WANG Hao; ZHANG Xiaoyuan; ZHANG Xiaoyu; LIU Ruowen; NING Xiaogang

doi:10.1007/s11442-024-2237-8

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地理学报(英文版) ›› 2024, Vol. 34 ›› Issue (5) : 1007-1036. DOI: 10.1007/s11442-024-2237-8

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Understanding coordinated development through spatial structure and network robustness: A case study of the Beijing-Tianjin-Hebei region

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Abstract

In the context of accelerated globalization, intercity factor flows are becoming increasingly dependent on a reasonable and orderly spatial structure. Therefore, an in-depth study of the optimization and adjustment of spatial structure is essential for coordinated development. This study quantitatively evaluated urban development levels and introduced network analysis methods to analyse the spatial structure and robustness of development. The results indicated the following: (1) The urban development level in the Beijing-Tianjin- Hebei (BTH) region increased in all dimensions, and the transmission efficiency significantly improved. (2) The spatial structure of the BTH region has been relatively stable, as illustrated by the main pattern of the spatial distribution of central cities, with a trend towards contiguous development. (3) The ranking of network robustness is environment>society>economy, and the core network and key nodes are primarily located within the radiation of the three central cities of Beijing, Tianjin, and Shijiazhuang. (4) The coordinated development of the BTH region is effective but still needs to be optimized and adjusted, and the strategic significance of edge cities has not been completely exploited. This study aims to provide an emerging analytical perspective for optimizing regional spatial structure and promoting regional coordinated development.

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urban network / spatial structure / network robustness / coordinated development / Beijing-Tianjin- Hebei (BTH) region

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WANG Hao, ZHANG Xiaoyuan, ZHANG Xiaoyu, LIU Ruowen, NING Xiaogang. [J]. Journal of Geographical Sciences, 2024, 34(5): 1007-1036 https://doi.org/10.1007/s11442-024-2237-8

WANG Hao, ZHANG Xiaoyuan, ZHANG Xiaoyu, LIU Ruowen, NING Xiaogang. Understanding coordinated development through spatial structure and network robustness: A case study of the Beijing-Tianjin-Hebei region[J]. Journal of Geographical Sciences, 2024, 34(5): 1007-1036 https://doi.org/10.1007/s11442-024-2237-8

1 Introduction

The rapid economic, technological, and information changes under the impact of globalization have led to the global urbanization of cities at an unprecedented scale and speed (Antrop, 2004). Under this rapid urbanization process, the intersection of economy, demography, labour market, and transportation facilities (Zou et al., 2019; Huang et al., 2020; Zhu et al., 2022) has given rise to the spatial polarization effect of urban development. Human-land conflicts (Adam et al., 2015; Ma et al., 2020), uneven economic development (Xu and Jiao, 2021) and ecological degradation (McDonald et al., 2011) occur frequently, and regional development inequalities are exacerbated by differences in development levels between regions (Hao and Wei, 2010; Liao and Wei, 2012; Li et al., 2022). As the process of globalization and the development of regional integration continue to advance, transportation infrastructure and information technology have reinforced intercity connections, which have become more complicated and diverse. Cooperative intraregional development is more vital than ever to counteract the disadvantages of globalization and achieve sustainable development (Hirschi, 2010). Revisiting the relationships and linkages among regional cities to promote integrated development by regulating and guiding the relationships of urban spatial interactions (Frank and Hua, 1981; Shen, 2002) is crucial for promoting current urban and regional development (Liu et al., 2020).

Coordinated development is in line with the current development trend and concept of regional integration and mainly emphasizes the relationships and degrees of connections between cities. It has become the prominent manifestation of regional development by promoting the joint development of multiple elements and valuing subsystems’ cooperation and mutually beneficial coexistence. Unlike the harmonious development proposed for addressing intraregional differences and achieving regional averages, coordinated development is proposed to solve the problems of regional connectivity and cooperation mechanisms, such as market fragmentation, and block the free flow of factors to achieve overall regional connectivity, synergy, and competitiveness. Therefore, many countries and regions have identified coordinated development as the basis for achieving sustainable social development.

The transformation from a disorderly structure to an ordered structure within a region constitutes one of the fundamental elements of collaborative development. Thus, the primary mission of overcoming the imbalance of regional development is to optimize the spatial layout structure of the region. The continual optimization of regional spatial structure is conducive to the best allocation of resources and the mutual benefit of cities in a region, so spatial structure has become an essential characteristic and premise for supporting coordinated development.

As economic globalization and information technology continue to advance, the space of flows gradually replaces the space of places as the dominant paradigm and vital structure of urban systems (Castells, 1996), modern society is deeply integrated with cyberspace (Xie and Wang, 2023). The definition of “region” has transitioned from “territorial scope” to “borderless and relational” (Amin, 2004), which has resulted in greater attention being given to intercity connectivity and mobility. In this context, the openness and networked character of regions have been gradually emerging, and the complex network of intercity connections and factor flows has become an essential aspect of the regional spatial structure (Parr, 2004; Wang et al., 2022); this coincides with the concept of coordinated development, which emphasizes intercity spatial connections.

Rapid urbanization in the BTH region has also contributed to an imbalance in intraregional development (Hu et al., 2017; Han et al., 2021). The high concentration of factors within the region has led to an imbalance in the scale system of urban agglomeration, and the number and scale of internal large and medium-sized cities remain small (Wang et al., 2019). The polarization effect of Beijing and Tianjin has led to a continuous outflow of population, resources, and capital from Hebei Province, and the development goals and directions of small cities are unclear (Zhen et al., 2019). Cities anticipate resolving common issues via synergistic development and establishing a close synergistic cooperation mechanism to achieve mutual benefit and a win‒win situation (Fang, 2017). In 2015, the Outline of Coordinated Development of the Beijing-Tianjin-Hebei Region was introduced to decongest noncapital core functions, adjust regional economic and spatial structures, and achieve intensive internal development. Nevertheless, the severe polarization of internal development levels and the disparity of comprehensive strength have exerted intolerable pressure on the coordinated development of Beijing, Tianjin, and Hebei, and the problems of imbalance in the structure of the urban system, insufficient flow of factors and resources, and weak policy effects persist. In this scenario, ways in which to improve the collaboration and interaction between cities by optimizing the spatial structure and reasonably allocating factor resources has become the critical breakthrough for advancing coordinated development.

2 Literature review

Coordinated development is characterized by the ability of cities to break through the boundaries of administrative divisions and develop regional competitiveness with complementary advantages to achieve joint regional development (Ye et al., 2019). Currently, the assessment of coordinated development is mainly focused on the coupled and coordinated evaluation of the social, economic, and environmental dimensions of cities in a region and explores the issue of development discrepancies at varying development levels (Cui et al., 2019; Li and Yi, 2020; Fang et al., 2021; Han et al., 2021; Wang, 2022). This approach can be used to identify and solve the problems and deficiencies in the existing regional development process but is relatively weak in exploring the factors that hinder the further advancement of synergistic development at a deeper level. Thus, this approach cannot meet the urgent needs of the current coordinated development situation.

Spatial structure refers to the spatial form that is generated by the interaction of numerous elements within a regional space. A logical and orderly urban spatial structure can serve as the platform and carrier for optimizing regional resources, spatial allocation, and high-quality, coordinated economic development. As a direct representation of internal urban spatial connections, this structure depicts how cities are organized in terms of scale, function, and location inside a specific region (Anas et al., 1998; Bertaud, 2004) and can be used to gauge regional stability and development levels. Examining regional spatial structure is tremendously valuable for effectively constraining dominant functions, promoting the proper and orderly flow of factors, and achieving coordinated development.

Following the principle that “understanding urban space implies knowing flows and networks” (Batty, 2013), people have steadily transformed their perspectives to address spatial structure-related issues in coordinated development. The positive interaction of economic, transportation, and information elements among cities has spawned the regional network coordinated development model, which has shifted the study of urban spatial structure to a networked, dynamic, and polycentric urban system and gradually replaced the hierarchy of central places as the primary form of intercity linkage (Castells, 2010). The urban network approach begins with a search for intercity linkages to reveal the spatial configuration of urban networks (Zhang et al., 2021), emphasizing the importance of the structural dominance of cities in contemporary global and regional systems (Meijers, 2005; Meijers, 2007), and can clearly and accurately reflect the complicated relationships of subsystems within regions.

As horizontal, non-hierarchical systems composed of cities with either complementary/vertical or synergistic/cooperative interrelationships (Camagni et al., 1994), urban networks always have a structure that determines their function (Strogatz, 2001). For many years, scholars have researched urban functions (Zhen et al., 2019; Fang et al., 2020; Feng et al., 2022; Wei et al., 2022), spatial structures (Zhang et al., 2020; Liu et al., 2021; Yang et al., 2022; Song et al., 2023), and network evolution mechanisms (Li et al., 2019; Li et al., 2020; Zhang et al., 2022a; He et al., 2023) based on intercity linkages from various perspectives (Wall and Van der Knaap, 2011; Lao et al., 2016; Chong and Pan, 2020; Zhang et al., 2021; Ma et al., 2023) but have neglected to investigate the robustness of network structures within a region. Although cities in the same region share similarities, subjective and objective factors, such as geographic location and policy guidance, cause disparities in the development level and scale of cities within the region. Due to their comprehensive strength and development scale, central cities play a radiation-driven role in guiding the development of neighbouring cities. However, the massive disparity in development levels causes small and medium-sized cities to both assume the “siphoning effect” of central cities and passively accept the factor resources they cannot fully utilize, which makes the overall network inclined towards centralization. The “pathological” expansion of the overall network threatens the stability of intercity connections. To promote the stable and coordinated development of a region, it is essential to evaluate the robustness of the urban network structure, diagnose structural weaknesses, adjust the network structure, and optimize regional resource allocation.

Furthermore, from the perspective of network theory, cities are nodes and hubs that are nested in hierarchical networks in which information, capital, and people flow continuously to reconstruct the hierarchy (Castells, 1996; Castells and Cardoso, 2006), and cities occupy distinct positions in various networks (Sigler and Martinus, 2017; Wei et al., 2022). Previous studies have primarily focused on central cities and stressed their preeminent role in coordinated development. However, cities with lower population and economic scales also have essential positions in a region’s coordinated development due to some notable urban functions. In the coordinated development process, the imbalance caused by the polarization effect of central cities should be avoided as much as possible. The timely decentralization of some of their functions facilitates the development of noncentral cities. Therefore, clarifying the location and function of noncentral cities in overall regional development is theoretically important. In addition, as a complex system, multidimensional network linkage measurement can be used to avoid the subjectivity and variability of a single dimension, and the geographic scope and spatial structure of city networks differ under various linkages (Wang et al., 2020). Thus, using different types of relational data to examine intercity network linkages has profound implications for exploring regional spatial structure (Neal, 2013).

In this study, an urban development level evaluation indicator system was constructed to measure the social, economic, and environmental development level of each district and county in the Beijing-Tianjin-Hebei (BTH) region. This addresses the shortcomings of existing research, such as the inadequate understanding of the multidimensional development level and spatial structure of cities, the absence of network structure robustness analysis, and the lack of core development nodes and network exploration. We constructed different dimensional networks based on the measurement results and evaluated the spatial structure characteristics and spatial and temporal patterns of these networks. This study aims to specify regional resource allocation and spatial linkage intensity and evaluate the efficacy of coordinated development from a network perspective by analysing structural evolution characteristics and robustness. Thus, this study provides a scientific foundation and emerging views for optimizing regional spatial structure and promoting coordinated development.

