3.2.1. Overall Spatial Characteristics of the Logistic Network
The directed multi-valued network was transformed into a binary one to explore the overall spatial characteristics of the logistic network in the Guangdong-Hong Kong-Macao Greater Bay Area and further eliminate the influence of maximal and minimal values. UCINET 6 measures the closeness and density of the logistic network in the Guangdong-Hong Kong-Macao Greater Bay Area [
29]. Regarding
Table 3, if the connection threshold is one, the network density is 0.7563, which is close to one, indicating a high network density. If the threshold is three or four (the median or mean of the secondary data), the network density drops to 0.5000 or 0.3455, respectively. In this case, the network density of the overall spatial linkage is stable, the overall level is relatively high, and the linkages among cities within the urban agglomeration are strong in the Guangdong-Hong Kong-Macao Greater Bay Area.
This study uses Netdraw software to generate a logistics linkage topology map to clearly describe the overall spatial characteristics of the logistic network in the Guangdong-Hong Kong-Macao Greater Bay Area. In
Figure 4, the connecting lines represent the logistics links between two cities, and the directional symbols of the connecting lines indicate that the city is taking the initiative in the logistics links. The more connecting lines a node has, the closer it is to the center of the topology diagram [
30]. Specifically, the absolute core of the logistic network includes four cities: Hong Kong, Shenzhen, Guangzhou, and Macao, while the other cities surrounding the central city form an integrated development within the center and the surrounding cities in the bay area.
3.2.2. Individual Spatial Characteristics of Logistic Networks
Centralization is a quantitative analysis, measuring the centrality degree of the whole network [
28]. The out-degree, in-degree, and betweenness centralization are 55%, 33%, and 17.09%, respectively, in the Guangdong-Hong Kong-Macao Greater Bay Area city network based on the role of urban spatially oriented linkages. From the degree of centralization, the economic linkage logistic network has a relatively intense concentration trend in the Guangdong-Hong Kong-Macao Greater Bay Area. This intense concentration implies that the cities with the highest degree of centralization in the network (i.e., Hong Kong, Shenzhen, Guangzhou, and Macao) have an absolute core dominant position, are strongly leading, and spillover effect on the whole network. In terms of betweenness centralization, the degree of centrality is low as an intermediary medium in the Guangdong-Hong Kong-Macao Greater Bay Area. In the context of “One Belt, One Road”, the Guangdong-Hong Kong-Macao Greater Bay Area is actively building an inter-city rapid transport network with high-speed, inter-city, and high-grade highways as the mainstay, which enhances direct access to cities and makes transportation more convenient [
31].
Degree centrality characterizes the number of city nodes that have a direct relationship with a city node to reflect the level of economic linkages and logistics connections among city nodes. According to
Table 4, Hong Kong, Shenzhen, Guangzhou, and Macao are the top four cities regarding the degree centrality and out-centrality. Based on
Table 4, these four cities have stronger connections with other cities, confirming their stronger radiation capacity and core position of the logistic network in the Guangdong-Hong Kong-Macao Greater Bay Area. The out-centralities of Foshan, Zhuhai, and Dongguan around the four logistics center cities are all higher than the in-centrality. This comparison implies that the radiation capacities of these cities are all greater than their receiving capacity. Additionally, these cities have a positive spillover effect on the logistic network of the Guangdong-Hong Kong-Macao Greater Bay Area.
Closeness centrality characterizes the average length of the shortest path from a city node to all other city nodes, to reflect the accessibility of city nodes in the economically linked logistic network [
32]. Based on
Figure 5, six cities have the top closeness centrality in the Guangdong-Hong Kong-Macao Greater Bay Area: Hong Kong, Shenzhen, Guangzhou, Macao, Foshan, and Zhuhai. Hence, these cities do not rely entirely on intermediate nodes for logistics and they are able to achieve higher efficiency in logistics communication. Hong Kong has the highest out-degree closeness centrality, reflecting its central position in the logistics of the Guangdong-Hong Kong-Macao Greater Bay Area. The logistics development of the Guangdong-Hong Kong-Macao Greater Bay Area belongs to the central city-driven model, with the ports of Hong Kong, Shenzhen, and Guangzhou in the Bay Area port cluster ranking among the top 10 container ports in the world. With the staggering development of these three ports from the economic, financial, and trade perspectives, their advantages complement each other and gradually spread and radiate to the surrounding cities [
33]. Except for Jiangmen and Zhaoqing, the out-degree closeness centrality is greater than the in-degree one in the other nine cities. For the most part, their out-degree closeness centrality is twice the in-degree closeness centrality. This implication indicates that the role of Hong Kong and the other nine cities in the Bay Area to the surrounding cities is greater than their degree of influence by the logistics radiation of other cities. In other words, the logistics radiation function is greater than the logistics agglomeration function in the nine cities. Among the nine cities, Hong Kong, Shenzhen, Guangzhou, and Macao have the most significant effects on the neighboring cities. This implication also reaffirms the prominent position of Hong Kong, Shenzhen, Guangzhou, and Macau as the central cities in the logistic network.
