The Primacy Evaluation and Pattern Evolution Mechanism of the Central City in Nanjing Metropolitan Area

Abstract

Economic globalisation has accelerated the cross-regional flow of resource elements and broken through the constraints of traditional regional administrative boundaries. Urban agglomerations are core carriers that drive and accelerate regional integration development and can promote the division of urban functions and cooperation. This study considers the Nanjing metropolitan area as a case study to construct a comprehensive first-degree evaluation index system for cities from a factor-flow perspective, focusing on economic, cultural, and transportation connections. We found that (1) Nanjing, which has long been ranked first, shows a downward trending score, dropping from 0.956 in 2017 to 0.937 in 2023; (2) The comprehensive first-degree spatial structure of metropolitan-area cities presents a network hierarchical development feature of “one core, multiple centres, and multiple areas”. With Nanjing as the regional core city, Chuzhou (0.879), Yangzhou (0.915), and Wuhu (0.897) as sub-centre cities, and other cities as sub-regional nodes, the urban system structure gradually forms; (3) The indicators of economic (0.166 **), cultural (0.226 **), and transportation (0.644 ***) element connections were interrelated and mutually reinforced, forming a unified entity with internal connections. This study quantitatively measured the level of integrated development in the Nanjing metropolitan area and provided a reference for formulating regional policies.

1. Introduction

In recent years, the rapid development of information technology and transportation infrastructures has significantly improved the mobility of various elements between cities [1]. In the process of global integration, China’s core big cities, such as Shanghai, Beijing, and Shenzhen, continue to develop and become important nodes in regional aviation, information, and financial networks, leading surrounding city clusters to participate in the division of labour and competition in the global economy [2]. Within urban agglomerations, the isolation effect of administrative divisions is gradually being broken, and the scope of the external functional radiation of regional central cities is constantly expanding. At the same time, they also face the challenge of the passive diversion of resource elements. Improving the primacy of central cities has become an important measure for promoting high-quality regional development [3]. Urban primacy refers to the population ratio of the largest and second-largest cities in a region [4]. This indicator is also commonly used to measure urban population size and development stage [5]. There have been many international research achievements regarding the primacy of cities, but few studies have evaluated the primacy of cities within a region by measuring the strength of the resource element connections between them [6].

Research into the theory of urban agglomerations has long been conducted, but it has mainly involved the definitions of urban agglomerations, spatial structures, and the evolution process [6]. Chinese scholars have focused on theoretical research into urban agglomerations in terms of functional positioning, development planning, and formation models [7]. Some scholars believe that small cities within metropolitan areas are interconnected through central cities to build regional urban networks jointly [8]. Additionally, other cities within the metropolitan area play the roles of external functional coordination and central city element connections [9]. From a conceptual definition perspective, the United States first proposed the concept of metropolitan areas in 1910, followed by French geographers who subsequently proposed similar concepts such as the “metropolitan belt” and “metropolitan continuous belt” [10]. After the 1950s, Japanese scholars proposed relevant theories on urban regional differentiation, forming the initial concept of “and metropolitan areas” [11]. This concept has evolved continuously and has become the theoretical basis for the current concept of metropolitan areas [12]. Scholars have defined an urban agglomeration as a geographical area that can receive certain functional services from the central city daily. The population size of a central city must exceed 100,000 [13]. With continuous improvements in high-speed railway networks, transportation connections between cities within metropolitan areas have become more convenient. Some studies have also defined metropolitan areas as those that can be reached within a one-hour commuting time range, with the central city as the core [14]. Currently, international research on the spatial structure of urban agglomerations mainly focuses on three aspects: the form [6], the evolution process [7], and the mode of element organisation [8]. Overall, there is a lack of research into the spatial structure of urban agglomerations, both domestically and internationally, and related theoretical research lags behind social practice [14].

Urban spatial governance within a region is an important research direction in urban agglomerations [15]. Research into regional spatial governance has focused on exploring the relationship between urban elements and spatial evolution processes within urban agglomerations under market conditions [16]. International research on regional governance focuses on carrying out urban agglomeration governance through policy formulation, departmental cooperation, and multiparty linkages, ultimately achieving regional coordinated development [17]. Scholars have compared the management models of urban agglomerations in China with those in the United States and believe that regional management models and structures conforming to the national political system are important guarantees for supporting regional economic development [18]. With the acceleration of urbanisation, China’s large urban agglomerations have rapidly expanded in scale. Research on urban agglomerations has focused on planning and construction [19], international experience [20], ecological environment governance [21], industrial coordinated development [22], equalisation of basic public services [23], and collaborative governance level measurements [24]. Spatial governance policies in urban areas relate to formulating reasonable spatial development plans, strengthening element connections, optimising spatial structures, and establishing a unified and orderly governance mechanism [25]. Overall, Chinese scholars have focused their research on regional collaborative governance policies, whereas there are relatively few studies on governance models from the perspective of urban factor connections [26].

Previous studies have revealed the functional types and positioning of central cities through the index of urban primacy within a region and proposed strategic paths for coordinated development between regional central and surrounding cities [27]. Scholars have used the first-degree index to measure regional economic growth and urban size distribution levels, screening indicators that expand from the population to fields such as the economy, industry, technology, and culture. The indicator system is constantly expanding [28]. Scholars have extended the concept of primacy by dividing it into element types and using the Analytic Hierarchy Process to determine specific weights [29]. With China’s rapid urbanisation, the administrative divisions of cities have been continuously adjusted, coordinated management of surrounding cities has been implemented, and their regional influence at the administrative system level as been expanded. Scientifically, understanding and measuring the primacy index of regional central cities has become an important topic for all sectors of society [30]. In fact, international research on urban primacy has already broken through the single-dimensional indicator of population, paying more attention to external functional radiation and cities’ factor connections, as well as the synergistic driving effect on other cities in the region [31]. However, empirical research that measures urban primacy indicators from the perspectives of factor flow, regional resource agglomeration, and distribution patterns is lacking [32].

At present, the analysis of urban primacy mostly uses statistical yearbook indicators, such as population size and economic total, for calculations. These are difficult to match with the current high-speed flow of factors between cities, and they cause a serious lag in local practices. The concept of urban primacy has shifted towards the radiative driving effect of primacy cities in surrounding areas. Primacy is seen as a policy tool for understanding and regulating the direction of urban socioeconomic development, thereby enhancing the city level. Therefore, we believe that urban primacy, as a comprehensive indicator of the position of a city in a region, cannot be measured simply using one or two indicators. It must be evaluated by constructing a scientific indicator system [14,18]. This indicator system should not only combine the traditional connotation of urban primacy, but should also consider the transformation trend of China’s new urbanisation from speed-driven to quality-driven and from scale expansion to connotation-based operation [22].

