization of social facilities and the urban form and development axis [13]. The ellipse of transportation facilities has the largest inclination of the major axis and the smallest aggregation range, mainly concentrated in Qinhuai, Gulo, and Jianye districts as well as other urban main roads and transportation hubs, showing its strong dependence on the urban backbone transportation network and functional node-oriented characteristics. Relatively speaking, the ellipse of tourist attractions has the largest coverage area and shows obvious spatial dispersion, whose range extends from the old city of Jiangnan along the Yangtze River to the Jiangbei New District and the peripheral areas such as Lishui and Gaochun, indicating that Nanjing’s tourism resources are widely distributed, including both urban historical and cultural attractions and natural ecological landscape resources. The ellipse directions of other facilities such as shopping, livelihood services, medical care, science, education, and culture are relatively consistent, and the contour lines with a relatively moderate area are highly overlapped in the main urban area (Qinhuai, Gulou, Xuanwu), indicating that these functional facilities mainly serve the densely populated and high-frequency demand groups in the core urban area. These results exhibit the resource concentration orientation in Nanjing’s urban spatial structure and also proves the typical expansion mode of social service facilities leaning toward the center and extending outward [18]. Additionally, we evaluated the traffic accessibility ranges of 5, 10, and 15 min in Nanjing. we assigned average travel speeds to different road types such as subway lines, bus lanes, and bicycle paths based on the Road Traffic Safety Law of the People’s Republic of China (Figure 9a). By combining these speeds with road lengths, we calculated travel times and used ArcGIS Pro’s network analysis tools to build a topological road network model. This allowed us to generate a network dataset and perform interactive spatial accessibility calculations. We visualized the results by mapping service areas within 5, 10, and 15 min of travel time, reflecting realistic accessibility coverage around each administrative center (Figure 9b). The results indicate that the 5, 10, and 15 min traffic accessibility zones are primarily significant in areas with a high score of rationality level. This aligns with our expectation that areas with a greater density of social facility POIs tend to have stronger traffic accessibility.

3.6. Comprehensive Assessment of the Rationality of Social Facilities in Nanjing

Referring to the influence weights of various social facilities determined by the Delphi method [40,41], we normalized all social facility elements, and incorporated the indicator of per capita facility quantity in Nanjing to reflect the level of service provision relative to the population demand. Subsequently, we used the grid calculator for spatial overlay analysis to generate a comprehensive assessment map of the rationality of social facilities in Nanjing, which is shown in Figure 10. Based on the specific characteristics of Nanjing’s urban spatial structure and expert consultation, we set the rationality level classification standard: a score of >90 indicates excellent facility configuration, 80–90 indicates good, 60–80 indicates average, and <60 indicates poor or extremely poor. The color in the figure decreases from dark red to light yellow, which directly reflects the changing trend of the rationality of the spatial configuration of social facilities. The evaluation results show that the main urban areas of Nanjing, such as Gulou, Qinhuai, and Xuanwu Districts, have the highest scores, the most reasonable layout of social facilities, and the densest concentration of facilities as well as the perfect service system, guaranteeing good spatial accessibility and service fairness; with these areas as the core, the rationality level of facilities decreases in a ring shape to Jianye, Yuhuatai, northern Jiangning, southern Pukou, and other areas, showing a strong orientation to the main axis of urban development. Peripheral areas such as Liuhe, Lishui, and Gaochun Districts generally have low scores and insufficient service levels, reflecting the imbalance in the allocation of social facilities at this stage. Overall, the rationality of social facilities services in Nanjing illustrates a spatial structural feature of superiority in the main city and weakness in the periphery, and its distribution pattern is closely related to population density, transportation network, and the development pattern of historical urban areas. This result provides an important empirical reference for the future optimization of public facilities allocation and spatial balanced development in Nanjing [16].