3 Study area and data sources

3.1 Study area

The BTH region (36°01′-42°37′N, 113°04′-119°53′E) is located in northern China (Figure 1) and includes two municipalities of Beijing and Tianjin that are under the jurisdiction of the central government and 11 prefecture-level cities in Hebei province, with a total of 200 districts and counties in the region. As of 2019, the gross domestic product (GDP) of the BTH region reached 8.5 trillion yuan, accounting for approximately 8.62% of the national GDP. The cities in the BTH region have a clear division of labour and have Progressively formed a “one core, two cities, three axes, four districts, and many nodes” structure, with Beijing as the core city; Tianjin, Shijiazhuang, Tangshan, Baoding, and Handan as the regional centre cities; and Langfang, Cangzhou, Hengshui, Xingtai, Qinhuangdao, Zhangjiakou, and Chengde as the node cities.

Figure 1 Location of the study area (Beijing-Tianjin-Hebei region)

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3.2 Data source and preprocessing

Regarding data validity and applicability, we selected the following data (Table 1) for our study:

Table 1 Research data sources and description

Name	Data source	Resolution	Brief description
Land use data	Geographic Condition Monitoring Data	2 m/yearly	Reflection of the actual development and construction of the urban area
Road network data	Geographic Condition Monitoring Data, OpenStreetMap dataset (https://www.openstreetmap.org/)	2 m/yearly	Quantification of the urban transportation development level
POI data	Geographic Condition Monitoring Data, POI data (https://www.amap.com/)	2 m/yearly	Indication of people’s living standards
Social and economic data	Beijing Regional Statistics Yearbook, Tianjin Statistical Yearbook, and Hebei Statistical Yearbook		Quantitative measurement of quality in all aspects of the city
PM2.5 data	ChinaHighPM2.5 (https://doi.org/10.5281/zenodo.6398971)	1 km/yearly	Characterization of the regional environmental conditions
Nighttime light data	EOG Group, Colorado School of Mines, USA (https://eogdata.mines.edu/products/vnl/)	500 m/yearly	Characterization of the regional economic development level
Remote sensing image	Landsat8 OLI (https://earthengine.google.com/)	30 m/yearly	Quantification of urban environmental quality
Administrative boundary	National Basic Geographic Information Database (https://www.resdc.cn)	/	Definition of the scope of the study area

(1) Land use data. The Geographic Condition Monitoring Data from the Ministry of Natural Resources were used as the data source for the surface coverage data in this study. The data cover the entire BTH region. Compared with similar land cover datasets, the advantage of this product is that the spatial resolution of the original image is better than 2 m, and the accuracy is guaranteed by field verification and quality inspection (Gao et al., 2020; Mao et al., 2021); therefore, this dataset accurately reflects the real land use situation of the city and enhances the accuracy and credibility of the results.

(2) Traffic road network data. We supplemented the road dataset with OSM road data based on the road dataset in the geographic state data, which mainly contains road network datasets of highways, county roads, residential roads, urban primary and secondary roads, and other elements.

(3) POI data. For this study, we crawled two categories of POI data, education and medical, to evaluate the urban public infrastructure level. Since big data have a finer spatial and temporal scale than conventional data, they have high spatial variability and regional instability (Cai et al., 2017; Lv et al., 2021). Therefore, these data served as a supplementary data source for Geographic Condition Monitoring Data.

(4) Socioeconomic data. To quantitatively measure the multifaceted development level of cities, socioeconomic indicators were selected from the statistical yearbooks of Beijing, Tianjin, and Hebei, as well as the statistical bulletins of prefecture-level cities, districts, and counties in the region, and some missing data were filled in using the interpolation method.

(5) Remote sensing data. In this study, nighttime light data and the ChinaHighPM2.5 dataset were used to reflect urban economic construction (Elvidge et al., 2021) and the atmospheric environment (Wei et al., 2021). Moreover, urban greenness, humidity and heat were calculated using Landsat 8 data to reflect the urban spatial environment.

The study data were all from 2015 and 2019, the spatial data were uniformly projected as CGCS2000_GK_CM_117E, and the remote sensing images were processed, such as by denoising and resampling.

4 Research methods

To clarify the characteristics of the evolution of the spatial structure of urban networks in different dimensions and the problems that exist in their existing development, we utilized the spatial interaction analysis method in geoscience combined with the concept of complex networks to analyse the spatial structure of networks and their robustness in the study area. The detailed procedure is as follows (Figure 2):

Figure 2 Research framework

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(1) Multidimensional urban network construction. Objective data from diverse sources were used to quantify urban development across multiple dimensions. These data were modelled into a network of nodes and edges using a modified gravity model.

(2) Analysis of network characteristics. Network indicators were employed to assess the urban network, pinpointing cities of significance based on both overall and individual characteristics.

(3) Analysis of network structure evolution. The evolution of the urban network structure from 2015 to 2019 was examined using community detection algorithms that were complemented by Sankey diagrams to trace transformations across clusters.

(4) Analysis of network robustness. The network’s spatial structural robustness was tested through simulated node attacks. Core networks and key nodes were identified to explore patterns of coordinated development.

4.1 Construction of the urban network

4.1.1 Theoretical foundation

Economic, social, and environmental aspects should be balanced in regional development (Sun et al., 2017; Feleki et al., 2018; Gonzalez-Garcia et al., 2018; Jing and Wang, 2020), as demonstrated by various studies (Li and Yi, 2020; Wang et al., 2021). We analysed the interconnections of these aspects in urban areas at the county level, transforming city subsystem development levels into a network to understand coordinated development and synergy. The economic subsystem is the resource backbone, the environmental subsystem sustains growth, and the social subsystem uses these resources to boost the economy and improve living standards. Together, these subsystems collectively promote regional development, as shown in Figure 3.

Figure 3 Interaction of the social, economic and environmental subsystems

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4.1.2 Evaluation indicator system construction

In this study, we considered the relationships among the social, economic, and environmental subsystems of cities and the existing research foundation (Zhang et al., 2016; Fan et al., 2019; Zhang and Chen, 2021; Mu et al., 2022; Zhang et al., 2022b), referred to the actual development status of cities in the region, and adhered to the principles of representativeness, comparability, and data accessibility to develop a comprehensive urban development evaluation index system (Table 2). The entropy weight method, which determines indicator validity and weight based on the entropy difference of index information, minimizes subjectivity and unpredictability in weight assignment, addressing the issue of redundant indicator information (Luo et al., 2021).

Table 2 The indicator system for evaluating the comprehensive development level of the ESE of cities

Guideline layer	Indicator layer & indicator type	Unit	Indicator meaning	Weight
Economy (ECO)	GDP (+)	10⁹ Yuan	Regional economic power	0.2186
	The percentage of added value of the tertiary industry of GDP (+)	%	Industrial and economic structure	0.0341
	per capita GDP (+)	10⁴ yuan	Residents’ living standards	0.0873
	The averages NTL data (+)	/	Economic development level	0.2282
	General public budget revenues (+)	10⁴ yuan	Regional financial strength	0.2354
	General public budget expenditure (+)	10⁴ yuan	Regional financial strength	0.1679
	Disposable income per urban resident (+)	yuan	Residents’ living standards	0.0285
Society (SCO)	Road network density (+)	km/km²	Infrastructure level	0.1325
	Urbanization rate (+)	%	Urban development potential	0.0202
	Population density (+)	people/km²	Population growth potential	0.2097
	Length of road per capita (+)	m/people	Convenience of transportation	0.1583
	Percentage of built-up area (+)	%	Land development intensity	0.0548
	Number of health facilities per 10,000 people (+)	Institute/10⁴ people	Health services level	0.0344
	Number of schools per 10,000 people (+)	Institute/10⁴ people	Education level	0.0455
	Open space area per capita (+)	people/km²	Population’s standard of living	0.3446
Environment (ENT)	PM2.5 concentration in the air (-)	μg/m³	Air quality levels	0.1837
	Percentage of Ecological space area (+)	%	Environmental quality levels	0.5204
	NDVI (+)	/	Urban greenness	0.1050
	LST (-)	/	Urban heat	0.0312
	WET (+)	/	Urban humidity	0.1597

Cities, as hubs of interactions and networks (Batty, 2013), use their development level to shape external connections. To simulate these spatial interactions, we applied an enhanced gravity model to construct economic, social, and environmental networks. This model, which is frequently used for quantifying intercity linkages, has been adapted for specific needs in recent studies (Kabir et al., 2017; Cao et al., 2018; Thompson et al., 2019; Li and Lu, 2021). By incorporating spatial interaction theory (Ullman, 1957), we measured intercity development as directed, using the Baidu Maps API to calculate the shortest driving distance and time between districts and counties, and defined time-cost distance as the product of these two factors.

C D I_{i j} = \frac{Q_{i}}{Q_{i} + Q_{j}} \times \frac{Q_{i} Q_{j}}{{(T_{i j} \times R_{i j})}^{2}}

(1)

where CDI_ij is the intensity of the development between two cities i and j under spatial interaction; Q_i. Q_j is the level of urban development between two cities i and j; T_ij is the shortest driving time between the two cities; and R_ij is the shortest driving distance between the two cities.

Moreover, we synthesized the city development levels under the three social, economic, and environmental dimensions to construct a network of comprehensive urban development levels. The formula is as follows:

C D I_{s u m} =3 \frac{{(C D I_{E C O} \times C D I_{E N T} \times C D I_{S C O})}^{\frac{1}{3}}}{C D I_{E C O} + C D I_{E N T} + C D I_{S C O}}

(2)

where CDI_ECO, CDI_ENT, CDI_SCO, and CDI_SUM represent the city’s economic, environmental, social, and comprehensive development levels, respectively.

Notably, we omitted the network edge data for the last 25% of the range of values for each network, considering that the interconnection of cities in the region is affected by geographic distance and differences in development level.

4.2 Analysis of network characteristics

Our study combined overall and individual network analyses to understand urban networks morphologically and functionally. Overall characteristics such as scale, density, and node interaction were examined through a city’s linkage strength, highlighting the importance of nodes and edges (Watts and Strogatz, 1998). Functional aspects such as linkage strength and directional balance were emphasized for individual characteristics (Burger and Meijers, 2012; Liu et al., 2016). Central to this is node centrality indicators, which aid in assessing node significance over time. This dual approach was helpful for identifying key cities and informing strategies for urban development and regional management (Table 3).