This study aims at regional collaborative development and constructs a comprehensive evaluation index system for the primacy of central cities from the perspective of factor flow space, quantitatively measuring the level of intercity factor connections. By comparing the first-degree change data for multiple years from 2017 to 2023, we analysed the trend of changes in the external functional positioning and functional connections of each city within the metropolitan area and proposed corresponding regional development strategies. The research results break through the existing administrative division governance pattern of urban agglomerations, combining the evaluation of urban primacy with the optimisation of urban agglomeration structure and proposing a regional collaborative governance model supported by elements such as economic connections, resource sharing, and project co-construction [33]. Specifically, this study expands the traditional evaluation model that only considers the population as a single indicator and constructs an indicator system consisting of six dimensions: urban scale, comprehensive economy, scientific and technological talents, industrial development, public services, and opening up to the outside world. This indicator system is used to measure the comprehensive primacy of central cities within the metropolitan area, identify the characteristics of resource agglomeration and factor flow between cities within the metropolitan area, and propose coordinated development strategies for various cities within the region.

2. Materials and Methods

2.1. Study Area

The Nanjing metropolitan area is a regional economic community centred around Nanjing, located in the core area of the urban agglomeration along the middle and lower reaches of the Yangtze River in eastern China. The geographical scope of the Nanjing metropolitan area includes Jiangsu and Anhui provinces, making it the first cross-provincial planning and construction metropolitan area in China [32]. According to the “Development Plan for Nanjing Metropolitan Area”, the geographical scope of the Nanjing metropolitan area includes eight cities, including Nanjing, Zhenjiang, Yangzhou, Huai’an, Wuhu, Ma’anshan, Chuzhou, and Xuancheng, as well as Jintan and Liyang in Changzhou. There are a total of 33 municipal districts, 11 county-level cities, and 16 counties, with a total area of 66,000 square kilometres [32]. By 2023, the permanent population of the Nanjing metropolitan area was approximately 35.3176 million. The permanent urban population is approximately 25.9281 million, and the urbanisation rate of the permanent population is approximately 73.41%. The scale and volume of the city is approximately CNY 4175.078 billion, with primary, secondary, and tertiary industries accounting for 4.67%, 42.45%, and 52.88%, respectively. The social and economic elements within the Nanjing metropolitan area are generally highly interconnected, and the flow of personnel, materials, and other elements between cities is convenient. It is an important sector that provides social and economic connections between the eastern and western regions of China [33] (Figure 1).

The Nanjing metropolitan area is the first inter-provincial collaborative metropolitan area in China and one of the three major metropolitan areas on which the Jiangsu Provincial Government has focused [34]. The travel time between cities within the metropolitan area, also known as the Nanjing one-hour metropolitan area, is just over an hour [35]. The Nanjing metropolitan area is a city cluster closely connected by a developed transportation network, rather than a fixed area with an actual administrative management authority [36]. On the other hand, the Nanjing metropolitan area is a cross-provincial urban agglomeration that includes some cities from Jiangsu and Anhui provinces. It is a regional economic belt formed around Nanjing, with cities working and developing together (

Table 1. Nanjing’s metropolitan area’s population and urbanisation rates in different years.

	Registered Residence Population (10,000 People)			Permanent Population (10,000 People)			Urbanization Rate of Permanent Residents (%)
	2017	2020	2023	2017	2020	2023	2017	2020	2023
Nanjing	697	738	792	733	812	894	71	78	82
Changzhou	382	418	435	421	462	488	74	79	83
Huai’an	562	589	632	592	631	667	62	70	75
Yangzhou	462	492	531	499	527	558	68	74	77
Zhenjiang	273	298	322	322	349	382	72	76	82
Xuzhou	456	483	521	413	433	457	56	64	73
Ma’anshan	231	267	298	242	287	312	69	73	78
Wuhu	391	432	467	378	392	413	67	72	77
Xuancheng	287	312	336	297	303	328	52	58	62
Total	3741	4029	4334	3897	4196	4499	67	72	79

).

2.2. Materials

2.2.1. Data Collection

This study focuses on nine prefecture-level cities in the Nanjing metropolitan area and obtains basic data through various channels. The content includes the city statistical yearbook, land use vector data, road network vector data, 30 m resolution remote sensing image data, and TERG-DEM digital elevation data from 2017, 2020, and 2023, all of which were obtained from the Chinese Academy of Sciences geospatial data cloud platform (https://www.gscloud.cn/, accessed on 22 July 2023). First, we spatially mapped the urban administrative boundary vector data, road vector data, and third land use survey data using the National 2000 Geodetic Coordinate System and Gaussian Kriging Projection to complete the data fitting (

Table 2. Data types and structure required for research.

Data Type	Data Content	Data Volume (10,000 Pieces)	Acquisition Year	Data Source
Land-use Data	Land-use Vector Data	1.7	2017, 2020, 2023	Chinese Academy of Sciences Geospatial Data Cloud
	TERG-DEM Digital Elevation Data	/
	Landsat 8 Satellite Remote Sensing Image Data	/
Urban Facility Data	Base Map of Urban Architecture	13.15		OpenStreetMap Data Platform(OSM)
	Urban Road Network (including expressways, main roads, and secondary roads)	0.8
Statistical Yearbook	China Urban Statistical Yearbook, Jiangsu Provincial Statistical Yearbook, Anhui Provincial Statistical Yearbook	0.1		Urban Public Service Data Platform

). Second, we cross-validated the accuracy of the urban land use survey results, including land use types and other attributes, by comparing high-resolution remote sensing images. Finally, we divided the land use types within the metropolitan area into six categories, including forest land, garden land, cultivated land, water bodies, construction land, and others.

2.2.2. Variables and Indicators

We constructed six primary indicators: economic, cultural, transportation, urban scale, public services, and level of openness to the outside world. The indicator system classified and measured the linkage levels of production factors, urban functions, health and library infrastructures, and other aspects between cities. We drew on existing research results and refined the decomposition of the primary indicators, dividing them into 17 secondary indicators [37]. Urban-scale indicators included two secondary indicators: population size and built-up area. The economic factor relationship included four indicators: annual GDP), fixed asset investment quota, trade exchange index, and investment and financing indices. Cultural element connection included three indicators: the number of academic conferences, art exhibitions, and science and technology exhibitions hosted. The transportation element connection included three indicators: daily high-speed rail trips, intercity bus trips, and intercity subway connectivity. Health and Libraries Infrastructure level was measured by indicators such as the number of public book collections and beds in health institutions, whereas the level of opening up to the outside world was measured by indicators such as the actual use of foreign investment, total import and export volumes, and tourism foreign exchange income (

Table 3. The Index System for the Urban Comprehensive Primacy Index.