4. Discussion

Based on the POI and multi-source geographic data, this study systematically explores the spatial distribution pattern of social facilities in Nanjing and their rationality evaluation by combining multiple spatial analysis methods involving kernel density analysis, average nearest neighbor analysis, standard error ellipse, and facility rationality evaluation [33,35,48]. The results show that the spatial distribution of social facilities in Nanjing presents a significant spatial heterogeneity with coexistence of central agglomeration and peripheral sparseness. The old urban areas such as Gulou, Qinhuai, and Xuanwu have the highest density of social facilities and the most complete service network due to the historical development accumulation and functional agglomeration effect, forming a typical core-dominated structure. Although the number of facilities in the new development areas such as Jiangning, Pukou, and Jianye is relatively rich, the density per unit area is far behind that in the main urban areas, indicating that the service capacity has not yet fully matched the speed of population agglomeration. The facilities in remote areas including Gaochun, Liushi, and Gaochun are clearly insufficient in configuration, with poor service accessibility, and the spatial development is relatively lagging, presenting problems of fragmented public service supply.

From the perspective of specific facility types, the spatial distribution of transportation facilities and shopping and consumption facilities is the densest, with high core density and wide service range, reflecting the strong linkage of urban functional networks and the high dependence of residents’ daily activities [20]. Although medical care and science and education culture are highly concentrated in the main urban area, they are insufficiently distributed in the new districts and peripheral areas, revealing the spatial inequality of the distribution of educational and medical resources. In particular, the spatial coverage of medical facilities is weak, which potentially affects the health accessibility of marginalized groups and the construction of urban resilience [11,19]. This study also reveals that the distribution direction of social facilities in Nanjing has obvious spatial main axis characteristics. Standard error ellipse analysis shows that the distribution of various facilities extends along the northwest–southeast direction as a whole, which is highly consistent with the flow direction of the Yangtze River, the urban development axis and the rail transit network [47,48,49]. This distribution pattern is the result of the combined effects of the city’s natural terrain, transportation channels, and policy orientation, and also suggests that the urban spatial structure has a structural risk of single-axis agglomeration at the planning level [12]. In the evaluation of the rationality of social facility configuration, we use the Delphi method to construct an indicator weight system [40,41], whose results exhibit that the service level in the main urban area is high and the facility layout is reasonable, and there is substantial room for improvement in the peripheral areas. The rationality level of social facilities illustrates a ring-core gradient attenuation pattern in space, indicating that the main urban area is the center and the trend gradually weakens outward, which is closely related to the urban development stage, land value differences, and population density [16]. We find that certain types of social facilities, such as shopping and consumption, medical care, and educational and cultural services, tend to exhibit strong spatial clustering and co-location. These patterns suggest the formation of composite service areas where multiple facility types concentrate together, reflecting the complex and integrated needs of urban residents. Such clustering can be considered rational when it enhances accessibility by allowing residents to meet multiple needs within a compact area, improves service efficiency through functional synergy, and supports the development of vibrant urban cores. The spatial patterns and disparities revealed in this study have direct implications for urban planning policy in Nanjing. The concentration of social facilities in the central districts, coupled with notable shortages in peripheral and newly developed areas, signals a need for policy interventions aimed at achieving a more balanced spatial allocation of public services. The identification of co-located facility clusters highlights areas where integrated service hubs could be further strengthened, while the detection of underserved regions provides clear targets for future facility investment. From a planning perspective, these results can inform the prioritization of infrastructure development, guide the selection of optimal facility locations, and support the implementation of differentiated service provision strategies based on local demographic and geographic contexts. By incorporating the identified disparities into decision-making, policymakers can adopt a data-driven approach to resource allocation, ensuring that investments in public facilities align with both current demand and anticipated urban growth trajectories. Furthermore, the methodological framework used here can be applied periodically to monitor the effectiveness of interventions, enabling adaptive policy adjustments that promote spatial equity and sustainable urban development.

