Identifying Spatiotemporal Patterns of Multiscale Connectivity in the Flow Space of Urban Agglomeration in the Yellow River Basin

Abstract

The United Nations Sustainable Development Goals (SDGs) and the rise of global sustainability science have led to the increasing recognition of basins as the key natural geographical units for human–land system coupling and spatial coordinated development. The effective measurement of spatiotemporal patterns of urban connectivity within a basin has become a key issue in achieving basin-related SDGs. Meanwhile, China has been actively working toward co-ordinated regional development through in-depth implementation of the Yellow River Basin’s ecological protection and high-quality development. Urban connectivity has been trending in urban planning, and significant progress has been made on different scales according to the flow space theory. Nevertheless, few studies have been conducted on the multiscale spatiotemporal patterns of urban agglomeration connectivity. In this study, the urban network in the Yellow River Basin was constructed using Tencent population migration data from 2015 and 2019. It was then divided into seven distinct communities to enable analysis at both the basin and community scales. Centrality, symmetry, and polycentricity indices were employed, and the multiscale spatiotemporal patterns of urban agglomerations in the Yellow River Basin were identified using community detection, complex networks, and the migration kaleidoscope method. Community connectivity was notably concentrated at the basin scale with a centripetal pattern and spatial heterogeneity. Additionally, there was a symmetrical and co-ordinated relationship in population migration between the eastern and western regions of the basin, as well as between the internal and external parts of the basin. At the community scale, there was significant variation in the extent of central agglomeration among different communities, with few instances of similar-level, long-distance, and interregional bilateral links. The utilization of multiscale spatiotemporal patterns has the potential to enhance the comprehension of economic cooperation between various cities and urban agglomerations. This understanding can aid decision-makers in formulating sustainable development policies that foster the spatial integration of the basin.

1. Introduction

In the context of globalization and informatization, transformations to the network paradigm are occurring in urban relations. With the continuous development of regional transportation and information infrastructure, the effect of space–time compression between cities has become increasingly significant, and various elements are frequently exchanged between cities across physical distances, thus allowing “flow space” [1,2]. Combining the “flow space” theory with the study of world cities to address the “attributes but not connections” limitation, Taylor innovatively used inter-enterprise relational data to research world city networks [3]. Since then, many scholars have used multisource data, such as traffic flow [4,5,6], population flow [7,8], information flow [9,10,11], and enterprise flow [12,13,14], to describe the urban network structure, functional connections between cities, organizational models, and impact mechanisms from different dimensions. Most of these studies have focused on the hierarchical differences in urban connection strength; however, the description of the connection direction needs to be further expanded. Using the gravity model, Chen et al. [15] simulated and analyzed the directional characteristics of interactions among cities. Alderson et al. [16] investigated the prestige and power of different cities in the world’s urban system through in-degree and out-degree. To characterize the asymmetry of intercity element exchanges, the concepts and quantification methods, such as node symmetry and link symmetry, were proposed to compensate for the limitation in research on urban networks, i.e., “emphasizing the strength of connection and neglect the direction of connection” [17].

The network embedding ability of cities (clusters) in multiscale regions has attracted increasing attention. The functional connections of cities in multiscale areas are not completely independent, and the interactive networking of enterprises within cities helps to improve the status of cities in the global network, which in turn can attract more elements to a city, resulting in a strong multiplier effect [18]. Urban agglomerations have gradually become the basic unit in which countries participate in global competitions and have come to play an important role in shifting the world’s economic center of gravity. Many studies have focused on the spatial connections among cities at different scales and within urban agglomerations. Ni et al. [19] measured the strength of Chinese cities’ external connections and the connection levels in the global city network on a global scale based on the office locations of multinational corporations. Some scholars have quantitatively analyzed China’s urban network and urban connections nationally based on the geographical distribution of the headquarters and branches of large financial enterprises such as banks within the country [20,21]. Additionally, the spatial connections within urban agglomerations are primarily concentrated in more mature urban agglomerations, such as the Yangtze River Delta, the Pearl River Delta, and the Bei**g–Tian**–Hebei region. Few multiscale studies analyzing urban agglomeration connections use agglomerations as the base unit. Fortune China Top 500 Enterprises data have been used to analyze the spatial connections between 19 urban agglomerations and 41 major cities in China [22]. Zhao and Cao et al. [23,24] conducted in-depth research on the functional differentiation and interaction effects of cross-scale networks in urban agglomerations. Hu et al. [25] analyzed the spatial structure, scale structure, and network node structure among five urban agglomerations, i.e., the Yangtze River Delta, the Pearl River Delta, Bei**g–Tian**–Hebei, the middle reaches of the Yangtze River, and Chengdu–Chongqing, based on origin–destination (OD) data on China’s railways.