Primary Indicators	Secondary Indicators
Economic element connection (X11)	Annual gross domestic product (X111)
	Fixed assets investment (X112)
	Trade exchange index (X113)
	Investment and financing index (X114)
Cultural element connection (X12)	Number of academic conferences hosted annually (X121)
	Number of art exhibitions hosted annually (X122)
	Number of science and technology exhibitions hosted annually (X123)
Transportation element connection (X13)	Number of daily high-speed rail trips (X131)
	Number of daily intercity bus trips (X132)
Urban scale (X14)	Total population size (X141)
	Built-up area (X142)
Health and libraries infrastructure (X15)	Number of books in public libraries (X151)
	Number of beds in medical institutions (X152)
Foreign capital utilization (X16)	Actual amount of foreign investment used (X161)
	Total import and export volume (X162)
	Tourism foreign exchange income (X163)

).

Previous research suggests that regional integration emphasizes proximity effects, regional connectivity, and efficiency improvement, which are reflected in the complementary functions and rational division of labor between different cities [13,21]. This article conducts a first-degree analysis of the Nanjing metropolitan area, focusing on measuring the flow level of economic, cultural, transportation, and other resources between different cities. Some studies suggest that regional transportation network infrastructure is the foundation for the connection of various resource elements, and the connection of various types of elements such as cultural resources, economic resources, and public service resources is a concrete manifestation of the urban connectivity degree [21,25]. We will supplement more indicators in subsequent research to reflect regional development trends such as green, low-carbon, and sustainable. These indicators include the level of technological innovation, green development, etc., which more comprehensively reflect the overall development level of the region.

2.3. Methods

2.3.1. Entropy Weighting Method

Commonly used objective weighting methods include the entropy weighting, coefficient of variation, and principal component analysis methods [38]. This study uses the entropy weighting method to weight indicators. The entropy weight method is based on the difference-driven principle combined with the original information of the indicators, and it determines the weight of the indicators based on the information entropy of each indicator [39]. This method can effectively avoid the interference caused by subjective judgments and ensure objective consistency in obtaining the weights for each indicator. During the calculation process, we normalised and standardised the data to eliminate dimensional differences among various indicators, making a horizontal comparison between multiple indicators easier.

The standardisation formula for positive correlation indicators is as follows:

$$F_{ij}=(x_{ij}-x_{min})/(x_{max}-x_{min})$$

(1)

The standardisation formula for negative correlation indicators is as follows:

$$F_{ij}=\left({x_{max}-x}_{ij}\right)/(x_{max}-x_{min}),$$

(2)

where $x_{ij}$ is the current value of the $i$-th object and the $j$-th indicator. $F_{ij}$ is the standardised value of the $j$-th indicator of the $i$-th object, and $F_{ij}$ ∈ [0, 1]. $x_{max}$ is the maximum value of the jth indicator group. $x_{min}$ is the minimum value of the jth indicator group. We calculated the feature proportion (i = 1, 2,…, n) of the $i$-th evaluation object under the $j$-th indicator (j = 1, 2,…, n) using the following formula:

$$p_{ij}=F_{ij}/{\sum }_{i=1}^n{F}_{ij}.$$

(3)

We calculated the entropy value of the indicator as:

$$e_j=-k{\sum }_{i=1}^n{p}_{ij}ln{p}_{ij}.$$

(4)

Among these, $k>0$, $e_j>0$, $k=1/lnn$. We calculated the coefficient of difference for indicators as:

$$g_j=1-e_j.$$

(5)

The comprehensive weight of indicators was calculated thus:

$${\omega }_j=g_j/{\sum }_{j=1}^p{g}_j.$$

(6)

Among these, ${\omega }_j$ was the normalised weight coefficient.

2.3.2. Element Flow Analysis Method

With the continuous expansion of the urban scale, various socioeconomic factors flow rapidly between cities, driving economic and trade connections in surrounding cities, which manifests as the core function of the central city [40]. We measured the characteristics of the urban spatial structure and outwards connectivity function from the perspective of factor flow, including the efficiency of urban external service output and the level of foreign trade [41]. Based on this, we measured the spatial structural characteristics of the external element connections of various cities within the Nanjing metropolitan area, as well as the differences in the degree of outwards orientation among cities within the metropolitan area.

Various urban factors drive the economic development of urban agglomerations. Urban factor flows include factors and resources such as population, information, technology, and capital flows. We defined the intensity of urban flow as the level of external factor connectivity among cities within a metropolitan area. Taking economic flow as an example, we chose the gross domestic product and import and export trade volume of the secondary and tertiary industries in cities as measurement indicators of economic and social factor flow in urban agglomerations. The formula used was

$$Q_{ij}={\displaystyle \frac{e_{ij}/e_i}{E_j/E}}.$$

(7)

Among these, $Q_{ij}$ represents the outwards function of the city, and $e_{ij}$ and $e_i$ represent the gross domestic products of industry j and the gross domestic product of city $i$. $E_j$ and $E$ represent the gross domestic product (GDP) of the $j$-th industry in the metropolitan area and the GDP of the metropolitan area, respectively. If $Q_{ij}$ ≤ 1, then there is no correlation between the gross domestic product of the $j$ industry in city $i$ and foreign trade. At this point, $e_{ij }=0$. The gross domestic product (GDP) of industry $j$-th in city $i$ mainly refers to foreign trade services that provide products and services to the outside world. Therefore, ${E_{ij}=e_{ij}-e_i(E}_j/E)$, and the total outwards functional connections of city $i$ are:

$$E_i={\sum }_{i=1}^n{E}_{ij}.$$

(8)

The urban flow model is F = NE, where F represents the intensity of economic and social factor flows, N represents the efficiency of urban functions, and E represents the total number of outwards functions. We use per-capita GDP to represent urban functional efficiency. Then, $N_i={GDP}_i/e_i$ and the socioeconomic factor flow is

$$F_i=N_i{E}_i=\left({\displaystyle \frac{{GDP}_i}{e_i}}\right)E_i={GDP}_i\left({\displaystyle \frac{e_i}{E_i}}\right)=k_i{GDP}_i.$$

(9)

In the formula, $k_i$ represents the ratio of the total foreign trade quota of city $i$ to the total industrial output of all the cities in the metropolitan area. This value reflects the difference in the degree of foreign trade between the total industrial output of city $i$ and the metropolitan area, indicating a tendency for urban flow.

2.3.3. Geospatial Regression Analysis Method

This study uses a geospatial regression model to measure the economic differences between cities within the metropolitan area, and the coefficient of variation as a measurement indicator to analyse the differences in economic element connections between cities within the metropolitan area at different time periods. Geographically weighted regression is an extension of ordinary linear regression models that embeds the spatial position of data into regression equations in the following form:

$$y_i={\beta }_0\left(u_i,v_i\right)+{\sum }_{k=1}^p{\beta }_k\left(u_i,v_i\right)x_{ik}+{\epsilon }_i i=\mathrm{1,2},3\dots ,n.$$

(10)

In the formula, $\left(u_i,v_i\right)$ is the coordinate of sampling point i, and ${\beta }_k\left(u_i,v_i\right)$ is the k-th regression parameter on sampling point i. During the estimation process, the geographic location was determined using the weight function method. The formula used to calculate the coefficient of variation is as follows:

$$CV={\displaystyle \frac{1}{X}}{\left[{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(X-X_i)}^2\right]}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}},$$

(11)

where $CV$ is the coefficient of variation. $X \mathrm{a}\mathrm{n}\mathrm{d} X_i$ represent the per capita GDP of each city within the Nanjing metropolitan area and the per capita GDP of city i and n is the number of cities in the study area.