In light of the above research findings, we propose the following optimization suggestions to enhance the spatial balance of social facilities and the quality of public services in Nanjing City. First, strengthen the concept of urban-rural integration and narrow the service gap in peripheral areas. The target should be regional coordinated development, and the construction of social facilities in far-out suburbs such as Gaochun, Lishui, and Gaochun Districts should be accelerated, especially in the areas involving healthcare, education, and community services, to improve the problems of weak infrastructure and excessive service radius. In line with the new urbanization and common prosperity policy orientation, promote the diffusion of facility construction from the central urban area to the periphery, and achieve the transformation of the urban service system from core radiation to balanced coverage. Second, optimize the layout of facilities in the main urban area to avoid excessive concentration and resource redundancy. The density of social facilities per unit area in the main urban area is significantly high. Through facility function integration, resource sharing, and hierarchical management, the efficiency of resource utilization should be improved, and redundant construction and overloading of urban space should be avoided. At the same time, encourage facilities to expand beyond the urban core and transfer some functions to secondary center areas such as Jiangning, Pukou, and Yuhuatai, guiding the rational dispersion of population and services, and alleviating the development pressure in the central area. Third, build a cross-river facility linkage system to enhance spatial connectivity and service fairness. As a typical cross-river city, the development of Nanjing is divided into two major sections by the natural water body, the Yangtze River. Special attention should be paid to the coordinated planning of facility resources on both banks of the river. The public service compensation mechanism between the Jiangbei New Area and the main urban area of the south should be strengthened, and the cross-regional integration capacity of infrastructure such as healthcare, education, and culture should be improved, promoting the formation of a cross-river integrated service network, avoiding spatial fragmentation [45]. Fourth, promote the integration of transportation systems and facility layout to enhance residents’ accessibility. By constructing a three-dimensional transportation network of railway, bus and pedestrian, effective connections should be made between social facility points, improving the accessibility and convenience of spatial services [48]. Especially in urban new districts and residential clusters, attention should be paid to the coordinated location of public transportation hubs and schools, hospitals, and commercial centers, strengthening efficient connections between functional blocks of the city, and ensuring fair access opportunities for different groups. Fifth, introduce multi-dimensional data and social participation to enhance the scientific rationality and responsiveness of planning. Current research mainly relies on expert opinions and spatial data for weight setting and service level judgment. In the future, dynamic data such as residents’ travel trajectories, satisfaction surveys, and facility usage frequency should be combined to improve the accuracy of the rationality assessment of social facilities. At the same time, guide the public to participate in the facility layout and planning and design process to enhance the resilience of urban governance. Based on the areas identified with relatively low rationality scores and considering the functional characteristics of each district, we propose the following targeted enhancements of urban facilities: strengthening shopping, consumption, and livelihood service facilities in Gaochun, Lishui, and Liuhe; improving transportation infrastructure in Gulou and Qinhuai; expanding science, educational, cultural, and medical healthcare facilities in Qixia, Pukou, and Jiangning; and developing tourist attraction facilities in Yuhuatai, Xuanwu, and Jianye. These recommendations aim to optimize the spatial allocation of urban facilities according to local needs and functional priorities. Comparative evidence from POI-based studies indicates that urban facility distributions in Lanzhou often cluster along transportation corridors and within historical urban cores [26], reflecting the influence of both geography and legacy development patterns. Research on Ningbo shows a strong alignment of commercial and service clusters with policy-driven functional zones [49], demonstrating the shaping power of targeted urban development strategies. In Zhengzhou, clustering patterns are closely linked to logistics and transportation hubs [49], underscoring the role of industrial specialization in spatial organization. While Nanjing exhibits certain similarities with these cases, its cross-river, multi-axis structure produces more pronounced spatial synergies among different facility types [50,51]. The present study extends existing research by integrating demographic, transportation, and functional coupling analyses to assess facility layout rationality within an equity-oriented urban planning framework. While substantial heterogeneity exists among facility subcategories (e.g., clinics versus tertiary hospitals, or convenience stores versus shopping centers), undertaking a systematic analysis across all subcategories would entail a level of analytical complexity and length that exceeds the feasible scope of the present work. As a robustness check, we therefore focused on medical facilities and performed separate kernel density analyses for clinics and general hospitals (Supplementary Figure S1). The resulting spatial distributions were highly consistent with those derived from the aggregated medical facilities, thereby substantiating the robustness and credibility of our principal findings in the face of potential classification aggregation effects. To address the concerns regarding the potential coarseness of using administrative districts as the spatial analysis unit, especially for large districts exceeding 1000 km² such as Jiangning District, we refined the analysis to the township scale to better capture intra-district variability. A finer-scale analysis at the 1 km × 1 km grid or community level was deemed impractical for most of these districts due to the scarcity of POI data at that resolution. Based on the refined township-scale data, we recalculated the facility density (Supplementary Table S3) and compared the effects of different spatial units on the rationality rating. The comparison results (Supplementary Figure S2) indicate minimal differences between the district-scale and refined-scale evaluations, thereby confirming the robustness of our findings. A comparative analysis with Wuhu has been incorporated into the revised manuscript, focusing on both the error ellipse assessment and the comprehensive rationality evaluation (Supplementary Figure S3). The results indicate that while the overall spatial distribution pattern of social facilities in Wuhu broadly resembles that of Nanjing, notable differences exist in both the degree of spatial aggregation and the directional distribution trends, which help to enhance the contextual interpretation of Nanjing’s findings.