Betweenness centrality indicates the probability that the shortest paths need to pass through a city to connect other city nodes, reflecting the transit role of city nodes in the logistic network [
32]. The betweenness centrality of Hong Kong is at the top of the logistic network in the Guangdong-Hong Kong-Macao Greater Bay Area. This rank implies that the shortest paths through Hong Kong are the most central in the logistic network in the Guangdong-Hong Kong-Macao Greater Bay Area, with strong control over resources. Hence, these paths have the ability to influence the logistics communication of most city nodes in the region. After Hong Kong, the clustering analysis shows that the second group includes Shenzhen, Guangzhou, and Macao in terms of betweenness centrality, whose values are greater than three. These three cities form the secondary core of the Guangdong-Hong Kong-Macao Greater Bay Area, which plays a crucial role as a bridge in logistics communication. In the third group, betweenness centrality ranges from zero to three in Foshan, Dongguan, Zhuhai, and Zhongshan, which are general city nodes in the Guangdong-Hong Kong-Macao Greater Bay Area. Finally, betweenness centrality is extremely weak, equal to 0, in Huizhou, Jiangmen, and Zhaoqing. Most of the cities’ logistics links are established through intermediary cities such as Hong Kong, Shenzhen, Guangzhou, and Macao. Each city acts as a “broker” for logistics links 2.273 times on average.
Figure 5 represents the correlation analysis of the statistics. According to
Figure 6, the Pearson correlation coefficient is 0.943 between real GDP per capita and betweenness centrality in the Guangdong-Hong Kong-Macao Greater Bay Area. This value indicates that the logistics importance of each city node is highly correlated with the development level of real GDP per capita in each city and does not jump out of the distribution pattern of GDP development. The high growth of GDP is the basis for the logistics industry to reduce costs and increase efficiency. The logistics industry is an inherent requirement for achieving high-quality economic development in the Guangdong-Hong Kong-Macao Greater Bay Area. Additionally, the logistics industry is an important lever for improving the industrial development and investment environment, which plays a critical role in cultivating new momentum for economic development in the Guangdong-Hong Kong-Macao Greater Bay Area. In addition, the logistics industry has a strategic importance to the leading and radiation-driven role of the greater bay area.
The above three types of centrality and centralization analyses show that Hong Kong is at the center of the logistic network in the Guangdong-Hong Kong-Macao Greater Bay Area. Additionally, Hong Kong has a strong ability to radiate logistics to the inner cities of the bay area, while it continuously absorbs the advantageous resources around it, complementing the inner cities of the bay area and forming a positive interaction. Hong Kong is a free port with an open economic system, which leads Shenzhen, Guangzhou, and Macao to form the core inner circle of the Guangdong-Hong Kong-Macao Greater Bay Area. Additionally, this port radiates the various resources of the core inner circle to the outer cities while it achieves significant development. In terms of degree and closeness centrality, out-centrality is greater than in-centrality in 70% of the cities, which has many implications. An indication is that the transportation system is convenient, advanced, and powerful in the Guangdong-Hong Kong-Macao Greater Bay Area. Another implication is that the cities actively exchange, cooperate, and trade in this area. These two implications pave the way for “going out”, stimulating the driving forces of economic development in the Bay Area, enhancing the complementary functions of Guangdong, Hong Kong, and Macao, and improving the people’s living standards [
33]. In terms of betweenness centrality, developing the logistics industry is highly correlated with the value of real GDP per capita in the cities of the Bay Area. This correlation indicates the cornerstone characteristics of the economy for the high-quality development of the logistics industry and that the economy and logistics are inseparable, mutually reinforcing, and develop together.
3.2.3. Stability of the Logistic Network Structure
In a network graph, a clique is a maximal complete sub-graph of at least three nodes. In this definition, “complete” means that any two nodes are directly correlated with and adjacent to each other in the sub-graph, and no node is associated with all points in the faction. Nodes in the same faction are closely correlated with one another [
34]. This research uses the faction (cliques) analysis function of UCINET 6 to set the clique size to five after running several trials in conjunction with the research question.
Table 5 shows a total of three cliques found in this way.
According to
Table 5, all the three cliques include Hong Kong, Macao, Shenzhen, and Guangzhou, implying the central and intermediary role of these four cities in the Guangdong-Hong Kong-Macao Greater Bay Area, growing their own logistic networks in the process of actively driving the logistics development of other cities. In addition to these four central cities, Cliques 1 and 2 involve Zhuhai, Foshan, and Dongguan, which to a certain extent illustrates the “hard connectivity” formed by the Hong Kong-Zhuhai-Macao Bridge, the Guangfo Metro, and other transport infrastructures that are geographically connected. Hard connectivity gradually makes the economy take off and radiate widely, leading to high-quality development of the logistics industry in the Greater Bay Area. Although Zhaoqing, in Clique 3, is the most economically backward, the Guangzhou-Foshan-Zhaoqing metropolitan area is gradually developing by opening transport facilities such as the Guangzhou-Foshan-Zhaoqing Intercity Railway and motorways. The central cities in the Guangdong-Hong Kong-Macao Greater Bay Area are driving Zhaoqing’s economic linkage to build a high-quality logistic network.