3. Results

3.1. Nanjing Has Long Been First in the Comprehensive Ranking, but Its Score Shows a Fluctuating Downward Trend

For indicator selection, we used the entropy weight method to measure the specific weights of the urban primacy indicators, as shown in

Table 4. The weights of various measurement indicators for urban comprehensive primacy.

Indicator Items	Information Entropy (e)	Information Utility (d)	Weight (%)
Annual gross domestic product (X111)	0.912	0.097	4.323
Fixed assets investment (X112)	0.843	0.089	3.672
Trade exchange index (X113)	0.947	0.117	3.166
Investment and financing index (X114)	0.782	0.104	3.018
Number of academic conferences hosted annually (X121)	0.793	0.114	2.132
Number of art exhibitions hosted annually (X122)	0.839	0.095	2.189
Number of science and technology exhibitions hosted annually (X123)	0.872	0.093	2.272
Number of daily high-speed rail trips (X131)	0.854	0.131	2.301
Number of daily intercity bus trips (X132)	0.817	0.118	2.351
Total population size (X141)	0.854	0.133	3.007
Built-up area (X142)	0.782	0.093	3.072
Number of books in public libraries (X151)	0.793	0.097	3.351
Number of beds in medical institutions (X152)	0.805	0.127	2.121
Actual amount of foreign investment used (X161)	0.791	0.118	2.054
Total import and export volume (X162)	0.786	0.097	2.378
Tourism foreign exchange income (X163)	0.722	0.083	2.733

. Among them, the number of permanent residents, built-up area, and amount of fixed asset investment are the three indicators with the highest priority weight, representing the scale and carrying the city’s capacity. Second, indicators such as economic and trade relations, transportation element relations, and cultural element relations represent the level of main urban functions and external functional relations with correspondingly high weights.

We used the above indicator system to conduct subitem calculations on the primary indicators of the central cities within the metropolitan area. Taking Nanjing as an example, we calculated the scores of 17 secondary indicator categories, with an urban primacy index score ranging from 1 to 5 points. We also conducted a horizontal comparison of the indicator values for three years (2017, 2020 and 2023). We used statistical yearbook data and entropy weight analyses to measure the primacy index and normalise the sub primacy index. The results are summarised in

Table 5. Ranking scores of sub items for Nanjing metropolitan area’s central cities in 2017, 2020, and 2023.

Primary Indicators	Secondary Indicators	Nanjing/Yangzhou
		2017	2020	2023
Economic element connection (X11)	Annual gross domestic product (X111)	1.2	1.2	1
	Fixed assets investment (X112)	4.4	1.4	1.3
	Trade exchange index (X113)	3.8	3	2.7
	Investment and financing index (X114)	2.5	2.4	2.1
	Subtotal	2.9	1.9	1.7
Cultural element connection (X12)	Number of academic conferences hosted annually (X121)	0.8	0.8	0.7
	Number of art exhibitions hosted annually (X122)	2.2	1.4	1.4
	Number of science and technology exhibitions hosted annually (X123)	3.6	2.3	2.3
	Subtotal	2.2	1.5	1.5
Transportation element connection (X13)	Number of daily high-speed rail trips (X131)	3.2	2.8	3.1
	Number of daily intercity bus trips (X132)	4.9	4.8	4.8
	Subtotal	3.4	3.5	3.4
Urban scale (X14)	Total population size (X141)	1.8	1.8	1.8
	Built-up area (X142)	4.3	3.1	2.8
	Subtotal	2.3	1.9	1.9
Health and libraries infrastructure (X15)	Number of books in public libraries (X151)	1.8	2.1	1.8
	Number of beds in medical institutions (X152)	5.3	3.1	3.4
	Subtotal	3.6	3.3	3.3
Foreign capital utilisation (X16)	Actual amount of foreign investment used (X161)	1.4	1.5	1.6
	Total import and export volume (X162)	5.7	0.9	1.5
	Tourism foreign exchange income (X163)	3	6.5	3.3
	Subtotal	3.6	3.4	3.1
Comprehensive primacy value		3.7	3.5	3.3

. As the core city of the metropolitan area, Nanjing’s comprehensive urban primacy index has been continuously decreasing over the past six years, from 3.7 in 2017 to 3.3 in 2023, indicating that the radiation impact of the central city on the surrounding areas has weakened. In addition, the urban primacy index of economic factor linkage has also decreased from 2.9 in 2017 to 1.7 in 2023, marking a significant decline in the scale of trade exchanges and investment and financing between Nanjing and surrounding cities. The urban primacy index of cultural element connections showed no significant fluctuations over the six-year period, maintaining at approximately 3.4 points. As a resource centre in the political, economic, and cultural dimensions of the region, Nanjing has an absolute advantage in the configuration of large venues and facilities. The corresponding number and scale of events such as academic conferences, art exhibitions, and science and technology exhibitions also demonstrate obvious advantages [33].

3.2. The Comprehensive Primary Index Ranking Score Presents the Spatial Structure of “One Core, Multiple Centres”

We measured the comprehensive primacy index of eight major cities within the metropolitan area using the above method and normalised the scoring dimension. We sorted the comprehensive first-place index of each city in 2017, 2020, and 2023, and the results are shown in

Table 6. Ranking of top cities in the Nanjing metropolitan area in 2017, 2020, and 2023.

Rank	City List	Comprehensive Primacy Value (2017)	City List	Comprehensive Primacy Value (2020)	City List	Comprehensive Primacy Value (2023)
1	Nanjing	0.956	Nanjing	0.931	Nanjing	0.937
2	Wuhu	0.916	Yangzhou	0.908	Yangzhou	0.915
3	Huai’an	0.893	Wuhu	0.875	Wuhu	0.897
4	Zhenjiang	0.721	Xuancheng	0.839	Chuzhou	0.879
5	Ma’anshan	0.738	Zhenjiang	0.812	Huai’an	0.831
6	Chuzhou	0.702	Huai’an	0.773	Zhenjiang	0.779
7	Yanghzou	0.682	Ma’anshan	0.708	Ma’anshan	0.754
8	Xuancheng	0.677	Chuzhou	0.684	Xuancheng	0.662

. As the capital city of Jiangsu Province, Nanjing consistently ranks first in terms of social and economic factors. The comprehensive first-degree indices for the three years were 0.956, 0.931, and 0.937, respectively. Although the first-degree score decreased slightly, it consistently ranked first in metropolitan areas. As a national historical and cultural city, Yangzhou has a leading level of social and economic development in the region and has long ranked second in terms of urban agglomeration. Except for the first two rankings, the priority ranking of subsequent cities shows a fluctuating trend over time, which is consistent with various city attributes and socioeconomic development stages.