There are some limitations in our research. Although this study has established a relatively systematic spatial analysis framework, there are still some shortcomings. For instance, although POI data can reveal the density of facilities, it is difficult to reflect the service intensity and quality [11]. The weighting method of the Delphi method still has a certain degree of subjectivity and lacks feedback verification from the users [40]. Moreover, we do not cover the differences in social group stratification and explore the vulnerability of the elderly and low-income groups in terms of facility accessibility [20]. Future research can integrate multi-source big data (such as LBS trajectories, bus card data, and community surveys), and introduce spatio-temporal evolution models to enhance the depth of analysis and the operability of policy implementation [19]. We integrated several key external factors, including Nanjing’s administrative boundaries, urban road networks, population spatial distribution, and the digital elevation model (DEM), to provide essential context for analyzing the spatial distribution of social facilities. Nevertheless, other significant external influences such as economic development levels, land use policies, and environmental conditions were not involved. These factors may also play a crucial role in shaping the distribution and accessibility of social facilities. Future research could be conducted to integrate these additional variables to achieve a more comprehensive and nuanced understanding of the drivers behind spatial equity in urban public service provision. In this study, the Delphi method was used to determine the importance weights of various types of social facilities based on expert consultation. The assigned weights reflect subjective judgments, which may not fully capture the dynamic and heterogeneous nature of facility demand and utilization across different population groups and urban contexts. Additionally, the rationality evaluation primarily relies on these weighted scores combined with spatial data, but lacks direct empirical validation using user behavior, service usage statistics, or socio-economic factors. Future research could enhance the robustness of the assessment by integrating more diverse data sources and employing complementary quantitative methods to better represent the complex realities of social facility usage and accessibility. We did not analyze facility accessibility for vulnerable groups such as low-income residents, the elderly, or people with disabilities due to the lack of fine-grained spatial data at the intra-city scale. This constitutes a limitation, and future research could incorporate such data to enhance the equity assessment. Another limitation of this study is the unavailability of detailed age-specific population data and precise information on medical beds per thousand people and elderly population proportions. The current analysis does not fully capture the impact of age structure on facility demand, and future work would seek to incorporate these data to improve the demand–supply assessment. In this study, the 15 min living circle analysis was implemented by assigning average travel speeds to different road types and combining these with road lengths to construct a topological road network model. While this approach provides a reasonable representation of accessibility patterns, it does not take into account additional factors such as real-time public transportation schedules, terrain barriers (e.g., slope effects), or facility opening hours. These limitations may lead to a certain degree of simplification in the accessibility estimates. Nevertheless, the high consistency between the accessibility zones and the spatial distribution of social facility POIs indicates that the adopted method effectively captures the main accessibility patterns, while future research could further refine the analysis by incorporating multi-source dynamic datasets.

5. Conclusions

In this study, based on POI data from Gaode Map and various basic geographic information data of Nanjing, we systematically analyzed the spatial distribution patterns, clustering characteristics, and spatial coordination relationships of six types of social facilities, including shopping and consumption, livelihood services, transportation facilities, science and education culture, medical care, and tourist attractions. The results show that social facilities in Nanjing generally display a pattern of high concentration in the city center and low density in peripheral areas. The main urban area has sufficient service supply and a compact layout, while the Jiangbei New District and urban fringe areas face notable gaps in facility coverage, structural completeness, and accessibility. These disparities reveal underlying challenges in achieving fairness-oriented rationality in social facility distribution. Nanjing’s spatial pattern is also shaped by atypical factors, such as its role as the provincial capital, the presence of multiple national-level development zones, and a high degree of cross-river connectivity supported by dense transport channels, combined with a GDP exceeding one trillion yuan. Our study provides a valuable empirical basis for targeted planning interventions and contributes to a deeper understanding of spatial equity in rapidly evolving megacities.