
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)13654-7
10.1016/j.heliyon.2024.e37623
e37623
Research Article
Analysis of spatial-temporal evolution and investment model of industrial cross-regional investment network-taking the Pearl River Delta urban agglomeration as an example
Tan Youwei ae
Wang Yiting d
Duan Lipeng a
Gu Zhihui gzh@email.szu.edu.cn
abc⁎
a School of Architecture & Urban Planning, Shenzhen University, Shenzhen, 518060, China
b State Key Laboratory of Subtropical Building and Urban Science, Shenzhen, 518060, China
c Shenzhen Key Laboratory of Building Environment Optimization Design, Shenzhen, 518060, China
d Xinqiao Sub district Office of Bao'an District of Shenzhen, Shenzhen, 518125, China
e Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, 999077, China
⁎ Corresponding author. School of Architecture & Urban Planning, Shenzhen University, Shenzhen, 518060, China. gzh@email.szu.edu.cn
07 9 2024
15 9 2024
07 9 2024
10 17 e3762315 3 2024
12 8 2024
6 9 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cross-regional investment behavior plays a pivotal role in enterprise development and regional economic growth. Nonetheless, existing investment network analyses often adopt a broad perspective, most studies tend to invest in network models and focus on a particular industry, and pay less attention to investment models in different industries. Therefore, this paper will combine the dual perspectives of space and network to observe the spatial and temporal evolution characteristics of enterprise investment and its investment model. Additionally, it delves into the unique features of investment networks within various industries at the district and county levels. The results show that enterprise investment agglomeration exhibits a development pattern characterized by points, bands, and surfaces, with a notable distance attenuation trend in investment distances. The overall structure of the industry investment network showcases characteristics of being multi-centered and multi-nodal. The investment models across different industries can be categorized into four distinct types. The research conclusion is of great significance to optimize multi-scale intercity investment, realize industrial gradient transfer and promote the coordinated development of industry.

Keywords

Capital flow
Intercity investment
Space-time characteristics
Investment network
==== Body
pmc1 Introduction

With the development of economic globalization and regional integration, Urban development has shifted from ' space of location ' relying on functional characteristics to ' space of flow ' based on network connection [1,2], and provides externalities [3,4] through complementarity and synergy between different levels of urban nodes. In particular, the urban network constructed based on the network traffic index makes the connection between cities more complex and forms different urban network spatial characteristics [5,6]. For example, in the network of innovation and technology network, the spatial form is mostly a significant core edge structure and presents the dual characteristics of aggregation and dispersion [7]. The traffic network has obvious spatial distribution heterogeneity, and the city node level is clear, showing a significant relationship with the city level [8].

At present, the research perspective of urban network mainly focuses on transportation, information, population, innovation and other networks [9]. In the formation of urban networks, enterprises are often the main body of economic activities [10,11], while other transportation, innovation, information, and personnel exchanges are often based on enterprise connections [12]. Based on the perspective of investment linkage, urban network development can better reflect the ability of urban industries to radiate outward and the ability of surrounding cities to accept radiation [13]. In recent years, the phenomenon of enterprise investment behavior crossing geographical factors has become more and more significant, and the investment network formed has become more and more complex [14]. In this context, the type and number of enterprises are growing rapidly, forming a research trend based on cross-regional investment [15].

The predominant approach in urban network studies, from an enterprise perspective, involves utilizing data related to departmental structures within enterprises to translate the quantity and hierarchy of headquarters and branches (subsidiaries) into the strength of inter-city connections [16]. Existing research primarily constructs urban networks by considering factors such as the spatial relationships between enterprise headquarters and branches, as well as enterprise-specific or industry-specific networks [17,18]. These studies often delve into analyzing various facets of the industrial investment network [19], the roles of node cities, regional investment patterns, and their evolution [20]. However, the current research has the following shortcomings. First of all, most of the research is based on the internal links of enterprises to build urban networks, and there has been limited research conducted at the actual inter-enterprise connection level. This is partly because each enterprise will invest abroad or receive financing, which makes it difficult to collect data. Secondly, most of the existing research tends to focus on the characteristics of the entire industry or a specific industry's investment network within a city [21], with relatively few comparative studies conducted on the industrial investment networks across different sectors.