We conducted a spatial mapping of the primary ranking indicators of major cities within the metropolitan area in 2017, 2020, and 2023. The 2017 data suggested the metropolitan area is centred around Nanjing, including the sub-regional centres of Wuhu and Huai’an. The Wuhu subregion includes several cities such as Wuhu, Ma’anshan, Xuancheng, and Chuzhou. The Huai’an sub-region includes the entire Huai’an region and some areas in the northern part of Yangzhou, and the urban primacy index pattern of the urban agglomeration presents a “multi core” distribution feature. However, with the acceleration of Nanjing’s urbanisation, the resources of the cities surrounding Nanjing are constantly gathered towards the central city. Compared to the data from 2020, the top three cities with the highest ranking within the metropolitan area are more clustered, exhibiting a typical “single core” distribution characteristic. With the continuous strengthening of urban and external functional connections in Nanjing, its status as a regional city centre has significantly improved. In 2023, the spatial characteristics have emerged, with Chuzhou, Yangzhou, and Wuhu as sub-centres, and the Nanjing metropolitan area has gradually shown an urban primacy index spatial distribution pattern of “one main and multiple sub centres” (Figure 2).

Through the analysis of the superior and inferior distance method, the results indicate that the Nanjing metropolitan area presents a spatial characteristic of “one core and three centres”, which can be used to construct a regional cluster with Nanjing as the core city and Chuzhou, Yangzhou, and Wuhu as the sub-centre cities (Figure 3). The metropolitan area is centred on Chuzhou as a sub-regional city, connecting the northern region of Anhui to the west. Taking Wuhu as the sub-regional central city, it connects the southern regions of Anhui, such as Ma’anshan and Xuancheng Cities, to the west. Taking Yangzhou as the sub-regional centre city, it has a northward functional connection with northern Jiangsu areas such as Huai’an and Suqian. This is similar to existing research results, which have found that the geographical spatial pattern and element distribution of the Nanjing metropolitan area generally exhibit a “one core, multiple poles” characteristic [21,25,30].

3.3. The Element Connections between the Central City and Surrounding Cities Exhibit Spatiotemporal Heterogeneity Characteristics

We spatially mapped indicators such as economic, transportation, and cultural element connections among cities within the metropolitan area, as shown in Figure 4. The overall spatial pattern conforms to “one core, multiple centres, and multiple areas”. Among these, “one core” refers to the scope of Nanjing City. As the capital city of Jiangsu Province, Nanjing has significant advantages in public services, regional transportation, financial trade, cultural tourism, and other aspects in terms of level and quantity. “Multiple centres” refer to areas around Nanjing, including Yangzhou City in the northeast and some parts of Chuzhou City in the west. These areas have relative advantages in terms of economy, culture, and transportation, which can drive functional complementarity and element connections between cities in surrounding subregions. In addition, cities along the Yangtze River had a relatively high degree of primacy. As an important waterway transportation channel, the Yangtze River facilitates convenient, inexpensive, and efficient transportation of resource elements in cities along the route. “Multiple districts” refer to the secondary areas on the east, west, and south sides of Nanjing, where the elements are relatively closely connected. The connections between cities within the region are closer than those outside the region, and the central city serves as a hub to drive the connections between cities within the region.

3.4. The Endogenous Mechanism of the Comprehensive Primacy Distribution Patterns of Metropolitan Areas

The VAR model is a commonly used econometric model [22]. The VAR model regresses several lagged variables for all variables using all current variables in the model. The VAR model is suitable for stationary multi-time series data, such as the E-G cointegration test and the error correction model (ECM) for single equations. For non-stationary multi-time series data, Johansen cointegration and vector error correction models (VECM) can also be established. We constructed a Vector Autoregressive (VAR) analysis model and stationarity tests on the indicator variables used in this paper. The model follows the LLC criterion; sets the lag order of the VAR model to two; measures evaluation statistics such as AIC, SC, and LR; uses Johansen’s method for cointegration testing. The trajectory statistics and maximum eigenvalue test values in

Table 7. The co-integration test of the VAR model for inter-city factor connections.

Vector	Null Hypothesis	Eigenvalues	Trajectory Statistics	5% Critical Value	p-Value
Annual gross domestic product (X111)	None	0.398	10.355	15.494	0.07 *
	Atmost 1	0.204	3.191	3.861	0.05 **
Fixed assets investment (X112)	None	0.357	8.371	15.431	0.01 ***
	Atmost 1	0.142	2.137	2.987	0.72
Trade exchange index (X113)	None	0.317	8.632	16.175	0.26
	Atmost 1	0.148	2.089	3.177	0.05 **
Investment and financing index (X114)	None	0.377	9.128	14.977	0.24
	Atmost 1	0.158	3.145	2.989	0.06 *
Number of academic conferences hosted annually (X121)	None	0.357	7.362	13.498	0.31
	Atmost 1	0.187	2.563	2.732	0.07 *
Number of art exhibitions hosted annually (X122)	None	0.318	8.277	14.956	0.23
	Atmost 1	0.139	2.361	2.787	0.05 **
Number of science and technology exhibitions hosted annually (X123)	None	0.372	8.101	15.304	0.27
	Atmost 1	0.144	2.312	2.733	0.03 **
Number of daily high-speed rail trips (X131)	None	0.357	7.362	13.498	0.31
	Atmost 1	0.187	2.563	2.732	0.07 *
Number of daily intercity bus trips (X132)	None	0.318	8.277	14.956	0.23
	Atmost 1	0.139	2.361	2.787	0.05 **

Note: The smaller the p-value, the lower the probability of the original hypothesis occurring. According to the principle of small probability, we have reason to reject the original hypothesis. *** represents p < 0.01, ** represents p < 0.05 and * represents p < 0.1.

indicate that the six sets of urban element connection vectors we set did not pass the cointegration test, and there was no cointegration relationship. Thus, they are unsuitable for constructing a modified VECM. Meanwhile, all first-order differential sequences passed the cointegration tests; therefore, they were more appropriate for constructing a VAR model for the first-order differential.

We further conducted unit root tests on various indicators of the VAR model, and the test results are presented in

Table 8. The unit root test of comprehensive primacy index for each city.