Table 3 Overall and individual network indicators

Indicator name	Description	Equation
Network density (D)	Refers to the degree of correlation between network nodes, i.e., the probability of connection between nodes.	$D = \frac{l}{n (n - 1)}$ (3)
Average path length (L)	Measures the level of network reachability and the average distance between nodes.	$L = \frac{2}{n (n - 1)} \sum_{i \neq j} d_{i j}$ (4)
Average clustering coefficient (C)	Indicates the degree of node aggregation in the network and enables the calculation of the probability that two neighbours of a node may be connected to each other.	$C = \frac{1}{n} \sum_{i \in n} \frac{2 m_{i}}{k_{i} (k_{i} - 1)}$ (5)
Reciprocity (R)	The ratio of bidirectionally connected edges to all edges in a directed weighted network (Garlaschelli and Loffredo, 2004) and is able to measure the closeness of the interaction between two nodes.	$R = \frac{L_{b i}}{L_{b i} + L_{u n i}}$ (6)
Degree centrality (DC)	Measures a node’s connectivity and influence, differentiating between its ability to receive and exert influence in directed networks.	$D C_{i} = \sum_{j = 1}^{n} a_{j i} w_{j i} + \sum_{j = 1}^{n} a_{i j} w_{i j}$ (7)
Closeness centrality (CC)	Characterizes the correlation between a city’s development and that of other cities, demonstrates superior efficiency of external interactions in regional development networks.	$C C_{i} = \frac{n - 1}{\sum_{j \neq i}^{n} d^{w} (i, j)}$ (8)
Betweenness centrality (BC)	Reflects the ability of cities to play a communicative and coordinating role in regional development, and to control or influence the flow of resources and information.	$B C_{i} = \frac{2}{(n - 1) (n - 2)} \sum_{j < k}^{n} \frac{N_{j k} (i)}{N_{j k}}$ (9)
Eigenvector centrality (EC)	Reflects the degree to which the urban entity itself is connected to key nodes in the vicinity (Li et al., 2016), demonstrating the centrality of the nodes	$E C_{i} = λ^{- 1} \sum_{j = 1}^{n} a_{i j} x_{i j}$ (10)

4.3 Analysis of network structure evolution

City development levels vary due to factors such as location, infrastructure, resources, the external environment, and policies, leading to distinct urban clusters. Understanding these clusters is key for planning spatial development. The Infomap algorithm (Rosvall and Bergstrom, 2008), which is based on information entropy and flow (Girvan and Newman, 2002; Lancichinetti et al., 2008), was used to analyse the evolution of network clusters in the BTH region from 2015-2019. This algorithm efficiently partitions network communities by compressing information flow paths and considering node interactions, making it effective for real network community analysis (Rosvall et al., 2010; Zhong et al., 2014). The formula is as follows:

L (M) = q H (Q) + \sum_{1}^{m} p_{i} H (P_{i})

(11)

where L(M) denotes the average coding length expectation of the paths along which random wanderings occur within and between communities; q and p_i denote the probability of random wanderings occurring between and within communities, respectively; m denotes the number of communities; and H(Q) and H(P_i) denote the entropy of the probability of random wanderings moving between and within communities, respectively.

4.4 Analysis of network robustness

Central cities are key to regional development but have limited capacity. Excessive development can hinder their growth and affect neighbouring cities, potentially causing a cascading network failure in which one node’s failure leads to others’, possibly resulting in large-scale network collapse. This concept, which is known as cascade failure (Motter and Lai, 2002), is increasingly relevant in real network analysis (Dong et al., 2020; Dui et al., 2020).

Regional development depends on the robustness of its spatial structure to shocks. Changes in network nodes affect the overall structure, which is evident in the BTH region’s development and is marked by significant disparities. Understanding node capacity and network robustness is essential for future planning. In this study, we used the cascade failure model to simulate attacks on urban networks from 2015 to 2019 using three methods. Random Attack (a random attack on network nodes, RA) was used to simulate random failures or disruptions that may occur in a network, such as accidents, natural disasters, or random acts of violence that disrupt the normal operation of network nodes. Degree Attack (a sequential attack based on node degree size, DA) was used to simulate the chain reactions triggered by the collapse of a central city that is unable to assume a leadership role in an uncontrolled development model. Edge Weight Attack (a sequential attack based on edge weight size, WA) was used to simulate the impact of the reduction and disappearance of cooperative communications such as population flows, trade, and environmental resource sharing if the central city maintained the status quo development level with other cities. We assessed network robustness using specific indices (Table 4) and analyse the results to identify core networks and key nodes.

Table 4 Network robustness evaluation indicator system

Indicator name	Description	Equation
Network efficiency	Reflects the ease of network operation, the more efficient the network, the better the network connectivity	$E = \frac{1}{n (n - 1)} \sum_{i = 1}^{n} \sum_{j = 1 (i \neq j)}^{n} H_{i j}$ (12)
Isolated node ratio	Reflects the proportion of nodes that have no edges connected to them when the network is under attack	$Δ N = (1 - \frac{n^{}}{n}) 100$ (13)
Relative size of maximum connected subgraphs	Reflects the size of the largest subgraph during network fragmentation in the event of an attack, providing a visual representation of the extent of network disruption	$G = \frac{P^{*}}{P}$ (14)

5 Results

5.1 Network development evaluation

Spatial linkage calculations in the BTH region from 2015 to 2019 revealed varying network linkage strengths across multiple dimensions, categorized into six levels using logarithmic grading (Figure 4). The region’s network grew rapidly during this period, with an increase in high-grade connections within cities, improved communication with neighbours, and overall developmental progress. Central cities such as Beijing, Tianjin, Tangshan, and Shijiazhuang expanded their network connections, creating a significant “connection corridor” that drove regional development and benefited peripheral cities. While the regional network structure strengthened, disparities and gaps in development persisted, especially in the northern higher elevation areas, due to natural and other factors.

Figure 4 Evolution of various networks in the Beijing-Tianjin-Hebei region from 2015-2019

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The primary goal of BTH coordinated development was to minimize disparities among districts and counties. In 2015, central cities such as Beijing (including Beijing-Zhangjiakou, Beijing-Baoding-Shijiazhuang, and Xingtai-Handan) had strong internal linkages, but economic disparities between cities remained by 2019. The regional network was mainly concentrated in Beijing and Tianjin, with weaker networks in Zhangjiakou, Chengde, and Hengshui. Social networks developed rapidly, improving connections region-wide. Environmental development was stable, with potential for enhancement through ecological policies. Zhangjiakou and Chengde emerged as key players in environmental linkages. Overall, since the implementation of the coordinated development policy, the network in the BTH region has improved, especially in southern counties, with an increase in high-grade links and a reduction in cross-municipal linkage imbalances, although regional development imbalances still exist.

5.2 Analysis of network characteristics

5.2.1 Overall network characteristics analysis of the BTH region

We measured the overall network characteristics to elucidate the spatial structure of the different dimensional networks (Table 5). The development of different-dimensional networks from 2015-2019 resulted in network density, network efficiency, and reciprocity, all of which showed an increasing trend, while the decrease in the average path length revealed the network’s rich internal network paths and hierarchical network space structure.

Table 5 Overall network structure characteristics

Name	2015ENT	2019ENT	2015ECO	2019ECO	2015SCO	2019SCO	2015SUM	2019SUM
D	0.503	0.609	0.416	0.562	0.483	0.719	0.514	0.642
L	1.558	1.416	1.686	1.467	1.582	1.283	1.548	1.373
C	0.765	0.801	0.719	0.778	0.754	0.844	0.777	0.826
R	0.830	0.861	0.598	0.693	0.692	0.804	0.839	0.902

In 2015, the density of the BTH network, an indicator of overall connectivity, was close to 0.5, revealing both high intercity connections and significant economic inequalities within the network. This loose spatial structure provided opportunities for enhancing intraregional connections. By 2019, network connections stabilized with an increase greater than 10%, and social network density improved, indicating a narrowing of social development gaps. Transmission efficiency, measured by the average path length, improved across all networks, with social networks demonstrating the highest interaction capacity and forming more functionally complementary regional clusters than economic and environmental networks. The clustering coefficients from 2015 to 2019 suggested dense intercity connections and fewer isolated nodes, enhancing the network’s robustness, particularly with the active participation of central cities in regional development. Despite this progress, the reciprocity index revealed that nearly 30% of nodes were still economically passive and struggled to form effective two-way connections, which highlights the need for continued focus on economic development within the network.

5.2.2 Individual network characteristics analysis of the BTH region

To quantify the impact of coordinated development strategies on urban nodes in the regional network, we evaluated the difference in node centrality results from 2015-2019. We depicted the spatialized results hierarchically using natural breaks (Jenks) (Figure 5). By evaluating the variations in the centrality of various nodes horizontally and comparing the dynamics of node centrality vertically, we could discover the crucial nodes and regions involved in regional synergy.

Figure 5 Network centrality differences among different subsystems in the Beijing-Tianjin-Hebei region from 2015 to 2019

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From 2015 to 2019, the network city nodes in the BTH region maintained stable weighted degree centrality, with emerging economic synergy and polycentric development in cities such as Shijiazhuang, Baoding, and Cangzhou. The environmental quality initially declined due to rapid urbanization. Overall network analysis indicated that Beijing had a strengthening core position, with significant growth in Cangzhou and Shijiazhuang. Closeness centrality increased across most cities, suggesting more efficient intercity cooperation and a shift from Beijing and Tianjin’s single-core dominance to more distributed regional development. Betweenness centrality showed that central cities still controlled the region’s development, but peripheral cities faced locational constraints. Eigenvector centrality revealed enhanced city standing due to urban expansion, forming significant clusters such as Beijing-Tianjin and Xingtai-Handan, although central regions, particularly around Shijiazhuang and Hengshui, still faced development challenges. This highlights the need for targeted development aid, especially in central areas such as Shijiazhuang, to address social and environmental disparities.

5.3 Analysis of network structure evolution

Based on the variance in the intensity of spatial interactions, the region is divided into distinct clusters. We delineated urban development clusters from the perspective of spatial aggregation and intercity node linkages for different dimensional networks. We named the clusters with central cities to represent the spatial structure of BTH region in the context of coordinated development.

From 2015 to 2019, the economic network in the BTH region was stable, with core cities such as Beijing and Tianjin maintaining their clusters, as shown in Figure 6a. Minor changes included Chengde joining the Beijing-Tianjin cluster and significant shifts in southern clusters such as Baoding, leading to the formation of a new Hengshui-centred cluster. The environmental network, as shown in Figure 6b, saw the Beijing-Tianjin cluster divide, with parts merging into the Baoding cluster and enhanced cohesion in the Shijiazhuang and Xingtai-Handan clusters. The social network, as shown in Figure 6c, indicated a trend towards regional integration, especially in border areas. Overall, the region’s community structure, consistent with administrative boundaries, as shown in Figure 6d, saw cities focusing on their central areas and the formation of a few peripheral joint clusters.

Figure 6 Evolution of various networks in the Beijing-Tianjin-Hebei region from 2015-2019 (Note: Different colours represent different clusters, and the width size represents the number of city transfers.)

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To further elucidate the spatial pattern of the network following intercommunity urban transfer, we spatialized the three-dimensional network clusters’ spatial structure (Figure 7). The economic cooperation in the BTH region is defined by the strong link between Beijing and Tianjin and the independent growth of other cities, with the only significant change being the contraction of the Baoding cluster due to the development of Hengshui. Social cooperation remains stable, and the linkage of peripheral areas has become a new type of development. Environmental dynamics have significantly evolved, particularly in the Shijiazhuang and Xingtai-Handan areas, splitting into two parts based on their geographical location to the north and south. Furthermore, environmental disparities in the Beijing-Tianjin-Langfang region weakened their previously close ties. Despite industrial policy impacts, Beijing maintains its core position, and areas such as Cangzhou-Hengshui and Tangshan-Chengde are developing a “leading the weak with the strong” approach. City transfers within urban clusters typically follow administrative boundaries and involve cities with similar development but lacking distinct features and strong connections. The coordinated development of the region is challenged by significant disparities in development levels among cities, highlighting the need to accelerate development in certain clusters to advance the goal of contiguous regional development.

Figure 7 Results of city clustering in different dimensions in the Beijing-Tianjin-Hebei region from 2015-2019 (Note: Different classes represent different urban clusters.)

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5.4 Analysis of network robustness

5.4.1 Robustness of the urban network structure under different attack methods

Using the random attack method, we can examine the evolution of the network’s actual robustness and overall coordination capacity; using the deliberate attack method, we can assess the pressure-bearing capacity and influence of the BTH region on the development of different networks (Figure 8).

Figure 8 Variations in network robustness characteristic value under different node attack methods

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During random attacks, network efficiency linearly declined, and isolated nodes increased with a decrease in the maximum connectivity subgraph. Overall, each network remained stable, but robustness decreased after significant node attacks in 2015, with economic networks collapsing at 100 nodes and social and environmental networks at 120 nodes. By 2019, this threshold improved by 20 urban nodes, reflecting better functional distribution and enhanced network robustness. Environmental networks were the most robust, followed by social and economic networks, aligning with the BTH region’s development.