Due to the constraints of traditional localism and the “administrative area economy”, regional units often physically separate the integrity of the natural geographical units set by mobile resource elements, resulting in the fragmentation of regional governance and imbalances in social, economic, and environmental development [26,27]. To meet the need for high-quality development and ecological civilization construction, the Chinese government has attached increasing importance to the high-quality development of natural geographical units, such as deltas, bay areas, and basins. To study urban networks, administrative, azimuth, type, and policy areas have been expanded to geographic unit areas dominated by natural geographical or system units [28,29]. In 2019, as a major national strategy, China proposed the ecological protection and high-quality development of the Yellow River Basin. However, the basin still faces problems, such as insufficient overall development, unbalanced regional development, and insufficient innovation and radiation ability of central cities. It is necessary to scientifically analyze the multiscale network connections of the Yellow River Basin urban agglomerations, clarify the functional positioning of the core cities and urban agglomerations, promote the spatial integration of urban agglomerations with network integration, and provide a more effective spatial organization foundation for the implementation of ecological protection and high-quality development strategies in the Yellow River Basin than there are at present [30]. This paper focuses on identifying spatiotemporal patterns in multiscale connectivity in urban networks. Based on the Tencent population migration data in 2015 and 2019, the network was constructed and then divided into communities, allowing for analysis at both the basin and community scales. Centrality, symmetry, and polycentricity indices were employed, and the multiscale spatiotemporal patterns of urban agglomerations in the Yellow River Basin were identified using community detection, complex networks, and the migration kaleidoscope method.

The remainder of this paper is organized as follows. Section 2 describes our study area and data. Section 3 introduces the methodology frameworks. Section 4 examines the spatiotemporal patterns in multiscale connectivity on the flow space of urban agglomerations in the Yellow River Basin. Section 5 discusses the paper’s findings. Section 6 provides a concise summary of the paper.

2. Study Area and Data

2.1. Study Area

The Yellow River Basin is the birthplace of Chinese civilization. It spans China’s three major economic zones and nine provincial-level administrative regions from west to east, with a total length of 5464 km and a basin area of 795,000 km². The overall development level of the Yellow River Basin is low, and the regional development is imbalanced [31]. By the end of 2021, the permanent population of the nine provinces along the river was 420 million, accounting for 29.79% of the national total; the regional gross domestic product (GDP) was CNY 28.7 trillion, accounting for 24.97% of the national GDP; the per capita GDP in the basin was CNY 68,000, which was CNY 12,000 lower than the national average; and the range in the provincial per capita GDP of the nine provinces was CNY 44,000. The urban agglomerations that support the high-quality development of the Yellow River Basin present a “3 + 4” spatial organization pattern [32]; the Shandong peninsula urban agglomeration, Central Plain urban agglomeration, and Guanzhong Plain urban agglomeration are three regional urban agglomerations with a relatively high degree of development and are distributed in the middle and lower reaches of the Yellow River. The **zhong urban agglomeration, Hubao–Eyu urban agglomeration, Ningxia urban agglomeration, and Lanxi urban agglomeration are four local urban agglomerations that are relatively poorly developed and are distributed in the middle and upper reaches of the Yellow River. Based on the scope of the Yellow River Basin delimited by the Yellow River Conservancy Commission (YRCC) of the Ministry of Water Resource, China, the study area includes 68 prefecture-level cities (autonomous prefectures and leagues) in nine provinces (autonomous regions), i.e., Shandong, Henan, Shanxi, Shaanxi, Inner Mongolia, Ningxia, Gansu, Qinghai, and Sichuan. Due to the administrative regions of these 68 cities overlap** with the scope of the basin, they are defined as cities within the basin. On the contrary, 295 cities with no overlap between the administrative regions and the basin scope were identified as cities outside the basin. We employed boundary data from the Resource and Environment Science and Data Center of the Chinese Academy of Sciences (https://www.resdc.cn/ (accessed on 1 June 2022)) to create Figure 1.