Vector	Original Sequence Test (α = 0.05)			First Order Difference Test (α = 0.05)
	ADF-Value	p-Value	State	ADF-Value	p-Value	State
Annual gross domestic product (X111)	−3.071	0.054	Non-stationary	−6.327	0.001	Stationary
Fixed assets investment (X112)	−2.437	0.156	Non-stationary	−4.237	0.006	Stationary
Trade exchange index (X113)	−1.551	0.481	Non-stationary	−3.812	0.015	Stationary
Investment and financing index (X114)	−1.939	0.305	Non-stationary	−4.092	0.012	Stationary
Number of academic conferences hosted annually (X121)	−3.081	0.056	Non-stationary	−6.912	0.001	Stationary
Number of art exhibitions hosted annually (X122)	−2.381	0.156	Non-stationary	−5.789	0.001	Stationary
Number of science and technology exhibitions hosted annually (X123)	−2.791	0.237	Non-stationary	−3.782	0.001	Stationary
Number of daily high-speed rail trips (X131)	−2.636	0.182	Non-stationary	−4.072	0.001	Stationary
Number of daily intercity bus trips (X132)	−2.791	0.237	Non-stationary	−3.782	0.001	Stationary

Note: The ADF value refers to the results of the Augmented Dickey–Fuller (ADF) test. This method is used to test whether time-series data have unit roots, and it is commonly used to detect the stationarity of data.

. The original sequence index was non-stationary, but it passed the integration test. The various indicators of the first-order differential variables were stationary sequences, and the model results verify the rationality of constructing a first-order differential VAR model.

This study used geospatial regression analysis methods to conduct factor and interaction detection to identify the mechanisms by which each indicator element affects the comprehensive primacy of the central city. From the perspective of urban functional positioning and external factors, the indicators of economic, cultural, and transportation factors are interrelated and mutually reinforced, forming a unified entity with internal connections. We adopted the Jenks natural best breakpoint classification method to stratify and classify the ten secondary indicators in these three aspects, transforming them from numerical to type variables [42]. We took the comprehensive primacy of the city as the dependent variable and the indicators of economic, cultural, and transportation factors as independent variables. We conducted factor and interaction detection through a geographic spatial regression analysis; the results are shown in

Table 9. Detection results of the interaction between various indicator factors of urban primacy.

	X111	X112	X113	X114	X121	X122	X123	X131	X132	X133
X112	0.7318 ***
X113	0.7697	0.5264 **
X114	0.7725	0.6924	0.5417 ***
X121	0.7592	0.6332	0.6159	0.1660 **
X122	0.7704	0.6601	0.6418	0.3772	0.2616
X123	0.7710	0.6230	0.6831	0.4413	0.4777	0.2266 *
X131	0.7672	0.5908	0.6795	0.4862	0.4629	0.4967	0.3824
X132	0.7755	0.6379	0.5759	0.3747	0.4545	0.4836	0.5824	0.2531 *
X133	0.7963	0.7023	0.6983	0.6933	0.7067	0.7360	0.6888	0.6726	0.6440 ***	/

Note: Values on the diagonal in the table represent the single-factor q value and significance, where * p < 0.1, ** p < 0.05, and *** p < 0.01. Bold numbers indicate nonlinear enhancement, where the interaction q value between two factors was greater than the sum of the q values of the two factors. All other indicators show a dual-factor enhancement, where the interaction q value of the two factors is greater than the larger value of the two factors but less than the sum of the q values of the two factors.

.

The factor detection results showed that economic, cultural, and transportation factors had a significant impact on the comprehensive urban primacy index, and all secondary indicators passed the significance test. Among them, the number of daily high-speed rail trips, number of academic conferences held, and trade exchange index have the strongest impacts, whereas the number of books collected by the library, investment and financing index, annual GDP, fixed assets investment, and other indicators have a weak impact on comprehensive primacy. Interaction detection results showed that the impact of all influencing factors after the interaction was stronger than that of single factors, which manifested as dual-factor and nonlinear enhancement. The interactions among economic, cultural, and transportation factors jointly promoted urban primacy. The interaction between the economic and transportation factors was relatively high, and the nonlinear correlation effect between these two indicators was the most significant in the model. This conclusion is similar to that of existing research, which suggests that economic and cultural factors are influenced by regional transportation infrastructure. In terms of reflecting the comprehensive priorities of cities, these three indicators have significant cross-correlation [43].

4. Discussion

4.1. The Comprehensive Primacy Index Reflects the Diversity of Functional Attributes in Large Cities

The current spatial structure of the Nanjing metropolitan area exhibits the overall characteristics of single-core-driven and polarised development, with an insufficient sub-centre-level scale. The analysis of the centrality of the factor flow network shows that the Nanjing metropolitan area presents an urban hierarchical system with Nanjing as the absolute core, whereas the sub-centres represented by Wuhu and Yangzhou still exhibit a significant gap with the development of Nanjing (Figure 5). From the trend of changes in Nanjing’s urban primacy index score data over the years, the indicators of the cultural element connection between the urban primacy and the public service urban primacy index were relatively stable. Although the scores decreased, the magnitude of the change was relatively small.

The urban primacy index of economic ties exhibited a significant downward trend, indicating that Nanjing’s foreign economic and trade ties are gradually weakening. Compared with existing research, some scholars believe there is a difference between broad and narrow economic factor connections. The narrow concept of economic connection measurement indicators is represented by the ratio of the total economic output of two cities, whereas the broad concept of economic indicators reflects the comprehensive strength of economic development [44]. Scholars have analysed the impact of investment and consumption on Italy’s economic growth [45], and some scholars have studied the primacy of Jinan’s urban economy with indicators such as city size and fixed asset investment [46]. In recent years, the primary indicators of urban scale and volume have shown a slow decline, followed by stable development.

In recent years, the primary indicators of urban scale and volume have shown a slow decline, followed by stable development. The urbanisation rate in Nanjing increased from 62% in 2017 to 87% in 2023. Urbanisation has entered the middle and later stages, and the urban scale is becoming increasingly stable. The overall size of a city is expressed as the stage of urban development and degree of urbanisation based on its population and land use, which is also an important measurement indicator of the urban primacy index. Some scholars believe that during the rapid urbanisation process, the distribution of urban size is highly concentrated, mainly reflected in the primacy of cities [47]. Scholars have also used the populations and built-up area sizes of each urban area to reflect the primacy of urban size and have achieved relatively accurate measurement results [48]. The connection between cultural elements reflects the functional radiation and driving effect of the cultural resources of a city on surrounding cities. Scholars have studied the importance of industrial development from the perspective of structure and efficiency. Using the spatial panel Durbin model, they verified that urban primacy positively promotes economic growth and cultural industry development [49]. Research has found that the development of cultural industries has an explanatory power of 88.5% for Shanghai’s economic growth, and cultural resource elements can effectively drive economic and trade connections between cities [50].