Deliberate attacks showed varying degrees of network degradation, and there were “critical points” that could hasten the collapse of the whole network. The economic network was most affected, collapsing after 30 nodes due to reliance on central nodes and significant differences in varied city economies. However, the 2019 data indicated a delayed collapse point, suggesting that coordinated development alleviated economy-led imbalances among nodes. Both deliberate and random attacks on the environmental network in the BTH region followed a similar declining pattern due to its extensive core network and balanced node communication. Notably, the network’s collapse threshold decreased from 80 to 72 core nodes in 2015, reflecting the impact of rapid urbanization on its robustness. However, the stability against weight attacks indicated that this decline in robustness was temporary. Similarly, the social network exhibited a linear decline before a sharp drop, but its robustness and overall development improved significantly, showing greater consistency.

In summary, the robustness of networks in the BTH region has increased, as indicated by the delayed critical points of network failure and a shift from monocentric dominance to multicentric coexistence. The convergence of change curves under various attack methods reinforces this transition. Furthermore, the overall robustness strength suggests that evaluating urban network robustness from a single perspective may be limited, and considering multiple flow aspects can bolster network resilience.

5.4.2 Identification of the core network and key nodes

By comparing the changes in the robustness of each network in response to random and deliberate attacks, we discovered that various attacks led to different mutation points for network robustness. However, deliberate attacks are highly focused, resulting in more severe network failure. Thus, we used the mutation points in the degree attack curve to investigate the core network in each dimensional network and the mutation points in the weight attack to determine the core nodes in each network.

The core network of the BTH region was concentrated in the central region and had distinctive characteristics in all dimensions (Figure 9). By 2019, all of the dimensions of the core network of the BTH region, which was initially concentrated in the central area, improved significantly. The economic network evolved from a primarily Beijing-Tianjin focus to include stronger connections with Baoding and Cangzhou and a more developed “Beijing-Baoding-Shijiazhuang” corridor. This network transitioned from a “triangular” to a “funnel” topology. The environmental network was upgraded cohesively, with Shijiazhuang and Baoding emerging as hubs, although Zhangjiakou and Chengde remained outside the network due to geographic constraints. The social network expanded markedly, with Tangshan, Cangzhou, and Hengshui developing robust medium-level connections, demonstrating resilience to network attacks and benefiting significantly from coordinated development efforts. Consequently, the BTH region’s core network stabilized, especially the “Beijing-Tianjin-Shijiazhuang-Baoding” network, which matured with close internal links and regular exchanges, extending its influence to peripheral cities.

Figure 9 Multidimensional core network in the Beijing-Tianjin-Hebei region (Note: Different levels represent the contact strength, where the first level is the highest; the grading criteria are the same as those in Figure 4.)

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According to the results of identifying core nodes (Figure 10), the whole region’s core nodes consisted of each city’s centre and adjacent counties. From 2015 to 2019, the number of core nodes in the BTH region, encompassing city centres and adjacent counties, increased, with significant spatial overlap; however, the central role of some city nodes in coordinated development decreased. The economic network (Figure 10(b)) initially had the most core nodes in Beijing, Tianjin, Tangshan, and Shijiazhuang, with fewer in the less robust southern region. By 2019, these nodes had expanded to include neighbouring nodes, forming large clusters in Beijing and Tianjin. The southern region, led by Handan, started integrating into the main network, replacing Xingtai’s central role, while the northern mountainous region remained isolated. The environmental network, with its numerous core nodes and small clusters in all cities, showed balanced environmental progress, except for significant changes within Hengshui. The social network evolved from independent core areas to contiguous regional cooperation, with Shijiazhuang, Baoding, Hengshui, and others drawing closer together, while the range of Beijing and Tianjin’s core nodes contracted. Overall, future network robustness improvements should focus on the northern region and connection enhancement.

Figure 10 Core nodes of the multidimensional network in the Beijing-Tianjin-Hebei region at county level

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6 Discussion

6.1 Effectiveness of the BTH coordinated development

City cooperation within the BTH region is becoming more frequent, and the central city has continuous but unstable external communication. From 2015 to 2019, city cooperation within the BTH region increased, with central cities such as Beijing, Tianjin, and Shijiazhuang at the heart of regional growth but experiencing a decline in their dominant positions. The economic network, initially led by the Beijing-Tianjin core, expanded to include frequent communications with Shijiazhuang and the integration of Cangzhou and Handan, resulting in a richer and more diverse network. This led to the development of new network branches, such as the “Beijing-Tianjin-Cangzhou-Hengshui” route, enhancing the overall network structure. The region’s linkage strength has transitioned from primary to intermediate, with high-grade linkages still concentrated around the four core areas of Beijing, Tianjin, Tangshan, and Shijiazhuang. However, their dominant position decreased, while Cangzhou’s role as an intermediary within the southeastern BTH region increased. In the urban network system, cities no longer develop separately but instead extend their interactions to other regional urban nodes (Xia et al., 2019). By inspecting the spatial network linkages between the cities in the BTH region, we found that the overall linkage strength of the region has been in transition from primary to intermediate. The high-grade linkages across administrative boundaries were still concentrated in Beijing-Tianjin-Tangshan-Shijiazhuang’s four core development areas. There are “core-core” and “core-edge” linkages within the region. The “agglomeration effect” produced by nodal cities brings together mobile network resources to achieve scale effects, and as node functions are strengthened, the region becomes more unequal (Meijers et al., 2018).

The spatial structure will continue to improve and be upgraded, affecting not only the intraregional factor of resource flow but also the hierarchical and coupling relationships of intercity spatial interaction and exchange and intracity activities. Thus, a network structure can be used to reflect the current situation and issues of regional coordinated development. Although the overall network appears dense, it exhibits hierarchical inequalities. Cities such as Hengshui, as weaker elements in the core network, struggle to gain attention and support from major cities such as Beijing, Tianjin, and Shijiazhuang, highlighting their vulnerability in the development process. Peripheral cities, while close to core cities, often do not benefit from their advantages, leading to a significant “siphoning effect” (Liu et al., 2017) in which economic and social ties are predominantly concentrated around Beijing and Tianjin. This has exacerbated regional competition and amplified the “Matthew effect,” in which stronger regions continue to grow while weaker regions lag behind. Additionally, the impact of industrial downsizing, particularly in traditional sectors in Hebei and Tianjin, has become apparent, with the economic network showing little change over the past five years and even a decline in areas such as the Binhai New Area.

Most noncentral city locations and regional functions within the region are not well utilized. Intercity collaboration and involvement constitute network advantages, and the existence of intercity functional networks can provide synergies and complementarities (Capello, 2000) and further serve as an intrinsic motivation for network development (Meijers et al., 2008). The rising regional core position of Cangzhou reflects the cohesion of its central city in terms of spatial structural clustering and centrality, hence contributing to the progressive establishment of a closed-loop structure in the central BTH regional network. Among the centrality results, implementing the BTH coordinated development policy has more significant results, with the initial single-centre development model gradually evolving into a multicentre coordinated development model. The three major central cities of Beijing, Tianjin, and Shijiazhuang remain at the regional development centre. The rapid increase in development in Cangzhou has made it a key conduit for Beijing and Tianjin to communicate with the southern region, which is centred on Shijiazhuang. In contrast, the majority of noncentral cities have potential for improvement.

During the present period of the coordinated development of the BTH, the greatest obstacle is that many cities need distinct positioning, which makes it challenging for them to utilize their respective development advantages. As the absolute core and radiating centre of the region, Beijing should retain the integrity of its spatial structure; nevertheless, the outlying districts and counties of Yanqing, Miyun, and Fangshan have been detached from each other in various aspects of development. The central city’s self-development has gradually increased internal differences, which have now spread to Zhangjiakou and Chengde, where internal and external communication capacities are severely limited due to geography and functional positioning. Similarly, the smaller changes in the development clusters demonstrate the absence of resource circulation and communication within the region, and the disparities between the development levels of the cities persist. Beijing, Tianjin, and Hebei have distinct resource endowments and development stages, and their respective interest goals and demands do not conflict. The results of the urban network indicated that the BTH region has formed prominent connection corridors and is “branching out” incrementally. In the future, coordinated development of the BTH should strengthen the multilevel linkages between cities and take advantage of the spatial structure of “one core, two cities, three axes, four districts, and multiple nodes.”

With the support of network robustness evaluation, we discovered that several aspects of network features and expression are distinct, which echoed the existing research (Mu et al., 2022). For instance, there are apparent central nodes and “channel” networks in economic and social networks, which is conducive to optimizing regional resource allocation. The channel network can facilitate the flow of factors from highlands to other locations, whereas the “trickle-down effect” of mobile factors moving from high to low levels limits polarization and uneven regional development (Van Nuffel and Saey, 2005). The results of the degree attack and the edge attack have demonstrated that the absolute dominance of the central city in the region hinders the development of the region. At the same time, with industrial transfer, cities that traditionally rely on manufacturing and other forms of single industries will decline, which may even lead to the disruption of cooperation chains with the central city, reducing population and capital flows, which weakens the efficiency of integrated linkages. Similarly, we discovered that low-cost network nodes have some benefits. Low-cost nodes refer mainly to core or edge nodes in the core network that have geographical benefits but are not outstanding in their development (e.g., Hengshui and Langfang). From the perspective of network robustness, these nodes help to distribute the development pressure of core nodes and prevent the collapse of the core nodes, which paralyzes the overall network. To achieve balanced and sustainable development, it is necessary to fulfil morphological and functional polycentricity, prevent the negative externalities of agglomeration, and enhance regional competitiveness (Wei et al., 2020).

6.2 Coordinated development policy suggestions

Therefore, based on the results of this study and the current situation of development in the BTH region, we propose the following specific recommendations:

(1) Developmental pressure from central cities to surrounding cities based on local factors should be alleviated to prevent homogenous rivalry. Resource-rich cities should share their internal development resources with adjacent cities, fully consider regional characteristics and related implications based on existing development relationships, and maximize the benefits to surrounding cities. For example, Beijing needs to pay attention to the growth of Yanqing, Huairou, and other districts while decentralizing its functions to progressively realize outwards expansion and lessen internal fragmentation caused by its imbalance through “point to area” development. Industrial transfer is more feasible in the BTH region, which has an entirely distinct industrial structure. The ideal strategy is to utilize industrial synergy to propel the growth of interregional economic transportation and other aspects of coordinated development.

(2) City functional positioning should be defined. The BTH region has a lengthy history and complicated and diverse city positions. Most resource-depleted cities are confronted with transformation challenges and stagnated development, so strategic options for coordinated development are needed as an impetus. Moreover, from the perspective of the characteristics of network nodes, increasing the importance of noncentral cities can support the regular operation of the network and facilitate the movement of elements and resources within the network. Each city in the BTH region should actively utilize its unique assets and avoid disadvantages to achieve the same purpose and mutual benefits.

(3) The spatial structure of the coordinated development of BTH should be continuously optimized. The spatial structure of the BTH region is typically complex, with local communities dominating, but administrative boundaries must be more strictly adhered to. Diverse clusters make internal functional positioning unclear and muddled, so the government-led establishment of regional spatial units, such as urban agglomerations and metropolitan areas, is needed to coordinate inter-cluster development and prevent the existence of isolated core structural clusters that disrupt regional coordination. Future coordinated development of the Beijing, Tianjin, and Hebei regions should rely on locally appropriate policy planning, consider the development of small- and medium-ranking districts and counties, establish a proven mechanism for the division of labour and cooperation, and break the current trend of a gradual widening development gap between two cities and one province.