Hence, this study leverages big data and enterprise investment data from the Pearl River Delta (PRD) in 2020 to establish an investment database for the PRD urban agglomeration. It selects key research industries and investigates the spatial distribution and network structure of enterprises interconnecting across various sectors. The primary research questions addressed in this paper are as follows: (1) investigate the overarching spatial and network evolution patterns in industrial investment within the PRD urban agglomeration across different time periods. Additionally, analyze the spatial attributes and network connectivity characteristics of inter-city investments within key industries. (2) examine the changes occurring in the overall industrial investment model within the PRD urban agglomeration and synthesize the investment models specific to key industries. Enterprise cross-regional investments serve as indicators of industry development directions and transfer trends. Understanding the spatial and network attributes of actual economic activities undertaken by enterprises can provide valuable strategic insights for future efforts in division of labor, coordinated development, and bolstering the core influence of urban agglomerations.

The rest of this article is organized as follows. The literature review summarizes the research progress and existing problems of investment network. The data and method section introduces the enterprise investment data and usage methods used in this paper. The results part introduces the investment space-network characteristics and investment models of enterprises in the PRD. The discussion part compares the results of this study with the existing research results from the perspective of urban network and flow space. The last section is the conclusion, which traces the research conclusions of this study and the spatial characteristics of capital flows. It also describes a series of policy implications and future research approaches.

2 Literature review

As economic development and global economic ties become closer, the space for mobility has gradually replaced the space for location. From the perspective of urban network theory, enterprises and cities are embedded and coupled with each other. Enterprise investment network is an important part of urban network, and provides impetus for the development of enterprise investment and business activities at different levels, so as to promote the formation and evolution of inter-city economic relationship network, promote the renewal of regional urban network and constantly enrich the research perspective and data sources of urban network [22].

The off-site investment of enterprises, as the fundamental driver behind the development of urban networks, has consistently been a prominent subject of study for scholars both domestically and internationally [23].Different spatial organization modes of enterprises will affect the organization mode of urban space. Enterprise network is essentially a network system based on enterprise interconnection. From the perspective of research data sources, it can be roughly divided into two categories. One is the internal network of enterprises, and the other is the inter-enterprise connection network [24]. The first is to measure the relationship between cross-regional enterprises based on enterprise ownership, mainly based on enterprise headquarters-branch data to complete the spatial distribution and network structure of urban investment network. Taylor's pioneering work, exemplified by the Globalization and World Cities (GaWC) series, investigates urban network structures by analyzing the location data of corporate headquarters and branches [25,26].

This approach primarily relies on factors such as the frequency of investment events between enterprises [27], the number of inter-enterprise connections [28], the presence of equity investments, and the extent of enterprise clustering to establish the basis for network construction [29,30]. However, based on the headquarters-branch data, it is assumed that there is an inevitable connection between headquarters and branch companies located in different regions, and this connection is transformed into a connection between cities, but this connection is not necessarily a real capital, innovation or information exchange., thereby failing to accurately depict the actual strength of connections between enterprises [31]. Consequently, some scholars have endeavored to conduct urban network research from the perspective of economic interactions between enterprises [[32], [33], [34]]. Moreover, the emergence of global production networks has led to extensive inter-enterprise connections within the same or different industries [35]. Therefore, inter-firm linkages are considered a suitable metric for quantifying inter-city connections [36].

As previously mentioned, the exploration of inter-firm linkages represents a novel angle in urban network research, but there are currently relatively few studies in this area [37]. This is primarily due to the challenges associated with collecting and quantifying data on inter-firm relationships [36]. Given that each company is interconnected with others in various ways, it often results in extremely large datasets that are challenging to compile. Research on urban networks based on inter-firm linkages primarily concentrates on national [38,39] and regional scales [40]. From the perspective of industry types, there are producer services [41], manufacturing [42], film industry and so on [43]. For example, Hoyler and others have created urban networks in China, Germany, France and Brazil based on joint project production relationships between film companies [44]. Yeh et al. studied the urban network of producer services in the PRD through a questionnaire survey of business relationships between enterprises [45].