4.2. High-Level Cultural Facilities Can Effectively Drive the Flow of Urban Agglomeration Elements into the Central City

From the perspective of cultural connections, the number of academic conferences, art exhibitions, and science and technology exhibitions hosted are the most important indicators. From 2017 to 2023, the average scores of these three primary indicators in Nanjing were 3.2, 4.1, and 3.5, respectively, which was far higher than those of other cities in the urban agglomeration. This indicates that large cultural and artistic venues, science and technology exhibition halls, and other resources in the Nanjing metropolitan area were mainly concentrated in the central city, and resource allocation in surrounding cities was insufficient. The connection of cultural elements reflects a city’s ability to drive external functions, such as culture, technology, and innovation. It is a concrete manifestation of its competitiveness.

Some studies suggest that the level of technological and cultural development in central cities can enhance the innovation capabilities of surrounding cities. Scholars have analysed the scientific and technological levels of each urban area in the metropolitan area and the urban primacy index of research and technological talent among practitioners. They measured the urban primacy index of urban scientific and technological innovation in Jinan from the indicator of invention patent ownership [51], and then measured the comprehensive impact of indicators such as urban scientific research expenditure, patent authorisation, and the number of students in university research institutes on urban innovation capacity [52].

We suggest that the Nanjing metropolitan area needs to improve the construction mechanism for scientific and technological talent, continuously increase scientific research investment, and attract domestic and foreign venture capital funds to join scientific research. Nanjing can utilise the R&D advantages of universities, research institutes, and research and experimental development funds to enhance its attractiveness for scientific and technological talent. At the same time, the peripheral cities of Ma’ anshan, Xuancheng, and Chuzhou in the metropolitan area should be guided to establish teaching and research branches for higher schools in Nanjing within the scope of policy permission. The establishment of branch offices of research institutes in Jintan, Changzhou, Liyang, Xuancheng, and Chuzhou, where research institutes are located in Nanjing, should also be encouraged. Investments in research and development funds should be increased, and the leading and driving role of Nanjing’s central city in scientific and technological innovation should be explored, while independent innovation capabilities are enhanced [53].

In Figure 6, the large circle represents the central city of the metropolitan area, the middle circle represents the potential secondary central cities within the region, and the small circle represents general small towns. Starting from the central city, taking a certain radius direction and following a simple distance attenuation rule, we drew a graph of the relationship between the influence of urban agglomerations and their spatial scope. Due to the emergence of secondary centres, the influence of urban agglomerations has rebounded far from the central city. In the same external environment, urban agglomerations with multicentre networked structures have a larger spatial range of functional radiation.

The construction and improvement of transportation infrastructure can promote regional economic development, enhance regional accessibility, reduce transportation costs, attract investment and talent, and enhance regional economic competitiveness. For example, the construction of highways can save time costs in personnel and goods transportation, reduce trade costs, and promote productivity improvement in service and manufacturing enterprises. Meanwhile, the level of regional economic development can affect the construction and improvement of transportation infrastructure. Regions with faster economic development usually have stronger financial and technological capabilities to invest in transportation projects, thereby improving the level and efficiency of transportation services. In addition, regional culture is an important component of coordinated economic and social development, which can influence people’s values, behavior patterns, and consumption habits, thereby having an impact on economic development. Therefore, regional cooperation is an important aspect of economic connections between different regions, which helps to break down barriers to the flow of production factors between regions, promote the optimal allocation of factors, and promote the realisation of regional coordinated development and spatial integration.

4.3. Positive Fiscal Policies Can Effectively Promote the Cities’ Industrial Divisions within the Metropolitan Area

From 2017 to 2023, there was a significant decline in indicators, such as the trade volume index, investment and financing index, and total import and export volumes in Nanjing. This indicator first changed from high to low. The results indicate that Nanjing City does not yet have an agglomeration capacity in terms of regional economics and trade, and the metropolitan area’s industrial structure and system are relatively balanced. In addition, the primacy index of fixed asset investment has remained at approximately 4.8 points for a long time, indicating Nanjing has a strong ability to gather fixed assets, such as real estate, that far exceeds that of other surrounding cities. The urban scale of Nanjing in 2023 was 1.8 trillion yuan, and the huge urban economic volume required Nanjing to build an industrial system with complementary functions and reasonable division of labour with surrounding cities. As a regional central city, Nanjing should optimise its tertiary industrial structure, gather innovative resources and high-end industrial chains, gradually withdraw from traditional manufacturing, and strengthen the layout of high-value-added industries such as innovative, financial, and cultural services [54].

In addition, studies have pointed out that the financial policies of various cities within the metropolitan area should be coordinated, and investment scales in major regional infrastructure projects and livelihood development projects should be actively carried out to continue enhancing Nanjing’s central city function [55]. Other cities within the metropolitan area must seize their own resource endowment characteristics, gradually improve their social security system, increase resident income, regulate market order, create a good consumption environment, guide the diffusion and inflow of high-end consumption demand in Nanjing to surrounding cities, and drive the rational division of labour and cooperation among cities [50]. In addition, there are functional connections between cities at different levels within the metropolitan area, and the functional radiation ranges of the central and sub-central cities overlap with each other, forming a “core edge” spatial connection classification area. From Figure 7, as the scale of subcentral cities in urban agglomerations continues to increase, their functional radiation range also expands, thus compressing the functional scope of the central cities. The peripheral areas of urban agglomerations are more susceptible to the elemental connections of the subcentral regions, and the entire urban agglomeration ultimately forms a networked hierarchical spatial structure.

4.4. The Well-Developed Transportation Network Can Effectively Enhance the Connectivity of Elements between Cities within the Metropolitan Area

The level of health and libraries infrastructures reflects the configuration and service capacity of urban health and libraries infrastructure facilities, as well as the comprehensive impact on the population demand of surrounding cities. Scholars have used indicators such as the number of beds in health institutions and the collection of public libraries to calculate the first-place index of health and libraries infrastructure s in Jiaxing City [37], whereas others have studied the first-place index of health and libraries infrastructure s in Zhengzhou City [54] using the medical service and social security indices. The measurement results are consistent with the actual development-level ranking of the region. It is suggested that further strengthening the regional transportation network can help improve the accessibility of basic health and libraries infrastructure resources within the metropolitan area, enhance the efficiency of the flow of health and libraries infrastructure elements between core and surrounding cities within the metropolitan area, and promote the integration of basic public services and social security.

The daily number of high-speed rail trips, intercity bus trips, and intercity subway connectivity reflects the degree of closeness between the city and the outside world. The external transportation factor connectivity index of Nanjing City is at a regional average level, with a range of 3.1 to 3.6, showing a fluctuating downward trend. As a port city along the Yangtze River and a regional transportation hub, Nanjing should strengthen its transportation infrastructure and continuously enhance its ability to provide external transportation services. Nanjing’s urban opening-up indicators are constantly weakening, and it is necessary to leverage regional transportation networks to expand cooperation and connections between Nanjing and surrounding cities. Moreover, improvement of indicators such as foreign investment volume, actual scale of foreign investment use, total import and export volume, and tourism foreign exchange income through regional transportation networks should be developed. Previous studies conducted research analyses from the above four aspects and obtained conclusions consistent with the results of this study, confirming the correlation between the indicators and the rationality of the results [52].