(4) Communication and collaboration with peripheral regions should be enhanced to foster regional coordinated development with differentiation. The network robustness evaluation results clearly reveal the weak points in the BTH region, and the lack of attention given to peripheral areas causes the overall network to concentrate on the development of the central region. However, there are still vulnerable areas in the core network. The radiation function of the central city is fully utilized, while the central city’s load is reduced to prevent network cascade failure due to excessive pressure. Simultaneously, coordinated development cannot rely solely on Beijing’s radiation drive for the whole region or particular localities. Leveraging regional subcentres has an equivalent investment value for urban development. The Tongzhou subcentre and Xiong’an New Area serve as transition hubs for regional development resources and enhance the regional development network.

6.3 Limitations

This study still has the following limitations:

(1) There is a lack of measurement of the development level of science and technology, innovation, etc. An information-oriented society makes science and technology innovation a vital engine of urban development in the new era. However, the limited availability of county-level data makes it difficult for our indicator system to reflect the innovation level of each district and county. Moreover, quantifying policy impacts is crucial for evaluating development levels. The need for more relevant data and indicators will be one of the most significant challenges for future studies.

(2) Regional development needs more exploration into the principles of spatial structure evolution and influence mechanisms. According to the findings of this study, central cities have a limited ability to drive the surrounding areas, and too many cities impede the advancement of coordinated development. However, the radiation and driving range of different development phases vary. In other words, the integration of different cluster networks within the region is the linchpin of the coordinated development stage, and determining the spatial scale evolution law and influence mechanism of clusters within the region during the coordinated development process will be a significant focus in the future.

(3) This study lacks in-depth analysis from a multiscale network perspective. Since the degree of development and radiation capacity of each subnetwork within a region varies, there are also disparities in spatial structure and network robustness between networks. Thus, urban networks at various scales should be further considered in the context of globalization and decentralization (Swyngedouw, 2010). In the future, we should analyse the spatial structure characteristics of each cluster network in the region, quantify the contributions of different subnetworks to the overall network evolution process, and comprehend the interrelationship between spatial structure and coordinated development on a finer scale.

7 Conclusions

In the context of globalization and networks, spatial interactions and their spatial patterns impact regional integrated development considerably, and the analysis of spatial interactions can offer policy-makers regional information and guidance (He et al., 2017). In this study, we constructed economic, environmental, and social urban development evaluation indicators for each district and county in the BTH region from 2015 to 2019. We transformed the assessment results into network forms and quantified the characteristics of various dimensional networks using overall network indicators and individual network characteristics. We used the Infomap algorithm to delineate the spatial pattern of regional development, estimated the robustness of different dimensional networks, and identified regional core networks and key nodes by simulating various network attack methods. The main conclusions are as follows:

(1) The development in the BTH region is increasing rapidly. The development level of cities in the BTH region has improved in all dimensions, with basic coverage of high-grade connections, improvement of low-grade connections, and a reduction in the disparity between cross-regions and cities in terms of connection strength. The density of multidimensional networks in the BTH region has increased progressively, and interregional connectivity and transmission efficiency are greatly enhanced. The characteristics of multidimensional networks have gradually evolved from the original single-centre development mode to the multicentre coordinated development mode, although disparities in regional development levels persist.

(2) The spatial structure of the BTH region is relatively stable and tends to be complicated and scalable. The 2015-2019 spatial pattern of regional development shows no significant changes, and the regional spatial clusters have a spatial structure dominated by local clusters supplemented by cross-municipal clusters in peripheral areas (CangHeng, XingHan, and TangQin) and a development trend of contiguity.

(3) The network robustness of cities in the BTH region has continuously increased, and the central clustering of core networks and nodes is prominent. Overall, the robustness of the network in the BTH region is ranked as follows: environment > society > economy, with the robustness of the comprehensive network between the environment and society. Currently, most core nodes are in Beijing, Tianjin, and Shijiazhuang, primarily in the central city and its surroundings, and the core networks are restricted to these three cities.

(4) The coordinated development of the BTH region is effective, but much potential for improvement remains. An increase in the number of core nodes indicates that more cities can contribute to coordinated development. However, the status changes of some core nodes imply that they are not yet stable. In this phase, the BTH region is primarily driven by the radiation of the central node, which exponentially increases the risk of cascade failure, necessitating a re-evaluation of the strategic significance of edge cities.

The in-depth study of urban spatial structure can clarify the potential and scale of urban development, promote the sensible allocation of factor resources, and provide a theoretical foundation for designing regional development planning strategies. This study can be applied to evaluating regional development and problem analysis studies in similar places.

Supplementary material (Notations)

l is the total number of network connections

n is the overall number of nodes in the network

d_ij is the optimal path length between nodes i and j

m_i is the number of interconnected edges between point i and all neighboring nodes

k_i is the degree value of point i

L_bi is the number of two-way connections between two nodes in the network

L_uni is the number of edges with only one-way connections between nodes

a_ji denotes the linkage edge with starting point j at end point i

w_ji denotes the linkage weight with starting point j at end point i

a_ij denotes the linkage edge with starting point i at end point j

w_ij denotes the linkage weight with starting point i at end point j

N_jk denotes the total number of shortest paths from node j to node k

N_jk(i) denotes the number of shortest paths between node j and node k through a node i

λ denotes the maximum value of the eigenvector of the adjacency matrix, for all nodes i, the initial value is 1, and the final result is obtained after convergence of iterations

H_ij denotes the reciprocal of the distance between the node i and the node j

n* denote the number of isolated nodes

P* denotes the maximum connected subgraph size

P denotes the initial subgraph size

参考文献

列表( 原文顺序 | 文献年度倒序 | 文中引用次数倒序 ) 可视化分析

[1]	Adam Y O, Pretzsch J, Darr D, 2015. Land use conflicts in central Sudan: Perception and local coping mechanisms. Land Use Policy, 42: 1-6. 本文引用 [1]

[2]	Amin A, 2004. Regions unbound: Towards a new politics of place. Geografiska Annaler: Series B, Human Geography, 86(1): 33-44. 本文引用 [1]

[3]	Anas A, Arnott R, Small K A, 1998. Urban spatial structure. Journal of Economic Literature, 36(3): 1426-1464. 本文引用 [1]

[4]	Antrop M, 2004. Landscape change and the urbanization process in Europe. Landscape and Urban Planning, 67(1-4): 9-26. 本文引用 [1]

[5]	Batty M, 2013. The New Science of Cities. Cambridge, MA, USA: MIT Press. 本文引用 [2]

[6]	Bertaud A, 2004. The spatial organization of cities: Deliberate outcome or unforeseen consequence? Berkeley, CA: Institute of Urban and Regional Development, University of California. Working Paper Number 2004-01. 本文引用 [1]

[7]	Burger M, Meijers E, 2012. Form follows function? Linking morphological and functional polycentricity. Urban Studies, 49(5): 1127-1149. 本文引用 [1]

[8]	Cai J X, Huang B, Song Y M, 2017. Using multi-source geospatial big data to identify the structure of polycentric cities. Remote Sensing of Environment, 202: 210-221. 本文引用 [1]

[9]	Camagni R, Diappi L, Stabilini S, 1994. City networks:an analysis of the Lombardy region in terms of communication flows. In: Cuadrado-Roura J, Nijkamp P, Salva P eds. Moving Frontiers: Economic Restructuring, Regional Development and Emerging Networks. 本文引用 [1]

[10]	Cao Z, Derudder B, Peng Z W, 2018. Comparing the physical, functional and knowledge integration of the Yangtze River Delta city-region through the lens of inter-city networks. Cities, 82: 119-126. 本文引用 [1]

[11]	Capello R, 2000. The city network paradigm: Measuring urban network externalities. Urban Studies, 37(11): 1925-1945. 本文引用 [1]

[12]	Castells M, 1996. The Rise of the Network Society. The Information Age:Economy, Society, and Culture. New York, USA: Blackwell, 1:656. 本文引用 [2]

[13]	Castells M, 2010. Globalisation, networking, urbanisation: Reflections on the spatial dynamics of the information age. Urban Studies, 47(13): 2737-2745. 本文引用 [1]

[14]	Castells M, Cardoso G, 2006. The Network Society: From Knowledge to Policy. Washington, DC: Johns Hopkins Center for Transatlantic Relations, 1: 3-23. 本文引用 [1]

[15]	Chong Z H, Pan S, 2020. Understanding the structure and determinants of city network through intra-firm service relationships: The case of Guangdong-Hong Kong-Macao Greater Bay Area. Cities, 103: 102738. 本文引用 [1]

[16]	Cui X G, Fang C L, Liu H M et al., 2019. Assessing sustainability of urbanization by a coordinated development index for an urbanization-resources-environment complex system: A case study of Jing-Jin-Ji region, China. Ecological Indicators, 96: 383-391. 本文引用 [1]

[17]	Dong S J, Yu T B, Farahmand H et al., 2020. Probabilistic modeling of cascading failure risk in interdependent channel and road networks in urban flooding. Sustainable Cities and Society, 62: 102398. 本文引用 [1]

[18]	Dui H Y, Meng X Y, Xiao H et al., 2020. Analysis of the cascading failure for scale-free networks based on a multi-strategy evolutionary game. Reliability Engineering & System Safety, 199: 106919. 本文引用 [1]

[19]	Elvidge C D, Zhizhin M, Ghosh T et al., 2021. Annual time series of global VIIRS nighttime lights derived from monthly averages: 2012 to 2019. Remote Sensing, 13(5): 922. 本文引用 [1]

[20]	Fan Y P, Fang C L, Zhang Q, 2019. Coupling coordinated development between social economy and ecological environment in Chinese provincial capital cities: Assessment and policy implications. Journal of Cleaner Production, 229: 289-298. 本文引用 [1]

[21]

Fang

C L

, 2017. Theoretical foundation and patterns of coordinated development of the Beijing-Tianjin-Hebei urban agglomeration. Progress in Geography, 36(1): 15-24. (in Chinese)

https://doi.org/10.18306/dlkxjz.2017.01.002

本文引用 [1] 摘要

Promoting coordinated development of the Beijing-Tianjin-Hebei Urban Agglomeration is not only a major national strategy, but also a long-term complex process. It is necessary to apply scientific theories and respect the laws of nature to realize the strategic target of common prosperity, share a clean environment, share the burden of risk of development, and build a world-class metropolis for the Beijing-Tianjin-Hebei Urban Agglomeration. This article examines the scientific foundation and patterns of coordinated development of the Beijing-Tianjin-Hebei Urban Agglomeration. Synergy theory, game theory, dissipative structure theory, and catastrophe theory are the theoretical basis of coordinated development of the Beijing-Tianjin-Hebei Urban Agglomeration. Synergy theory is the core theory for the coordinated development of the Beijing-Tianjin-Hebei Urban Agglomeration. The coordinated development process of the Beijing-Tianjin-Hebei Urban Agglomeration is a non-linear spiral progress of game, coordination, mutation, game, resynchronization, and mutation. Each game-coordination-mutation process promotes the coordinated development of the urban agglomeration to a higher level of coordination, and the progress fluctuates. This process includes eight stages: assistance phase, cooperation phase, harmonization phase, synergy phase, coordination phase, resonance phase, integration phase, and cohesion phase. Further analysis shows that the real connotation of coordinated development of the Beijing-Tianjin-Hebei Urban Agglomeration is to realize the coordination of planning, transportation, industrial development, urban and rural development, market, science and technology, finance, information, ecology, and the environment, as well as the construction of a collaborative development community. The Beijing-Tianjin-Hebei Urban Agglomeration will achieve advanced collaboration from low-level collaborative phase through regional coordination on planning, construction of traffic network, industrial development, joint development of urban and rural areas, market consolidation, science and technology cooperation, equal development of financial services, information sharing, ecological restoration, and pollution control. This study may provide a scientific foundation and theoretical basis for the coordinated development of the Beijing-Tianjin-Hebei Urban Agglomeration.