2.2. Data Sources and Processing

To comprehensively reveal the spatial connections among cities and urban agglomerations of different scales in the Yellow River Basin, in this study, the top ten migration data for 363 cities in 2015 and 2019 with various modes of transportation, such as rail, road, and air (from 1 January to 30 June) were crawled on the Tencent Location Big Data service platform (https://heat.qq.com/qianxi.php (accessed on 5 June 2022)). Tencent, a prominent Internet corporation in China, holds significant influence within the digital landscape and boasts a broad user base encompassing nearly all Chinese smartphone users. In December 2019 and June 2023, Tencent WeChat had 1.151 and 1.327 billion monthly active user accounts, respectively. In other words, most of China’s population uses WeChat at least once a month (https://www.statista.com/statistics/255778/number-of-active-wechat-messenger-accounts (accessed on 5 June 2022)). The dataset captures the mobile trajectory of users’ travel patterns, making it well-suited for assessing the intercity migration of the population in the Yellow River Basin [33]. The data attributes include the year, o_code, o_city, d_code, d_city, busvalue, trainvalue, airvalue, and allvalue. Gephi software was employed to merge the inflow and outflow population migration data, and the standardized “allvalue” was selected to represent the strength of intercity connections [34,35]. Consequently, 16,162 directed connections in 2015 and 19,678 in 2019 were obtained (

Table 1. Samples of Tencent location big data.

2015			2019
o_code	d_code	Allvalue	o_code	d_code	Allvalue
623000	360100	24,703	620200	410100	16,208
623000	360700	1705	620200	620700	321,661
620400	61010	157,470	62040	61010	197,850
···	···	···	···	···	···

and

Table 2. Detailed description of the migration data.

Year	Inside the Basin			Outside the Basin
	Cities	Intercity Connections	External Connections of Cities	Cities	Intercity Connections
2015	68	898	3106	295	12,158
2019	68	852	3480	295	15,346

). The connection from o_city to d_city is regarded as an outflow connection, while the connection from d_city to o_city is regarded as an inflow connection [36]. Both o_city and d_city are located inside the basin, thus classifying this urban connection as intercity connections inside the basin (898 records in 2015 and 852 records in 2019). If only one of o_city or d_city is inside the basin, this urban connection is identified as the external connection of cities inside the basin (3106 records in 2015 and 3480 records in 2019). If neither o_city nor d_city is inside the basin, this urban connection is identified as the intercity connection of cities outside the basin (12,158 records in 2015 and 15,346 records in 2019) [37]. In addition, in January 2019, **an City and Laiwu City merged to form the new **an City. To maintain the coherence and accuracy of the data, in this study, Laiwu City is still regarded as a separate prefecture-level city. The AMap platform (https://ditu.amap.com/ (accessed on 20 June 2022)) provides POI data from 363 city government sites. Taking POI as the network nodes and urban population migration as the network connections, we constructed a multiscale-directed network of urban agglomeration in the Yellow River Basin.