We further explored the specific factors that led to the emergence of this trend. Various cities within the Nanjing metropolitan area are continuously strengthening industrial cooperation and emphasising the coordinated promotion of strong and complementary industrial chains. The industrial structure of the metropolitan area has been adjusted from 5.2:44.8:50.0 in 2016 to 4.3:43.6:52.1 in 2021, showing the characteristics of industrial and service industries jointly driving regional development. Especially since 2016, the construction of the transportation network in the Nanjing metropolitan area has accelerated, resulting in a denser regional transportation network and more optimised transportation modes. The “1 h transportation circle” within the metropolitan area has been basically formed, and Nanjing has achieved closer transportation connections with surrounding cities. The gradual optimisation and improvement of industrial structure and transportation infrastructure have further enhanced the overall development level of surrounding cities near Nanjing.

The specific measures to improve the overall competitiveness of the Nanjing metropolitan area include the following aspects: firstly, accelerating the construction of a rail transit system, creating a “one-day living circle” and a “one hour commuting circle” in the metropolitan area, optimising the railway trunk network, promoting the construction of intercity railways and suburban railways, and forming a “meter” shaped high-speed railway network centred on Nanjing. Secondly, the region will jointly build a modern industrial system, focusing on manufacturing industry landmarks such as new energy vehicles, new displays, smart grids, and biomedicine and promoting the high-end and branded development of traditional industries. In addition, we will strengthen the radiation spillover effect of Nanjing as a globally influential innovative city and create an open and cooperative urban innovation system. Finally, promote regional collaboration in the fields of healthcare, education, culture, and tourism and build an integrated basic public service system.

5. Conclusions

5.1. Key Findings

This study aims at regional collaborative development and constructs a comprehensive evaluation index system for the primacy of central cities from the perspective of regional factor flow space, quantitatively measuring the level of intercity factor connections. This study breaks through the existing administrative division governance pattern of urban agglomerations, combines the evaluation of urban primacy with the optimisation of the urban agglomeration structure, proposes a regional collaborative governance model supported by elements such as economic connections, resource sharing, and project co-construction, as well as corresponding regional development strategies. This study used factor flow and geographic spatial regression analyses to quantitatively measure and spatially map the primary indicators of urban sub-items and obtained the following results:

(1) Nanjing has long ranked first in the comprehensive ranking; however, its score has shown a fluctuating downward trend, dropping from 0.956 in 2017 to 0.937 in 2023. The results indicate that the comprehensive level of Nanjing, as the central city of the metropolitan area, is constantly weakening, and its functional driving effect on the peripheral areas is also significantly weakened.

(2) The comprehensive urban primacy index spatial structure of cities within the metropolitan area presents a network hierarchical development feature of “one core, multiple centres, and multiple areas”. The regional urban system structure is gradually taking shape, with Nanjing as the regional core city; Chuzhou (0.879), Yangzhou (0.915), and Wuhu (0.897) as sub-central cities; and other cities as sub-regional functional nodes.

(3) From the perspective of the urban sub-item primacy score, the indicators of economic (0.166 **), cultural (0.226 **), and transportation element connection (0.644 ***) are interrelated and mutually reinforcing, forming a unified entity with internal connections, thus jointly promoting the improvement of urban comprehensive primacy.

5.2. Implications

With the continuous advancement of regional integration, relationships between cities have shifted from traditional hierarchical structures to emerging spatial networks. Multi-core and networked regional spatial structures have become a development trend in future regional urbanisation. Supported by the stream space theory and big data, there have been many in-depth studies on the spatial structure of regional networks; however, there is relatively little research on the spatial scope of regions based on the network space structure. Research has been conducted on the spatial scope of urban agglomerations based on an analysis of network spatial structures, mainly using spatial and social network analysis methods [55]. The former mainly conducts network feature analysis from the perspective of physical transportation networks [42], whereas the latter studies the “spatial structure relationship” between cities [41], evaluating the level of urban systems through the strength of element connections between different cities [52].

Overall, there is relatively little research on this paradigm, partly because the flow data of empirical network analysis are often difficult to obtain [49], and partly because the influence between cities under the network correlation structure can have cross effects. The multiple interactions and superposition of influences between cities weaken the constraints of administrative boundaries in space. This study is based on an analysis of the evolution process, mechanism, and effects of the spatial connection pattern between the core and edge areas of urban agglomerations. Further, it explores the evolution mechanism of this type of heterogeneous spatial unit. This is an extension and expansion of the theory of regional spatial interactions and core edges and, thus, a beneficial innovative exploration. This study uses the flow space analysis and geographic spatial regression models, as well as various research techniques and methods, such as geography and spatial economics, to comprehensively analyse the effect mechanism of the interaction of various urban elements. The “flow space” big data is combined with traditional mathematical models to comprehensively measure the strength of spatial economic connections, with a certain degree of integrated innovation.

5.3. Limitations and Future Research Directions

The indicator system constructed in this study may have subjective expert biases, and the indicator weights determined using the subjective entropy weight method may be limited by the limitations of the research sample. Due to the limited availability of data, the city primacy evaluation index system set in this study needs to be improved. In future research, we will improve the evaluation index system for comprehensive primacy of the Nanjing metropolitan area. Specific index content can be further improved, and quantitative methods can be used to measure sub-item primacy in the future to enhance the reasonability of the research results. In addition, this study did not clearly distinguish between similar concepts, such as the primacy index and effect. In the future, relevant theories, such as comprehensive urban competitiveness and regional integration, should be combined to systematically construct a conceptual system for the comprehensive primacy of urban agglomerations on a regional scale.

Existing studies generally use linear interpolation as a substitute for data that has not been obtained in practice, which weakens the authenticity of the data to a certain extent. In future research, accurate first-hand data can be obtained by requesting government data disclosure or other means. Meanwhile, in the next step of the research, we can incorporate vector data, such as housing prices and population density distribution, to conduct spatial analysis, rather than simply using macro statistical data for rough regression. In future research, we will expand the timescale and refine the indicator-scale range.

We further compared and analysed the development models and paths of different types of urban fringe areas to obtain more realistic spatial distribution patterns and provide a more accurate reference for the formulation of spatial optimisation development policies. The next research focus will be on further enriching the indicator system of urban agglomerations and exploring more reasonable research methods. We will focus on building an integrated innovative development mechanism that breaks the traditional administrative governance model. We will take urban agglomerations as the starting point, strengthen the connection of spatial elements, and achieve coordinated development of the regional economy.