[22]	Fang C L, Yu X H, Zhang X L et al., 2020. Big data analysis on the spatial networks of urban agglomeration. Cities, 102: 102735. 本文引用 [1]

[23]	Fang X, Shi X Y, Phillips T K et al., 2021. The coupling coordinated development of urban environment towards sustainable urbanization: An empirical study of Shandong Peninsula, China. Ecological Indicators, 129: 107864. 本文引用 [1]

[24]	Feleki E, Vlachokostas C, Moussiopoulos N, 2018. Characterisation of sustainability in urban areas: An analysis of assessment tools with emphasis on European cities. Sustainable Cities and Society, 43: 563-577. 本文引用 [1]

[25]

Feng

Z J

, Chen

Z N

, Cai

H C

et al., 2022. Evaluation of the sustainable development of the social-economic-natural compound ecosystem in the Guangdong-Hong Kong-Macao Greater Bay Area urban agglomeration (China): Based on complex network analysis. Frontiers in Environmental Science, 10: 938450.

本文引用 [1]

[26]	Frank W P, Hua C-I, 1981. An econometric procedure for estimation of a generalized systemic gravity model under incomplete information about the system. Regional Science and Urban Economics, 11(4): 585-606. 本文引用 [1]

[27]	Gao W C, Zhao H T, Mao W J et al., 2020. Construction research and application of fundamental geographic national condition monitoring quality control system. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, XLIII-B3- 2020: 1327-1331. 本文引用 [1]

[28]	Garlaschelli D, Loffredo M I, 2004. Patterns of link reciprocity in directed networks. Physical Review Letters, 93(26): 268701. 本文引用 [1]

[29]	Girvan M, Newman M E J, 2002. Community structure in social and biological networks. Proceedings of the National Academy of Sciences, 99(12): 7821-7826. 本文引用 [1]

[30]	Gonzalez-Garcia S, Manteiga R, Moreira M T et al., 2018. Assessing the sustainability of Spanish cities considering environmental and socio-economic indicators. Journal of Cleaner Production, 178: 599-610. 本文引用 [1]

[31]	Han H, Guo L, Zhang J Q et al., 2021. Spatiotemporal analysis of the coordination of economic development, resource utilization, and environmental quality in the Beijing-Tianjin-Hebei urban agglomeration. Ecological Indicators, 127: 107724. 本文引用 [2]

[32]	Hao R, Wei Z, 2010. Fundamental causes of inland-coastal income inequality in post-reform China. The Annals of Regional Science, 45(1): 181-206. 本文引用 [1]

[33]	He D, Chen Z X, Pei T et al., 2023. Analysis of structural evolution and its influencing factors of the high-speed railway network in China’s three urban agglomerations. Cities, 132: 104063. 本文引用 [1]

[34]	He J H, Li C, Yu Y et al., 2017. Measuring urban spatial interaction in Wuhan urban agglomeration, central China: A spatially explicit approach. Sustainable Cities and Society, 32: 569-583. 本文引用 [1]

[35]	Hirschi C, 2010. Strengthening regional cohesion: Collaborative networks and sustainable development in Swiss rural areas. Ecology and Society, 15(4): 299-305. 本文引用 [1]

[36]	Hu Y N, Peng J, Liu Y X et al., 2017. Mapping development pattern in Beijing-Tianjin-Hebei urban agglomeration using DMSP/OLS nighttime light data. Remote Sensing, 9(7): 760-773. 本文引用 [1]

[37]	Huang H J, Xia T, Tian Q et al., 2020. Transportation issues in developing China’s urban agglomerations. Transport Policy, 85: A1-A22. 本文引用 [1]

[38]	Jing Z R, Wang J M, 2020. Sustainable development evaluation of the society-economy-environment in a resource-based city of China: A complex network approach. Journal of Cleaner Production, 263: 121510. 本文引用 [1]

[39]	Kabir M, Salim R, Al-Mawali N, 2017. The gravity model and trade flows: Recent developments in econometric modeling and empirical evidence. Economic Analysis and Policy, 56: 60-71. 本文引用 [1]

[40]	Lancichinetti A, Santo F, Radicchi F, 2008. Benchmark graphs for testing community detection algorithms. Phys Rev E Stat Nonlin Soft Matter Phys, 78(4): 046110. 本文引用 [1]

[41]	Lao X, Zhang X L, Shen T Y et al., 2016. Comparing China’s city transportation and economic networks. Cities, 53: 43-50. 本文引用 [1]

[42]	Li J G, Li J W, Yuan Y Z et al., 2019. Spatiotemporal distribution characteristics and mechanism analysis of urban population density: A case of Xi’an, Shaanxi, China. Cities, 86: 62-70. 本文引用 [1]

[43]	Li L, Ma S J, Zheng Y L et al., 2022. Integrated regional development: Comparison of urban agglomeration policies in China. Land Use Policy, 114: 105939. 本文引用 [1]

[44]

, Wang

J E

, Huang

et al., 2020. Exploring temporal heterogeneity in an intercity travel network: A comparative study between weekdays and holidays in China. Journal of Geographical Sciences, 30(12): 1943-1962.

https://doi.org/10.1007/s11442-020-1821-9

本文引用 [1] 摘要

A largely unexplored application of “Big Data” in urban contexts is using human mobility data to study temporal heterogeneity in intercity travel networks. Hence, this paper explores China’s intercity travel patterns and their dynamics, with a comparison between weekdays and holidays, to contribute to our understanding of these phenomena. Using passenger travel data inferred from Tencent Location Big Data during weekdays (April 11-15, 2016) and National Golden Week (October 1-7, 2016), we compare the spatial patterns of Chinese intercity travel on weekdays and during Golden Week. The results show that the average daily intercity travel during Golden Week is significantly higher than that during weekdays, but the travel distance and degree of network clustering are significantly lower. This indicates temporal heterogeneity in mapping the intercity travel network. On weekdays, the three major cities of Beijing, Shanghai, and Guangzhou take prominent core positions, while cities that are tourism destinations or transportation hubs are more attractive during Golden Week. The reasons behind these findings can be explained by geographical proximity, administrative division (proximity of cultural and policy systems), travel distance, and travel purposes.

[45]	Li W W, Yi P T, 2020. Assessment of city sustainability: Coupling coordinated development among economy, society and environment. Journal of Cleaner Production, 256: 120453. 本文引用 [2]

[46]	Li X Y, Lu Z H, 2021. Quantitative measurement on urbanization development level in urban agglomerations: A case of JJJ urban agglomeration. Ecological Indicators, 133: 108375. 本文引用 [1]

[47]	Li Z F, Shi Y L, Xu M Q et al., 2016. Position of the Asian container ports in global liner shipping network. Economic Geography, 36(3): 91-98. (in Chinese) 本文引用 [1]

[48]	Liao F H F, Wei Y D, 2012. Dynamics, space, and regional inequality in provincial China: A case study of Guangdong province. Applied Geography, 35(1/2): 71-83. 本文引用 [1]

[49]

Liu

, Ma

, Li

G P

, 2017. Pattern evolution and its contributory factor of cold spots and hot spots of economic development in Beijing-Tianjin-Hebei region. Geographical Research, 36(1): 97-108. (in Chinese)

https://doi.org/10.11821/dlyj201701008

本文引用 [1] 摘要

The rapid and imbalanced economic development in the Beijing-Tianjin-Hebei region has widened the gap between Beijing-Tianjin and surrounding areas since the 1990s, therefore, it is an important social consensus to achieve coordinated development. In this paper, we analyzed the imbalanced economic development in the Beijing-Tianjin-Hebei region by proposing a GDP Index using the DMSP/OLS nighttime light data to represent the regional economic development. Then the Getis-Ord General G, Global Moran's I and Optimized Hot Spot Analysis were applied to qualify the spatial pattern of the GDP Index. Third, Space Time Pattern Mining, Spatial Lag Model (SLM) and Spatial Error Model (SEM) were employed to identify the dynamics of the spatial pattern and evaluate the effects of four factors, which were natural environment (elevation and gradient), infrastructure (road network), policy (land use cover) and administrative division (urban or rural area), to the imbalance in the economy, respectively. Results show that: (1) the study area can be divided into three groups based on the level of economic development: urban Beijing-Tianjin, rural Beijing-Tianjin and urban Hebei, and rural Hebei. And there are two economic development gaps caused by Siphon Effect between urban and rural Beijing-Tianjin, and Beijing-Tianjin and Hebei, which is different from the previous view that only one economic development gap between Beijing-Tianjin and Hebei. (2) The dynamics of spatial pattern of economic development are mainly constant hot spot, fluctuant hot spot and fluctuant cold spot. The degree of hot spot, which is mostly in Beijing-Tianjin, decreases from urban center to rural area as concentric circles. In contrast, the majority of cold spots, which have no obvious ring structure, are located in rural Hebei. (3) The economic development in the Beijing-Tianjin-Hebei region has non-linear relationship with natural environment, infrastructure, policy and administrative division. In the hot spot region where the economy is more developed, all four factors, especially infrastructure, policy and administrative division, are positively correlated with economic development. However, high gradient, insufficient infrastructure and improper policy limit the economic development in the place with less developed economy, i.e. the cold spot region. This research may be helpful to understand the process and current conditions of economic development in the Beijing-Tianjin-Hebei region, and useful to realize coordinated development in this region.

[50]	Liu X B, Yan X D, Wang W et al., 2021. Characterizing the polycentric spatial structure of Beijing metropolitan region using carpooling big data. Cities, 109: 103040. 本文引用 [1]

[51]	Liu X J, Derudder B, Wu K, 2016. Measuring polycentric urban development in China: An intercity transportation network perspective. Regional Studies, 50(8): 1302-1315. 本文引用 [1]

[52]	Liu Y L, Zhang X H, Pan X Y et al., 2020. The spatial integration and coordinated industrial development of urban agglomerations in the Yangtze River Economic Belt, China. Cities, 104: 102801. 本文引用 [1]

[53]	Luo D, Liang L W, Wang Z B et al., 2021. Exploration of coupling effects in the Economy-Society-Environment system in urban areas: Case study of the Yangtze River Delta urban agglomeration. Ecological Indicators, 128: 107858. 本文引用 [1]

[54]	Lv Y Q, Zhou L, Yao G B et al., 2021. Detecting the true urban polycentric pattern of Chinese cities in morphological dimensions: A multiscale analysis based on geospatial big data. Cities, 116: 103298. 本文引用 [1]

[55]

H T

, Wei

Y D

, Huang

X D

et al., 2023. The innovation networks shaped by large innovative enterprises in urban China. Journal of Geographical Sciences, 33(3): 599-617.

https://doi.org/10.1007/s11442-022-2065-7

本文引用 [1] 摘要

Studies investigating innovation networks shaped by large innovative enterprises (LI-ENTs), which play a very important role in intercity diffusion of technology and knowledge, are rather thin on the ground. Using location information of LI-ENTs in China, we performed a headquarter-branch analysis to generate intercity innovation linkages and analyzed the patterns and dynamics of the generated network of knowledge diffusion. Although the network covers 353 cities across China, its spatial distribution is extremely uneven, with a few cities and city-dyads dominating the structure of the network. Furthermore, intercity linkages of innovation within and of urban agglomerations, as well as their central cities, stand out. With regard to network dynamics, the economic development level, innovation ability, and administrative level of cities, as well as the geographical, institutional, and technological proximity between cities are all found to have a positive impact on intercity linkages of innovations, whilst the impact of FDI on the national distribution of Chinese innovative enterprises is negative. Most importantly, the status of cities within the urban agglomeration exerts a significant positive effect in relation to the innovative enterprises’ expansions, which reflects that the top-down forces of government and the bottom-up forces of market function together.