3. Methodology

The study framework is shown in Figure 2. Based on the urban POI data and Tencent population migration data from 2015 and 2019, a directed urban network in the Yellow River Basin is constructed. Second, the Louvain algorithm is used to identify the community structure of the urban network, and two network analysis scales of basin and community are formed. Finally, with communities and cities as analysis units, the indices of centrality, symmetry, and polycentricity are used to reflect the strength, direction, and equilibrium of the internal and external connections of the basin and community. Combined with spatial analysis and migration kaleidoscope visualization, the multiscale spatiotemporal patterns of urban agglomeration connections in the Yellow River Basin are identified.

3.1. Community Detection

In a complex network, a community refers to a network cluster with closely connected internal nodes and a specific organizational relationship; these network clusters embody the functional attributes of the system, and their essential characteristics are “high cohesion” and “low coupling” [38]. Community is sometimes referred to as “clustering” in sociology and computer science [39]. In urban geography, scholars use community to describe tightly connected urban groups [34,40]. The current mainstream community detection algorithms include Girvan–Newman, Fast-greedy, Label Propagation, Louvain, and Infomap. Among these, the Louvain algorithm proposed by Blondel et al. is based on graph clustering to optimize modularity at multiple levels and can effectively extract the inherent community structure in the mobile network [41]. Unlike other community detection algorithms, Louvain’s algorithm divides the community under the condition of unsupervised classification, which does not limit the number of communities, and its community detection results have high objectivity and practicability [42]. Modularity is usually used to measure the quality of community division; the formula is as follows:

$$\mathrm{Q}=\frac{1}{2\mathrm{m}}\sum _{\mathrm{ij}}\left({\mathrm{A}}_{\mathrm{i}\mathrm{j}}-\frac{{\mathrm{k}}_{\mathrm{i}}{\mathrm{k}}_{\mathrm{j}}}{2\mathrm{m}}\right)\delta ({\mathrm{c}}_{\mathrm{i}}-{\mathrm{c}}_{\mathrm{j}})$$

(1)

where $\mathrm{m}$ is the total number of links in the network, ${\mathrm{A}}_{\mathrm{ij}}$ is the flow from node $\mathrm{i}$ to node $\mathrm{j}$, ${\mathrm{k}}_{\mathrm{i}}$ is the degree of node $\mathrm{i}$, ${\mathrm{C}}_{\mathrm{i}}$ represents an assigned community of node $\mathrm{i}$, and $\mathrm{Q}$ is modularity. The closer the value is to 1, the more pronounced the network’s community structure and the better the division’s quality.

3.2. Centrality and Symmetry

Centrality and symmetry describe the multiscale network connection characteristics of the urban agglomeration in the Yellow River Basin from the strength and direction. Centrality is the sum of in-degree and out-degree and is used to reflect the status of cities and urban agglomerations in the network. The urban network of the Yellow River Basin is a directed weighted network. The in-degree and out-degree mentioned in this paper are the weighted in-degree and weighted out-degree, respectively. Limtanakool et al. [17,43] used symmetry to characterize the element relationships between cities and embody the flow elements’ directional attributes. Node symmetry describes the symmetrical relationship between the in-degree and the out-degree of a city; the formula is as follows:

$$\mathrm{NS}{\mathrm{I}}_{\mathrm{i}}=\frac{\sum {\mathrm{I}}_{\mathrm{i}}-\sum {\mathrm{O}}_{\mathrm{i}}}{\sum {\mathrm{I}}_{\mathrm{i}}+\sum {\mathrm{O}}_{\mathrm{i}}},$$

(2)

where ${\mathrm{I}}_{\mathrm{i}}$ is the in-degree of city $\mathrm{i}$, ${\mathrm{O}}_{\mathrm{i}}$ is the out-degree of city $\mathrm{I}$, and $\mathrm{NS}{\mathrm{I}}_{\mathrm{i}}$ is the nodal symmetry of city $\mathrm{i}$, with a range of $[-1,1]$. The more the node symmetry tends toward 0, the more symmetrical the node; if the node symmetry is greater than 0, there is a net inflow of the population, and if the node symmetry is less than 0, there is a net outflow of the population.