In addition to the clique analysis, UCINET 6 generates
Figure 7, which is a clique cluster diagram according to the number of cliques shared by each city node in the logistic network. In
Figure 7, the horizontal axis from left to right indicates that the number of shared cliques in each node decreases from three. The vertical axis reveals the name of each city node. The graph as a whole reflects the reciprocity between cities in the logistic network of the Guangdong-Hong Kong-Macao Greater Bay Area.
The concept of cliques is too complex, and the concept of n-cliques is easier for people to understand. An n-clique means that one of the subgraphs in a graph satisfies the condition that the distance between any two points in that subgraph (i.e., the length of the shortcut) does not exceed “n” at most. This study sets the maximum partition depth equal to one and the minimum value of n equal to the default value of three, using the n-cliques analysis function of UCINET 6, combined with the research problem, after several trial runs. As shown in
Figure 8, there is a very clear trend of integration in the Greater Bay Area. Many core cities in the Pearl River Delta region have integrated with Hong Kong and Macao, forming several metropolitan areas. These include the Hong Kong-Shenzhen-Dongguan-Huizhou metropolis circle, which is driven by technological innovation; the Australia-Zhuhai-Zhongjiang metropolis circle, emphasizing the development of a circular economy; and the Guangzhou-Foshan-Zhaojiang metropolis circle with modern manufacturing and industrial and commercial services as its leading industries [
35]. Under the “One Belt, One Road” initiative, regional industrial synergy is a prerequisite for dynamic economic development, and the economic growth of the Guangdong-Hong Kong-Macao Greater Bay Area is an enabler for the diversity, connectivity, and sustainability of the logistic network.
The k-core analysis means that all points in the network are adjacent to at least k other points. The k-core is a cohesive subgroup built based on the number of point degrees [
34]. The adjustment of the k-value allows one to obtain the status of the economic linkage logistic network in the Guangdong-Hong Kong-Macao Greater Bay Area. The network is stable if the value of k is high, whereas the network is dispersed if this value is low.
Table 6 represents the results of the k-core analysis of the logistic network in the Guangdong-Hong Kong-Macao Greater Bay Area with three levels and degrees of eight, seven, and four. In these three levels, the eight-core subgroup is a subset of the seven-core subgroup, and both the eight-core and seven-core subgroups are subsets of the four-core subgroup. These three subgroups consist of Hong Kong, Macao, Shenzhen, and Guangzhou, which are the center of the entire logistic network, with the most significant contribution to it. Zhuhai, Foshan, Huizhou, Dongguan, and Zhongshan form a denser grid structure around the central city, while the remaining two cities, Jiangmen and Zhaoqing, are only sparsely connected to other cities.
Lambda set analysis of the logistic network is the analysis of the edge connectivity at the network level, which can measure the overall stability of the logistic network structure in the Guangdong-Hong Kong-Macao Greater Bay Area. The smaller the value of edge connectivity, the more fragmented the connections between city nodes, whereas the larger the value of edge connectivity, the closer the connections between city nodes [
36].
This study uses the Lambda set analysis function of UCINET 6. The minimum edge connectivity is a concept based on the stability of network node connections. In this analysis, the horizontal axis is the Lambda value, which represents the minimum edge connectivity, and the vertical axis is the logistics node city.
Figure 9 shows the Lambda set tree diagram of the logistic network in the Guangdong-Hong Kong-Macao Greater Bay Area. Based on
Figure 9, the minimum, maximum, mean, and median edge connectivity values are 4, 10, 9, and 8 between any two cities in the Bay Area, respectively. Overall, the edge connectivity of the economically linked logistic network shows a very balanced state in the Guangdong-Hong Kong-Macao Greater Bay Area, consistent with the results of the clique analysis. Regarding the sum of their edge connectivity, the top four cities are Hong Kong, Macao, Shenzhen, and Guangzhou. Hence, these four cities have the most robust logistics linkage in the Guangdong-Hong Kong-Macao Greater Bay Area logistic network, forming the first echelon, followed by the second echelon of Zhuhai, Foshan, and Dongguan. According to
Figure 5 above, the real GDP per capita has exceeded 200,000 yuan in Hong Kong and Macao, and 100,000 yuan in Shenzhen, Guangzhou, Foshan, and Zhuhai since 2020. In addition, the real GDP per capita will exceed 100,000 yuan soon in Dongguan. The basic rule is that the more economically developed a region is, the higher the level of demand for logistics, and the more conducive it is to the high-quality development of the logistics industry.