[56]	Ma W Q, Jiang G H, Chen Y H et al., 2020. How feasible is regional integration for reconciling land use conflicts across the urban-rural interface? Evidence from Beijing-Tianjin-Hebei metropolitan region in China. Land Use Policy, 92: 104433. 本文引用 [1]

[57]	Mao W J, Zhao H T, Gao W H et al., 2021. Research on quality control method of land cover classification data oriented to national geographic condition monitoring. ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, V-3-2021: 265-269. 本文引用 [1]

[58]	Mcdonald R I, Green P, Balk D et al., 2011. Urban growth, climate change, and freshwater availability. Proceedings of the National Academy of Sciences, 108(15): 6312-6317. 本文引用 [1]

[59]	Meijers E, 2005. Polycentric urban regions and the quest for synergy: Is a network of cities more than the sum of the parts? Urban studies, 42(4): 765-781. 本文引用 [1]

[60]	Meijers E, 2007. From central place to network model: Theory and evidence of a paradigm change. Tijdschrift voor economische en sociale geografie, 98(2): 245-259. 本文引用 [1]

[61]	Meijers E, Hoekstra J, Aguado R, 2008. The Basque city network: An empirical analysis and policy recommendations. EUNIP International Conference, 10-12. 本文引用 [1]

[62]	Meijers E, Hoogerbrugge M, Cardoso R, 2018. Beyond polycentricity: Does stronger integration between cities in polycentric urban regions improve performance? Tijdschrift voor Economische en Sociale Geografie, 109(1): 1-21. 本文引用 [1]

[63]	Motter A E, Lai Y C, 2002. Cascade-based attacks on complex networks. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 66(6): 065102. 本文引用 [1]

[64]

X F

, Fang

C L

, Yang

Z Q

, 2022. Spatio-temporal evolution and dynamic simulation of the urban resilience of Beijing-Tianjin-Hebei urban agglomeration. Journal of Geographical Sciences, 32(9): 1766-1790.

https://doi.org/10.1007/s11442-022-2022-5

本文引用 [2] 摘要

The continuous growth of urban agglomerations in China has increased their complexity as well as vulnerability. In this context, urban resilience is critical for the healthy and sustainable development of urban agglomerations. Focusing on the Beijing-Tianjin-Hebei (BTH) urban agglomeration, this study constructs an urban resilience evaluation system based on four subsystems: economy, society, infrastructure, and ecology. It uses the entropy method to measure the urban resilience of the BTH urban agglomeration from 2000 to 2018. Theil index, standard deviation ellipse, and gray prediction model GM (1,1) methods are used to examine the spatio-temporal evolution and dynamic simulation of urban resilience in this urban agglomeration. Our results show that the comprehensive evaluation index for urban resilience in the BTH urban agglomeration followed a steady upward trend from 2000 to 2018, with an average annual growth rate of 6.72%. There are significant differences in each subsystem’s contribution to urban resilience; overall, economic resilience is the main factor affecting urban resilience, with an average annual growth rate of 8.06%. Spatial differences in urban resilience in the BTH urban agglomeration have decreased from 2000 to 2018, showing the typical characteristic of being greater in the central core area and lower in the surrounding non-core areas. The level of urban resilience in the BTH urban agglomeration is forecast to continue increasing over the next ten years. However, there are still considerable differences between the cities. Policy factors will play a positive role in promoting the resilience level. Based on the evaluation results, corresponding policy recommendations are put forward to provide scientific data support and a theoretical basis for the resilience construction of the BTH urban agglomeration.

[65]	Neal Z, 2013. Does world city network research need eigenvectors? Urban Studies, 50(8): 1648-1659. 本文引用 [1]

[66]	Parr J, 2004. The polycentric urban region: A closer inspection. Regional Studies, 38(3): 231-240. 本文引用 [1]

[67]	Rosvall M, Axelsson D, Bergstrom C T, 2010. The map equation. The European Physical Journal Special Topics, 178(1): 13-23. 本文引用 [1]

[68]	Rosvall M, Bergstrom C T, 2008. Maps of random walks on complex networks reveal community structure. Proceedings of the National Academy of Sciences, 105(4): 1118. 本文引用 [1]

[69]	Shen J F, 2002. A study of the temporary population in Chinese cities. Habitat International, 26(3): 363-377. 本文引用 [1]

[70]	Sigler T J, Martinus K, 2017. Extending beyond ‘world cities’ in World City Network (WCN) research: Urban positionality and economic linkages through the Australia-based corporate network. Environment and Planning A: Economy and Space, 49(12): 2916-2937. 本文引用 [1]

[71]	Song J H, Abuduwayiti A, Gou Z H, 2023. The role of subway network in urban spatial structure optimization: Wuhan city as an example. Tunnelling and Underground Space Technology, 131: 104842. 本文引用 [1]

[72]	Strogatz S H, 2001. Exploring complex networks. Nature, 410(6825): 268-276. 本文引用 [1]

[73]	Sun X, Liu X S, Li F et al., 2017. Comprehensive evaluation of different scale cities’ sustainable development for economy, society, and ecological infrastructure in China. Journal of Cleaner Production, 163: S329-S337. 本文引用 [1]

[74]	Swyngedouw E, 2010. Globalisation or ‘glocalisation’? Networks, territories and rescaling. Cambridge Review of International Affairs, 17(1): 25-48. 本文引用 [1]

[75]	Thompson C A, Saxberg K, Lega J et al., 2019. A cumulative gravity model for inter-urban spatial interaction at different scales. Journal of Transport Geography, 79: 102461. 本文引用 [1]

[76]	Ullman E L, 1957. American Commodity Flow. Seattle: University of Washington Press. 本文引用 [1]

[77]	Van Nuffel N, Saey P, 2005. Commuting, hierarchy and networking: The case of Flanders. Tijdschrift voor Economische en Sociale Geografie, 96(3): 313-327. 本文引用 [1]

[78]	Wall R S, Van Der Knaap G A, 2011. Sectoral differentiation and network structure within contemporary worldwide corporate networks. Economic Geography, 87(3): 267-308. 本文引用 [1]

[79]

Wang

H J

, Wu

, Deng

et al., 2022. Model construction of urban agglomeration expansion simulation considering urban flow and hierarchical characteristics. Journal of Geographical Sciences, 32(3): 499-516.

https://doi.org/10.1007/s11442-022-1958-9

本文引用 [2] 摘要

Since the launch of China’s reform and opening up policy, the process of urbanization in China has accelerated significantly. With the development of cities, inter-city interactions have become increasingly close, forming urban agglomerations that tend to be integrated. Urban agglomerations are regional spaces with network relationships and hierarchies, and have always been the main units for China to promote urbanization and regional coordinated development. In this paper, we comprehensively consider the network and hierarchical characteristics of an urban agglomeration, while using urban flow to describe the interactions of the inter-city networks and the hierarchical generalized linear model (HGLM) to reveal the hierarchical driving mechanism of the urban agglomeration. By coupling the HGLM with a cellular automata (CA) model, we introduced the HGLM-CA model for the simulation of the spatial expansion of an urban agglomeration, and compared the simulation results with those of the logistic-CA model and the biogeography-based optimization CA (BBO-CA) model. According to the results, we further analyzed the advantages and disadvantages of the proposed HGLM-CA model. We selected the middle reaches of the Yangtze River in China as the research area to conduct this empirical research, and simulated the spatial expansion of the urban agglomeration in 2017 on the basis of urban land-use data from 2007 and 2012. The results indicate that the spatial expansion of the urban agglomeration can be attributed to various driving factors. As a driving factor at the urban level, urban flow promotes the evolution of land use in the urban agglomeration, and also plays an important role in regulating cell-level factors, making the cell-level factors of different cities show different driving effects. The HGLM-CA model is able to obtain a higher simulation accuracy than the logistic-CA model, which indicates that the simulation results for urban agglomeration expansion considering urban flow and hierarchical characteristics are more accurate. When compared with the intelligent algorithm model, i.e., BBO-CA, the HGLM-CA model obtains a lower simulation accuracy, but it can analyze the interaction of the various driving factors from a hierarchical perspective. It also has a strong explanatory effect for the spatial expansion mechanism of urban agglomerations.

[80]	Wang J K, Han Q, Du Y H, 2021. Coordinated development of the economy, society and environment in urban China: A case study of 285 cities. Environment, Development and Sustainability, 24: 12917-129335. 本文引用 [1]

[81]	Wang T Y, Yue W Z, Ye X Y et al., 2020. Re-evaluating polycentric urban structure: A functional linkage perspective. Cities, 101: 102672. 本文引用 [1]

[82]	Wang Y F, 2022. Population-land urbanization and comprehensive development evaluation of the Beijing-Tianjin-Hebei urban agglomeration. Environmental Science and Pollution Research, 29(39): 59862-59871.

[83]

Wang

Z B

, Liang

L W

, Sun

et al., 2019. Spatiotemporal differentiation and the factors influencing urbanization and ecological environment synergistic effects within the Beijing-Tianjin-Hebei urban agglomeration. Journal of Environmental Management, 243: 227-239.

https://doi.org/S0301-4797(19)30555-9

https://www.ncbi.nlm.nih.gov/pubmed/31096175

本文引用 [1] 摘要

Numerous environmental problems have been seen due to the "high energy consumption, high pollution, high emissions" economic model in the Beijing-Tianjin-Hebei urban agglomeration (BTHUA). The coupling coordination degree model is applied to provide a coordination of urbanization and ecological environment composite system (CUECS) value while a geographic detector is applied to explore the dominant factors controlling it. This study reached the following conclusions. (1)The CUECS types are mainly low coordination, but which generally exhibit positive evolutionary trend. The change trends can be characterized as urbanization lags followed by system equilibrium followed by ecological environmental lags. (2)The CUECS conforms to a core-edge distributional pattern that comprises plain high mountain low, inland high coastal low. Industrialization played a key role in the development of BTHUA, the landform type was the important factor controlling CUECS. (3) Social consumer goods, gross domestic product, the disposable income of urban residents (all per capita) are the core factors controlling CUECS within different spatial units. Urbanization rate, per capita social consumer goods, the proportion of tertiary industrial population are the core factors controlling CUECS during different urbanization development stages. (4)The relative impacts of urbanization and ecological environmental subsystems on CUECS are (in decreasing order of importance) population urbanization, economic urbanization, social urbanization, ecological environment subsystem. Therefore, green urbanization remains the primary path for sustainable development within the urban agglomeration. It is unsuitable for rapid urbanization development model in the mountainous areas that encapsulate ecological and environmental security as their main functions, so the government urgently needs to amend its 'one size fits all' policy system.Copyright © 2019 Elsevier Ltd. All rights reserved.