Link symmetry identifies the asymmetry level of urban links. To highlight the advantages of link symmetry in vector descriptions, the link symmetry modified by Liu Zheng [36] is used. The formula is:

$$\mathrm{LS}{\mathsf{\Gamma }}_{\mathrm{ij}}=2{\mathrm{f}}_{\mathrm{ij}}-1,$$

(3)

where ${\mathrm{f}}_{\mathrm{ij}}$ is the flow ratio from node $\mathrm{i}$ to node $\mathrm{j}$ to the total flow between the two nodes. When $\mathrm{LS}{\mathsf{\Gamma }}_{\mathrm{ij}}<0$, the flow from node $\mathrm{i}$ to node $\mathrm{j}$ is smaller than the flow from node $\mathrm{j}$ to node $\mathrm{i}$; when $\mathrm{LS}{\mathsf{\Gamma }}_{\mathrm{ij}}=0$, there is a bidirectional equivalent flow, and when $\mathrm{LS}{\mathsf{\Gamma }}_{\mathrm{ij}}>0$, the flow from node $\mathrm{i}$ to node $\mathrm{j}$ is larger than the flow from node $\mathrm{j}$ to node $\mathrm{i}$. The range of $\mathrm{LS}{\mathsf{\Gamma }}_{\mathrm{ij}}$ is $[-1,1]$.

3.3. Polycentricity

Polycentricity is mainly employed as a metric to assess the level of equilibrium in the interconnections within an urban network. The measurement of polycentricity in scholarly research is primarily conducted through two methods: rank-size regression analysis on city centrality, as demonstrated by Burger and Meijers [44,45], or the utilization of the Gini coefficient, as explored by Huang et al. [46] and Li et al. [47]. However, these approaches have not adequately captured the polycentricity structure in terms of network interactions. Asymmetry is a defining feature of urban systems that are fully monocentric, wherein specialized functions are concentrated in a limited number of cities that solely receive flows without reciprocating them. On the other hand, symmetry characterizes fully polycentric systems, where the absence of dominant nodes in the network allows for horizontal flows of elements [17,48,49]. Hence, polycentricity may also be articulated as follows:

$$\mathrm{P}=1-\frac{\left|\sum _{\mathrm{i}=1}^{\mathrm{n}}\mathrm{NS}{\mathrm{I}}_{\mathrm{i}}\right|}{\mathrm{n}},$$

(4)

where $\mathrm{NS}{\mathrm{I}}_{\mathrm{ij}}$ is the node symmetry for city $\mathrm{i},$ and $\mathrm{P}$ is polycentric, with a range of $[0,1]$. The closer the value is to 1, the stronger the polycentricity is.

3.4. Migration Kaleidoscope

Chordal graphs have gained significant attention in the study of network topology in recent years [50,51,52]. However, these graphs do not provide a comprehensive representation of the directional and multilevel linkages inherent in complex network connections. Hence, this study employs the migration kaleidoscope developed by Gu et al. [53] to integrate the Voronoi-based kaleidoscope for network topology visualization. This approach aims to depict the comparative position of each node within the network as either an origin or a destination, thereby facilitating an understanding of the spatiotemporal evolution of urban network connections from multiple scales, regions, and periods.

4. Results

4.1. Urban Network Community Detection

The modularity values obtained by utilizing Gephi software for community detection in 2019 reveal a maximum modularity of 0.698 for in-basin communities and 0.491 for outside-basin communities (

Table 3. Results of community detection.

Year	Inside the Basin		Outside the Basin
	Number of Communities	Modularity	Number of Communities	Modularity
2015	7	0.708	8	0.380
2019	7	0.698	10	0.491

). These findings indicate the presence of distinct community structures within the Yellow River basin network and its surrounding areas. The basin consists of seven communities, namely, **an, Zhengzhou, Taiyuan, ** capacity have resulted in a relatively diminished network connectivity inside the basin. Consequently, the central region’s significance is more pronounced than that of other areas, with **’an and **’an community emerging as the primary hubs for intercity and intercommunity connectivity inside the basin. It is imperative for the **’an and **’an communities to leverage their pivotal positions and actively contribute to the holistic advancement of the surrounding regions. There is a need to enhance the division of urban functions, particularly by reinforcing the division of labor among core cities and core communities situated in the middle and lower sections of the river. Additionally, it is imperative to expedite the development and establishment of metropolitan areas surrounding the core cities located in the upper reaches of the Yellow River Basin. Finally, it is crucial to strengthen the interconnectivity and collaboration between cities and communities inside the basin by leveraging the transportation axes.