The cross-regional investment of enterprises is determined by their capital attributes, that is, one city enterprise invests in another city enterprise, connects the city through investment and shareholding, and forms a complex capital network. However, due to the difficulty in obtaining micro-enterprise capital flow data, the existing research based on inter-enterprise connections mostly analyzes China 's inter-regional capital flows from the perspective of credit capital flows, savings investment and venture capital [46,47]. The scale of research is mostly above the provincial scale, and few scholars study the spatial network and investment model of urban investment network from a multi-industry perspective. Therefore, this paper uses the data of corporate investment behavior from 1990 to 2020 to try to construct the capital investment network of the PRD cities, explore its spatial and temporal characteristics and multi-industry investment model, and supplement the existing inter-enterprise investment network literature with intra-regional and multi-industry investment networks. At the same time, because the investment network is based on the actual enterprise capital network, the research results have certain reference significance for enterprise investment, government investment attraction and enterprise space planning.

3 Data and method

3.1 Study area

The research area of this paper is the PRD urban agglomeration, including a total of nine cities (Fig. 1). Among them, except for Zhongshan and Dongguan, which have not set up districts and counties as sub-level city units, this study draws on the ' Zhongshan City Group Development Plan (2017–2035) ' and ' Dongguan City Master Plan (2005–2020) '. To facilitate the research, Zhongshan and Dongguan, which do not have sub-level districts and counties, are subdivided into five groups, resulting in a total of 59 administrative districts serving as the sub-city scale research units.Fig. 1 Location map of the PRD.

Fig. 1

3.2 Data sources

The research data for this paper comprises two main components: PRD enterprise big data and enterprise investment data. Enterprise big data covers a total of 3.57 million enterprises, including industry classification information of all enterprises. Meanwhile, the enterprise investment data primarily originates from existing shareholder data in Guangdong Province spanning from 1990 to 2020. The enterprise investment data comes from the enterprise investment and financing data platform (https://www.qcc.com/)), which has obtained investment and financing enterprises with investment funds of more than 1 million yuan, generating a data set of 108,635 items. Following data cleaning procedures, there remain 65,702 entries for investment and financing enterprises within the PRD. This dataset includes information such as the name of the financing enterprise, shareholder names, addresses, industry classifications, establishment dates, investment amounts, and more. Lastly, the dataset is cross-referenced with enterprise data from Guangdong Province to enhance the industrial classification information.

Therefore, on the basis of analyzing the cross-regional investment pattern of all industries, this paper further explores the investment pattern characteristics of six industries: I information transmission, software and information technology service industry (hereinafter referred to as industry I), L leasing and business service industry (industry L), K real estate industry (industry K), J financial industry (industry J), C manufacturing industry (industry C), F wholesale and retail industry (industry F). These six industries account for more than 80 % of investment (as shown in Table 1), so these six industries are selected as typical industries for analysis.Table 1 Overall analysis of industrial investment.

Table 1Classification of China's economic industries
(GB/4754-2011)	Investments in the same industry	Invest across industries	Total investment	
Amount (100 Million Yuan)	Percentage (%)	Amount	Percentage	Percentage	
A Agriculture, forestry, animal husbandry and fishery	5.70	7.64	68.90	92.36	0.14	
B Mining Industry	0.00	0.00	1.38	100.00	0.00	
C Manufacturing	1279.22	33.63	2524.24	66.37	6.95	
D Electricity, gas and water production and supply	1761.70	77.02	525.52	22.98	4.18	
E construction industry	505.16	26.91	1371.74	73.09	3.43	
F Wholesale and retail trade	922.29	26.75	2525.60	73.25	6.30	
G Transportation, warehousing and postal services	1354.36	53.16	1193.24	46.84	4.66	
H Accommodation and catering	0.00	0.00	75.15	100.00	0.14	
I Information transmission, software and information technology services	1526.83	17.68	7110.72	82.32	15.78	
J Financial Industry	29.41	0.43	6862.36	99.57	12.59	
K Real Estate Industry	4070.68	50.84	3935.79	49.16	14.63	
l Leasing and business services	4723.45	33.36	9436.84	66.64	25.87	
M Scientific research and technical services	296.35	19.75	1203.81	80.25	2.74	
N Water conservancy, environment and public facilities management	56.01	20.93	211.57	79.07	0.49	
O Resident services, repairs and other services	29.20	9.10	291.52	90.90	0.59	
P Education	19.09	4.14	441.92	95.86	0.84	
Q Health and Social Work	11.47	43.51	14.89	56.49	0.05	
R Culture, Sports and Entertainment	80.31	23.52	261.13	76.48	0.62	

3.3 Research methods

(1) Network multi-center measure

The '3S′ index method is employed to select the multi-center measurement index for the regional investment network. According to Limtanakool et al., regional multi-center analysis can be conducted by assessing the structure, strength, and symmetry of the regional system. The structural aspect of the regional system is employed to determine whether the network exhibits a multi-center or single-center configuration. Strength measures the significance of nodes within the network and, in this study, is further categorized into financing intensity and investment intensity.