[84]	Watts D J, Strogatz S H, 1998. Collective dynamics of ‘small-world’ networks. Nature, 393(6684): 440-442. 本文引用 [1]

[85]	Wei J, Li Z Q, Lyapustin A et al., 2021. Reconstructing 1-km-resolution high-quality PM2.5 data records from 2000 to 2018 in China: Spatiotemporal variations and policy implications. Remote Sensing of Environment, 252: 112136. 本文引用 [1]

[86]	Wei L, Luo Y, Wang M et al., 2020. Multiscale identification of urban functional polycentricity for planning implications: An integrated approach using geo-big transport data and complex network modeling. Habitat International, 97: 102134. 本文引用 [1]

[87]	Wei Y, Wang J E, Zhang S H et al., 2022. Urban positionality in the regional urban network: Through the lens of alter-based centrality and national-local perspectives. Habitat International, 126: 102617. 本文引用 [2]

[88]	Xia C, Zhang A Q, Wang H J et al., 2019. Bidirectional urban flows in rapidly urbanizing metropolitan areas and their macro and micro impacts on urban growth: A case study of the Yangtze River middle reaches megalopolis, China. Land Use Policy, 82: 158-168. 本文引用 [1]

[89]

Xie

Y S

, Wang

C J

, 2023. Spatial pattern of global submarine cable network and identification of strategic pivot and strategic channel. Journal of Geographical Sciences, 33(4): 719-740.

https://doi.org/10.1007/s11442-023-2103-0

本文引用 [1] 摘要

As a kind of large-scale connectivity infrastructure, submarine cables play a vital role in international telecommunication, socio-economic development and national defense security. However, the current understanding about the spatial pattern of global submarine cable network is relatively limited. In this article, we analyze the spatial distribution and connectivity pattern of global submarine cables, and identify their strategic pivots and strategic channels. The main conclusions are as follows: (1) The spatial distribution of global submarine cables is significantly unbalanced, which is characterized by the facts that the distribution of submarine cable lines is similar to that of sea lanes, and the agglomerations of landing stations are distributed unevenly along the coastline. (2) The connectivity pattern of global submarine cable network has a significant scale effect. At the micro, meso and macro scales, the connectivity structure presents chain model, cluster model and hub-and-spoke model, respectively. (3) The distribution of strategic pivots and strategic channels shows a pyramidal hierarchical feature. Singapore ranks highest among all the strategic pivots, while the Gulf of Aden and the Strait of Malacca rank highest among the strategic channels. Based on the identification of strategic pivots and channels, six strategic regions have been divided, which face various network security risks and need special attention and vigilance.

[90]	Xu H Z, Jiao M, 2021. City size, industrial structure and urbanization quality: A case study of the Yangtze River Delta urban agglomeration in China. Land Use Policy, 111: 105735. 本文引用 [1]

[91]

Yang

L J

, Wang

, Yang

Y C

, 2022. Spatial evolution and growth mechanism of urban networks in western China: A multi-scale perspective. Journal of Geographical Sciences, 32(3): 517-536.

https://doi.org/10.1007/s11442-022-1959-8

本文引用 [1] 摘要

Globalization and informatization promote the evolution of urban spatial organization from a hierarchical structure mode to a network structure mode, forming a complex network system. This study considers the coupling of “space of flows” and “spaces of places” as the core and “embeddedness” as the link and a relevant theoretical basis; then we construct a conceptual model of urban networks and explore the internal logic of enterprise networks and city networks. Using the interlocking-affiliate network model and data from China’s top 500 listed companies, this study constructs a directed multi-valued relational matrix between cities in western China from 2005 to 2015. Using social network analysis and the multiple regression of quadratic assignment program model (MRQAP), this study adopts a “top-down” research perspective to analyze the spatio-temporal evolution and growth mechanism of the city network in western China from three nested spatial scales: large regions, intercity agglomerations, and intracity agglomerations. The results show the following: (1) Under the large regional scale, the city network has good symmetry, obvious characteristics of hierarchical diffusion, neighborhood diffusion, and cross-administrative regional connection, presenting the “core-periphery” structural pattern. (2) The network of intercity agglomerations has the characteristics of centralization, stratification, and geographical proximity. (3) The internal network of each urban agglomeration presents a variety of network structure modes, such as dual-core, single-core, and multicore modes. (4) Administrative subordination and economic system proximity have a significant positive impact on the city network in western China. The differences in internet convenience, investment in science and technology, average time distance, and economic development have negative effects on the growth and development of city networks. (5) The preferential attachment is the internal driving force of the city network development.

[92]	Ye C, Zhu J J, Li S M et al., 2019. Assessment and analysis of regional economic collaborative development within an urban agglomeration: Yangtze River Delta as a case study. Habitat International, 83: 20-29. 本文引用 [1]

[93]	Zhang D N, Chen Y, 2021. Evaluation on urban environmental sustainability and coupling coordination among its dimensions: A case study of Shandong Province, China. Sustainable Cities and Society, 75: 103351. 本文引用 [1]

[94]	Zhang F, Ning Y M, Lou X Y, 2021. The evolutionary mechanism of China’s urban network from 1997 to 2015: An analysis of air passenger flows. Cities, 109: 103005. 本文引用 [2]

[95]	Zhang L, Xu Y, Yeh C-H et al., 2016. City sustainability evaluation using multi-criteria decision making with objective weights of interdependent criteria. Journal of Cleaner Production, 131: 491-499. 本文引用 [1]

[96]	Zhang P F, Zhao Y Y, Zhu X H et al., 2020. Spatial structure of urban agglomeration under the impact of high-speed railway construction: Based on the social network analysis. Sustainable Cities and Society, 62: 102404. 本文引用 [1]

[97]	Zhang W J, Gong Z Y, Niu C C et al., 2022a. Structural changes in intercity mobility networks of China during the COVID-19 outbreak: A weighted stochastic block modeling analysis. Computers, Environment and Urban Systems, 96: 101846. 本文引用 [1]

[98]	Zhang X Y, Wang H, Ning X G et al., 2022b. Identification of metropolitan area boundaries based on comprehensive spatial linkages of cities: A case study of the Beijing-Tianjin-Hebei region. ISPRS International Journal of Geo-Information, 11(7): 396. 本文引用 [1]

[99]

Zhen

, Qin

, Ye

X Y

et al., 2019. Analyzing urban development patterns based on the flow analysis method. Cities, 86: 178-197.

https://doi.org/10.1016/j.cities.2018.09.015

本文引用 [2] 摘要

Analyzing patterns of urban development should consider the network structure among cities as well as the formation of the function and role of each city in the network. The flow analysis of various factors between cities is based on urban network and space of flow theories. This study used Hebei Province of China as the case. The comprehensive status of each city in the regional urban network was measured by simulating the economic, information, traffic, and financial flow among cities. Results indicate that the development pattern can be divided into three levels with a multi-core and multi-node network structure. In addition, the flow analysis method can predict 67% of urban developmental level. Furthermore, some policy recommendations are put forward to facilitate regional integrated development in Hebei province.

[100]

Zhong

, Arisona

S M

, Huang

X F

et al., 2014. Detecting the dynamics of urban structure through spatial network analysis. International Journal of Geographical Information Science, 28(11): 2178-2199.

本文引用 [1]

[101]

Zhu

Y H

, Yang

, Lin

J P

et al., 2022. Spatial and temporal evolutionary characteristics and its influencing factors of economic spatial polarization in the Yangtze River Delta region. International Journal of Environmental Research and Public Health, 19(12): 6997.

本文引用 [1]

[102]

Zou

, Ou

X J

, Tan

J T

, 2019. Temporal and spatial characteristics and early warning analysis of economic polarization evolution: A case study of Jiangsu province in China. Sustainability, 11(5): 1339.

本文引用 [1]

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Abstract
Key words
引用本文
1 Introduction
2 Literature review
3 Study area and data sources
3.1 Study area
Figure 1 Location of the study area (Beijing-Tianjin-Hebei region)
3.2 Data source and preprocessing
Table 1 Research data sources and description
4 Research methods
Figure 2 Research framework
4.1 Construction of the urban network
4.1.1 Theoretical foundation
Figure 3 Interaction of the social, economic and environmental subsystems
4.1.2 Evaluation indicator system construction
Table 2 The indicator system for evaluating the comprehensive development level of the ESE of cities
4.2 Analysis of network characteristics
Table 3 Overall and individual network indicators
4.3 Analysis of network structure evolution
4.4 Analysis of network robustness
Table 4 Network robustness evaluation indicator system
5 Results
5.1 Network development evaluation
Figure 4 Evolution of various networks in the Beijing-Tianjin-Hebei region from 2015-2019
5.2 Analysis of network characteristics
5.2.1 Overall network characteristics analysis of the BTH region
Table 5 Overall network structure characteristics
5.2.2 Individual network characteristics analysis of the BTH region
Figure 5 Network centrality differences among different subsystems in the Beijing-Tianjin-Hebei region from 2015 to 2019
5.3 Analysis of network structure evolution
Figure 6 Evolution of various networks in the Beijing-Tianjin-Hebei region from 2015-2019 (Note: Different colours represent different clusters, and the width size represents the number of city transfers.)
Figure 7 Results of city clustering in different dimensions in the Beijing-Tianjin-Hebei region from 2015-2019 (Note: Different classes represent different urban clusters.)
5.4 Analysis of network robustness
5.4.1 Robustness of the urban network structure under different attack methods
Figure 8 Variations in network robustness characteristic value under different node attack methods
5.4.2 Identification of the core network and key nodes
Figure 9 Multidimensional core network in the Beijing-Tianjin-Hebei region (Note: Different levels represent the contact strength, where the first level is the highest; the grading criteria are the same as those in Figure 4.)
Figure 10 Core nodes of the multidimensional network in the Beijing-Tianjin-Hebei region at county level
6 Discussion
6.1 Effectiveness of the BTH coordinated development
6.2 Coordinated development policy suggestions
6.3 Limitations
7 Conclusions
Supplementary material (Notations)
参考文献

收稿日期	接受日期	出版日期
2023-07-29	2024-03-05	2024-05-25
发布日期
2024-05-31

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1 Introduction

2 Literature review

3 Study area and data sources

3.1 Study area

Figure 1 Location of the study area (Beijing-Tianjin-Hebei region)

3.2 Data source and preprocessing

Table 1 Research data sources and description

4 Research methods

Figure 2 Research framework

4.1 Construction of the urban network

4.1.1 Theoretical foundation

Figure 3 Interaction of the social, economic and environmental subsystems

4.1.2 Evaluation indicator system construction

Table 2 The indicator system for evaluating the comprehensive development level of the ESE of cities

4.2 Analysis of network characteristics

Table 3 Overall and individual network indicators

4.3 Analysis of network structure evolution

4.4 Analysis of network robustness

Table 4 Network robustness evaluation indicator system

5 Results

5.1 Network development evaluation

Figure 4 Evolution of various networks in the Beijing-Tianjin-Hebei region from 2015-2019

5.2 Analysis of network characteristics

5.2.1 Overall network characteristics analysis of the BTH region

Table 5 Overall network structure characteristics

5.2.2 Individual network characteristics analysis of the BTH region

Figure 5 Network centrality differences among different subsystems in the Beijing-Tianjin-Hebei region from 2015 to 2019

5.3 Analysis of network structure evolution

Figure 6 Evolution of various networks in the Beijing-Tianjin-Hebei region from 2015-2019 (Note: Different colours represent different clusters, and the width size represents the number of city transfers.)

Figure 7 Results of city clustering in different dimensions in the Beijing-Tianjin-Hebei region from 2015-2019 (Note: Different classes represent different urban clusters.)

5.4 Analysis of network robustness

5.4.1 Robustness of the urban network structure under different attack methods

Figure 8 Variations in network robustness characteristic value under different node attack methods

5.4.2 Identification of the core network and key nodes

Figure 9 Multidimensional core network in the Beijing-Tianjin-Hebei region (Note: Different levels represent the contact strength, where the first level is the highest; the grading criteria are the same as those in Figure 4.)

Figure 10 Core nodes of the multidimensional network in the Beijing-Tianjin-Hebei region at county level

6 Discussion

6.1 Effectiveness of the BTH coordinated development

6.2 Coordinated development policy suggestions

6.3 Limitations

7 Conclusions

Supplementary material (Notations)

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参考文献

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