An analysis of the external connectivity of basin communities shows that the communities of **an, Zhengzhou, and **’an, located in the middle and lower reaches of the basin, exhibit higher connectivity with external cities. Conversely, the communities situated in the middle and upper reaches of the basin, as well as those with east–west external links, demonstrate comparatively low levels of external connectivity. Hence, it is imperative to fully leverage the potential of the **an community seaward corridor and the Zhengzhou community transport hub, thus enhancing the core city’s capacity for acting as a leader and driving regional development. This would be an endeavor that aims to establish a nationally significant economic growth center and facilitate stronger external connections for the basin. The **’an community is a crucial point for expanding toward the western region. The community aims to enhance its collaborative advantages and foster synergistic development with neighboring areas. Additionally, the **’an community seeks to reinforce its role as a gateway to the Silk Road, facilitating connectivity among communities in the basin, particularly in the east–west direction.

6. Conclusions

Promoting integrated development inside the Yellow River Basin is an essential prerequisite for achieving co-ordinated development inside the basin. The paper utilizes Tencent’s population migration data from 2015 and 2019 to establish an urban connectivity network within the Yellow River Basin. The Louvain algorithm is employed to identify the community structure within this network. Subsequently, cities and communities are selected as analysis units to conduct multiscale analysis on the internal and external network connections, as well as on the evolutionary characteristics of these different analysis units. There are seven urban communities in the Yellow River Basin with close internal organization and few external connections. Most of these communities follow the provincial administrative boundaries, showing strong administrative area economic characteristics; furthermore, the divided urban communities and agglomerations in the Yellow River Basin’s middle and lower reaches are relatively consistent. The connection tightness between communities gradually increases.

The network connectivity is detailed at two different scales. At the basin scale, the community network exhibits a pronounced centripetal concentration and notable spatial heterogeneity. The **’an community serves as the central hub inside the community network, with the first links of the Zhengzhou, Taiyuan, Lanxi, and Yinchuan communities converging toward the **’an community. Over time, the **’an community has experienced the emergence of external radiation phenomena, resulting in a drop in node symmetry from 0.41 to 0.36. The Zhengzhou and **an communities, located in the middle and lower regions of the basin, exhibit relatively low network centrality. However, they demonstrate a strong capacity for external connections and clear traffic orientation characteristics. There has been a notable enhancement in the capacity of communities located in the middle and upper regions of the basin to establish connections with communities outside the basin. A trend of population backflow occurs in the middle and upper reaches of the basin. At the community scale, each community has obvious centripetal agglomeration characteristics, and the connections mostly point to provincial capitals or economically developed cities. The central agglomeration of different communities varies greatly. The Lanxi, **’an, **an, and Zhengzhou communities show apparent single-center agglomeration, and the central agglomeration of Yinchuan and Hohhot in the middle and upper reaches is relatively weak; the network connection shows a weak dual-center structure. For the external connection of community cities, there is an overall network connection pattern of a single-center agglomeration in **’an. The external connections are mainly concentrated in the border cities of the community and show obvious connection symmetry.

This paper provides a reference for clarifying the functional positioning of core cities and urban agglomerations in the Yellow River Basin and promoting the development of spatial integration. However, to gain more insights and arrive at more conclusions, further studies of the following three topics should be performed: (i) the dynamic changes in network connections from an evolutionary process perspective, (ii) the identification of influence factors for the urban network connections in the Yellow River Basin, and (iii) the interaction of these factors on urban network connections and quantitative outcomes.