To assess the structural dimension of the network, the entropy index (E) is utilized to characterize the overall degree of connectivity between nodes within the multi-center region:E=−∑i=1nZilnZilnn

In the formula: n represents the number of nodes in the network; Zi represents the proportion of the total flow of node i to the total flow of the network, and the E value is between 0 and 1. The closer E is to 0, it means that all flows flow to one node, so the region is completely single-center. On the contrary, the closer E is to 1, the stronger the flow is, the stronger the connection between nodes is, and the region should be regarded as a multi-center structure.

Strength reflects the degree of interaction between nodes, including investment intensity and financing intensity on a node i (i = 1, 2, …... n), its position in the network is measured by the dominance index (D).D=Ii∑j=1mIjm

In the formula: Ii is the total investment of other regions in i centers, Ij is the total investment of other regions in j centers, m is the number of regions. The strength of a node in the network is equal to the sum of investment strength and financing strength. D aims to measure the relative strength of a region on the network.(2) Linear density analysis

The linear density analysis tool is employed to compute the density of linear elements within a given vicinity. This tool operates by drawing a circular search area at the center of each grid pixel. It then calculates the sum of the products of the length of line segments that intersect the circle and their corresponding field values. This final sum is divided by the area of the circle, yielding the line density value for that area. In this study, the associated field values are represented by investment amounts.

The analysis of investment and financing's Origin-Destination (OD) line density is conducted using ArcGIS software tools. This analysis helps in assessing the extent of regional investment and financing agglomeration.

4 Results

4.1 The evolution characteristics of the overall investment of the industry

4.1.1 The overall spatial evolution characteristics of the industry

The investment data analyzed in this paper spans from 1990 to 2020, prompting the division of the study into three distinct stages for observing changes in industrial investment patterns. The designated time nodes are 1990–2000, 2000–2010, and 2010–2020, respectively (Fig. 2). During the first stage from 1990 to 2000 (Fig. 2a), enterprise investment and financing activities were predominantly concentrated in the connection between Guangzhou and Shenzhen. Specifically, the investment amounts in Guangzhou and Shenzhen accounted for 37 % and 36 % of the total investment in the PRD urban agglomeration, respectively. These figures were notably higher than those observed in other cities.Fig. 2 Evolution characteristics of the overall investment in the PRD.

Fig. 2

During the second stage, spanning from 1990 to 2010 (Fig. 2b), the central axis of investment and financing connections continued to be dominated by Shenzhen and Guangzhou. Vertical investment and financing links between Guangzhou, Dongguan, and Shenzhen experienced consistent reinforcement, exhibiting a zonal development pattern. Concurrently, the vertical connections between the core cities extended outward to include Foshan, Zhongshan, and Huizhou. It becomes apparent that, in addition to investments made within the same city, investment behaviors also extended across administrative boundaries during this period.

In the third stage, covering the period from 1990 to 2020 (Fig. 2c). The region encompassing Guangzhou, Dongguan, and Shenzhen has evolved into a more expansive shape, with closely interconnected investment links between the three cities. Furthermore, a band-like connection has emerged between Guangzhou, Zhongshan, and Zhuhai. This suggests that in the future, the development axis of Guangzhou-Zhongshan-Zhuhai may witness increased corporate investments and heightened capital agglomeration. Additionally, Huizhou has emerged as an “enclave” of investment agglomeration, gradually developing toward Shenzhen and Dongguan. This underscores the evolving dynamics of investment patterns in the region.

4.1.2 The overall network evolution characteristics of the industry

The connections between districts and counties within the PRD urban agglomeration are robust, indicating a multi-center network structure. However, it's notable that the degree of the multi-center structure has been gradually decreasing over the years. When considering the spatial form and the distribution of relative intensity in regional investment and financing network connections. During the first stage (Fig. 3a), the primary focus was on the connection between Guangzhou and Shenzhen. Simultaneously, connections between Guangzhou and districts/counties like Zhongshan and Zhuhai were more pronounced. Additionally, connections between Shenzhen and districts/counties such as Dongguan and Huizhou were also conspicuous.Fig. 3 The evolution characteristics of the industrial investment network in PRD.

Fig. 3

Between 1990 and 2010 (Fig. 3b), the primary linkage in terms of investment and financing occurred between Guangzhou and Shenzhen within the urban districts and counties of the PRD. However, it's worth noting that the intensity of the connection between Guangzhou and Shenzhen decreased during this period compared to the situation before 2000. From 1990 to 2020 (Fig. 3c), the key center for investment and financing activities has shifted to the connections between districts and counties in Shenzhen, with Guangzhou assuming a secondary center role. Moreover, the connections between Guangzhou and Shenzhen have notably strengthened during this period. In particular, the districts and counties located between Shenzhen, Dongguan, and Guangzhou have established a robust investment and financing network.

Furthermore, there is an observable trend where the number of county nodes and connections linked to the PRD urban network in certain “marginal” areas, such as Zhaoqing City, Jiangmen City, and Huizhou City, has been steadily increasing year by year. This indicates that the PRD urban agglomeration has progressively developed into a networked spatial pattern, characterized by distinct core-edge features.

The analysis of dominant indices for each district and county (as shown in Fig. 4) reveals several noteworthy trends. Firstly, the role intensity of Nanshan District and Longhua District in Shenzhen has experienced significant strengthening over time. Notably, their role intensity notably increased between 2011 and 2020, surpassing that of other districts and counties by a considerable margin. Before the year 2000, Tianhe District in Guangzhou held the highest influence within the overall investment and financing network. However, its influence gradually waned over time.Fig. 4 Leading index of the whole industry in the PRD in different years (Top 30 districts and counties).

Fig. 4

Conversely, Huangpu District and Yuexiu District exhibited a trend of initially rising in influence and then declining over time. It's important to note that the influence levels of these three districts fell far behind that of Nanshan District and Longhua District in Shenzhen during the period from 2011 to 2020.It can be seen that the center of the investment and financing network has shifted from the original core districts and counties in Guangzhou to the core districts and counties in Shenzhen. The strength of the role of the core districts and counties in Shenzhen is significantly higher than that of Guangzhou, becoming the absolute center of the investment and financing network.

4.2 Investment evolution characteristics of key industries

4.2.1 Evolution characteristics of investment space in key industries

It is evident that industries I, F, and J have their origins in Guangzhou and Shenzhen, gradually undergoing a development process with Guangzhou and Shenzhen as their primary focal points (as depicted in Fig. 5). These three industries are predominantly centered around Shenzhen, resulting in a band-like connection between Guangzhou, Dongguan, and Shenzhen. On the other hand, industries K and C have developed with Guangzhou and Shenzhen as their respective core areas, forming two distinct core development regions: one centered around Guangzhou and the other around Shenzhen. Industry L exhibits a dispersed spatial distribution, gradually expanding across space, ultimately achieving a balanced development. In terms of spatial agglomeration, a relatively distinct planar agglomeration has materialized in Guangzhou, Dongguan, and Shenzhen, followed by a narrower band-like agglomeration encompassing Zhongshan, Zhuhai, and Guangzhou.Fig. 5 Spatial characteristics of investment in key industries in the PRD.

Fig. 5

In summary, investment and financing activities are primarily concentrated among the six cities situated on both sides of the Pearl River. The degree of investment concentration follows this order: industry L > industry F > industry J > industry K > industry C > industry I. Among these industries: Industry I, F, and J have Shenzhen as their main core, resulting in a comprehensive and extensive band-like development pattern. Industry K and Industry C have adopted a development model with Shenzhen and Guangzhou as their cores. Industries L demonstrate a tendency toward balanced regional development.

Analyzing the economic output value data of these six industries in the PRD from 2000 to 2020, there is a certain similarity with the distribution of investment. The industrial output value exhibits a broad and extensive pattern. Specifically, Industries I, F, and J (Fig. 6a–c) are primarily centered around Shenzhen, with Industry F also having a significant base in Guangzhou. Industry K and Industry C show a more balanced trend between the two core cities (Fig.6d and f). While investment in industry L (Fig. 6e) indicates a balanced regional distribution trend, Guangzhou and Shenzhen still hold dominant positions in terms of output value scale.Fig. 6 Economic output data of six industries in the PRD from 2000 to 2021.

Fig. 6

4.2.2 Evolution characteristics of investment network in key industries

The polycentric structure and spatial configuration of different industries exhibit distinct differences (Fig. 7). The network structure of Industry I tends to be a single-center structure, with most network flows converging toward a single node. In terms of network connections, the overall network connectivity within the Information Transmission, Software, and Information Technology Service Industry (Industry I) is relatively sparse, primarily concentrated on connections between specific cities.Fig. 7 Investment network characteristics of key industries in the PRD.

Fig. 7

Industry F, C, L and K tend to have/show multi-center structure. Industry F shows the characteristics of high network density but not prominent core connection in network connection. The network takes Nanshan District of Shenzhen as the core, and the overall strength of connection with other districts and counties is not large but the number is high. The overall investment and financing network of industry C shows the characteristics of high density but the core of connection strength is not prominent. There is a close relationship between Shenzhen and Dongguan and Huizhou, while Guangzhou has a strong connection with Zhongshan and Zhuhai. The industrial L network is centered on Nanhai District of Guangzhou, but from the perspective of connection strength, the connection strength between this area and other districts and counties is not high. It can be seen that Nanhai District has the characteristics of low connection strength but high connection frequency in the network. The industrial K network as a whole shows high network density and strong connection. With Guangzhou as the center, a strong connection network has been formed in Guangzhou and Shenzhen.

Industry J exhibits a network structure that falls between a single-center and a multi-center structure. In terms of network connections, the investment and financing network of the Financial Industry (Industry J) as a whole is characterized by low network density but strong and concentrated core connections. Shenzhen serves as the central hub for the financial industry, and the investment and financing links among its districts and counties are notably strong. Additionally, there are strong connections between certain districts and counties in Guangzhou, as well as some connections with Huizhou, Zhongshan, and Zhuhai. The overall network is concentrated on both sides of the PRD.

4.3 Spatial investment model of key industries in PRD

4.3.1 Spatial investment distance of key industries in the PRD

The characteristics of the investment distance of the six key industries are analyzed (Fig. 8). Due to the inherent characteristics of each industry, there are clear variations in investment distances, categorizable into three types: single peak, large and small peak, and long tail. The single peak type refers to the situation where an industry's investment distances are concentrated within a specific range, resulting in spatial concentration. Industry I, for instance, is primarily centered around medium investment distances, with a relatively lower proportion of short-distance and long-distance investments. The large and small peak type indicates that an industry's investments are concentrated within two distinct distance segments, leading to the formation of two peaks, which exhibit a combination of spatial concentration and dispersion. Industry J, as an example, primarily focuses on short-distance and long-distance investments, with fewer investments in the medium-distance range.Fig. 8 Spatial distance characteristics of investment in key industries in the PRD.

Fig. 8

The long tail type describes the noticeable distance attenuation characteristics of industry investments in space. In this type, the investment amount is primarily concentrated in short-distance investments, gradually decreasing as the investment distance increases. This pattern exhibits features of increasing returns and significant spillover benefits, often closely associated with agglomeration economies. Industry K and L, for example, exhibit these characteristics. Based on the conclusions drawn above, it is evident that the law of diminishing investment distance does not universally apply to all industries. For instance, the Information Transmission, Software, and Information Technology Service Industry (Industry I) and the Financial Industry (Industry J) do not adhere to this law consistently, which can be attributed to the specific characteristics of these industries.

4.3.2 PRD key industry investment network center

Analyzing the dominant indices of each district and county (as shown in Table 2), it becomes evident that districts and counties with higher dominant indices in the Information Transmission, Software, and Information Technology Service Industry (Industry I), Wholesale and Retail Industry (Industry F), and Financial Industry (Industry J) investment and financing networks are primarily located in Shenzhen. Nanshan District and Longhua District in Shenzhen exert a relatively strong influence on the investment and financing network of the Information Transmission, Software, and Information Technology Service Industry (Industry I), significantly surpassing other districts and counties. In the Wholesale and Retail Industry (Industry F) network, Nanshan District, Futian District, and Luohu District in Shenzhen play significant roles, followed by Tianhe District in Guangzhou. The Financial Industry (Industry J) continues to be dominated by districts and counties in Shenzhen, with Guangzhou districts and counties following suit.Table 2 PRD sub industry leading index and concentration areas and counties.

Table 2Industrial classification	Network centrality index (E)	Concentrated districts and counties	
Industry I	0.333	Shenzhen (Nanshan District, Longhua District)	
Industry F	0.716	Shenzhen (Nanshan District, Futian District, Luohu District, Bao'an District); Guangzhou (Tianhe District)	
Industry J	0.566	Shenzhen (Nanshan District, Futian District, Pingshan District); Guangzhou (Nanhai District)	
Industry K	0.819	Guangzhou (Tianhe District, Haizhu District); Shenzhen (Futian District, Nanshan District, Luohu District)	
Industry L	0.781	Guangzhou (Tianhe District, Yuexiu District, Huangpu District); Shenzhen (Nanshan District, Futian District)	
Industry C	0.862	Shenzhen (Nanshan District, Guangming District), Guangzhou (Huangpu District, Nansha District), Dongguan Center Cluster	

4.3.3 Summary of investment mode of key industries in the PRD

Based on the evolution characteristics of industrial space and networks in the Pearl River Delta, as determined by spatial investment distance and network center measurements, the spatial organization modes of key industries can be categorized into four main types (Fig. 9): single-center network, one-core multi-sub-center network, dual-core multi-sub-center network, and multi-center network.Fig. 9 Investment mode of key industries.

Fig. 9

The single-center network pertains to a scenario where the districts and counties of a single city serve as the core without the formation of sub-centers. It exhibits close connections with neighboring nodes. The core districts and counties possess strong attraction and resource allocation capabilities for the industry's production factors. Enterprise investments primarily occur between these core districts and counties, as seen in Industry I. A one-core multi-sub-center network involves a sub-center district and county with a single city as the core, connecting one or more other cities, and featuring a hierarchical structure in the connections.

The dual-core multi-sub-center network involves two cores and multiple sub-centers, with the two cores closely interconnected. An example is Industry F, with Shenzhen and Guangzhou as the centers. The multi-center network, on the other hand, lacks a strong core county, and the core county has weak radiative capacity. This network is composed of multiple secondary sub-centers with close and relatively uniform connection distances. When the development levels of each district and county in the network are similar, they are closely related to each other. An example is Industry C and K.

5 Discussions

Most enterprise networks are based on headquarters-branch enterprise data, but the investment and financing links between different enterprises may better reflect the real connection strength between industries. Therefore, this study believes that the connection between enterprises can better show the real capital flow network between enterprises than the internal connection of enterprises. Compared with other networks such as passenger flow, logistics and people flow, the enterprise investment network more follows the core-periphery theory.

First of all, The enterprise networks of different industries are special. Previous studies have focused on manufacturing and producer services. In the existing research, it is basically recognized that the PRD investment network presents the phenomenon of Guangzhou-Shenzhen dual-core [13,48]. This study supports this conclusion to a certain extent, but it can be seen from the investment patterns of different industries that this dual-core exists in some industries such as Industry F, and some industries such as Industry I are single-core development with Shenzhen as the core. Therefore, how to play the guiding role of core cities and guide inter-city cooperation in the development of different industries will have more considerations.

Secondly, the investment distance of different industries will have a certain impact on urban nodes. In the past, urban network research paid more attention to the network connection centrality to determine the strength of nodes, paying too much attention to the network and ignoring spatial proximity [33,39]. From the investment distance and network nodes of different industries, it can be seen that some industries have a wider investment distance in the region, while some industries have a relatively concentrated investment distance, such as industry K. This leads to a certain difference in the distribution of nodes in the development of industry investment. The single-center industry network has sub-center nodes in the middle distance or long distance, and the multi-center network usually has sub-center nodes in the short distance.

Finally, compared to previous studies, this paper offers several significant contributions. Firstly, it delves deeper into research by focusing on the county scale, which is a more detailed perspective compared to previous urban-scale studies. This shift in perspective enhances the applicability of the findings for enterprise investment location decisions. Secondly, previous studies mainly focused on a single industry investment network, ignoring the comparative analysis of cross-industry investment networks. Our research provides insights into the differences in investment networks between different industries. Lastly, by integrating the spatial and network perspectives, this paper identifies differences in investment models across various industries, offering valuable insights for corporate investment strategies.

6 Conclusions

This study takes the PRD urban agglomeration as the research object, constructs the capital flow network of different industries, studies its spatial distribution characteristics and network flow characteristics, and further explores the investment models of different industries from the perspective of space-network. The main conclusions are as follows.

The investment and financing activities in the PRD urban agglomeration consistently exhibit a point-belt-surface development trend across three distinct periods. When enterprises engage in cross-regional investments, they consistently demonstrate distance attenuation and hierarchical connections, emphasizing the significant influence of geographical proximity on investment behavior. The investment agglomeration and distance are closely tied to the characteristics of their respective industries, and not all industries follow the distance attenuation pattern.

The capital flow network reveals several key observations. First, the investment network structure is multi-centered and multi-nodal, with a trend towards “large agglomeration and small dispersion.” Manufacturing tends to be decentralized, while services show agglomeration tendencies. Second, enterprise investment networks within cities display short-distance multi-sub-centers, medium-distance multi-nodes, and long-distance fewer sub-centers. Lastly, industry network structures fall into four categories: single-center, one-core multi-sub-center, dual-core multi-sub-center, and multi-center networks, each with unique characteristics.

6.1 Policy implications

According to the research results, from the perspective of enterprise investment, two suggestions are put forward for future urban capital linkage and policy adjustment. The first is to break administrative barriers and build a multi-level network structure with Guangzhou and Shenzhen as the core. There are still obvious administrative marginalization in the enterprise investment network in the Pearl River Delta region, and enterprises show the characteristics of distance attenuation and hierarchical connection when investing across regions. It is necessary to break through the barriers that hinder the free circulation of factors, such as the difficulty of institutional innovation in avoiding the joint action of two competitive cities on the governance scale.

The second strategy is to optimize multi-scale intercity investment and achieve industrial gradient transfer. Analysis of key districts and counties reveals that Shenzhen's Nanshan District transfers investments to Dongguan's central manufacturing hub. This approach can be extended to the coordinated development of the Guangdong-Hong Kong-Macao Greater Bay Area and the PRD region, promoting industry growth by fully integrating regional production factors. Specifically, this involves strengthening regional cooperation by selecting cities with strong investment links and high development potential, increasing policy support, and promoting coordinated development of surrounding cities to maximize positive spillover effects while minimizing negative impacts. Additionally, it requires enhancing connections between the core areas of Shenzhen and Guangzhou with traditional processing industries in the PRD region, gradually transferring high-end, general, and heavy manufacturing industries outward, expanding the service hinterland of the Pan-Pearl River Delta, and forming a gradient industrial zone.

6.2 Limitations and future research

However, it's essential to acknowledge the limitations of this study. Firstly, regarding research methods, the determination of the timing of corporate investment behavior is relatively coarse, and we can only approximate the occurrence time of such behavior. It's worth noting that there may be differences between the actual investment subscription date and the true occurrence time of investment behavior. Secondly, while this paper thoroughly analyzes the characteristics of investment space and network evolution, it does not delve deeply into the mechanisms driving these changes. Further research is needed to explore the underlying factors that influence these processes.

Funding

This research is supported by the major project of 10.13039/501100001809 National Natural Science Foundation of China (No.62394335): intelligent planning decision-making technology and verification of multi-factor coordination of land space; 10.13039/501100004791 Shenzhen Science and Technology Program (No. 20231122141204001 ) -Spatial aggregation evolution mechanism and spatial coordinated development of electronic information industry cluster in the 10.13039/100015351 Pearl River 10.13039/100002465 Delta .

Data availability statement

The data related to the research of this paper is not stored in the public repository ? The data used in this study will be provided on request.

CRediT authorship contribution statement

Youwei Tan: Writing – original draft, Methodology, Formal analysis, Conceptualization. Yiting Wang: Software, Resources, Data curation. Lipeng Duan: Writing – review & editing, Project administration. Zhihui Gu: Writing – review & editing, Supervision, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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