Spatial and temporal evolution of Guangdong tourism economic network structure from the perspective of social networks

This study uses social network analysis and modified gravity model methods to empirically analyse the network spatial correlation structure and spatiotemporal development trend of 21 cities in Guangdong Province from 2000 to 2020 based on tourism economic development data. The findings show that, first, Zhuhai has the greatest potential for growth as the centre of the spatial and temporal evolution trend of the network structure of the tourism economy in Guangdong Province, ahead of Shenzhen, Huizhou, Zhaoqing, Zhongshan, Jiangmen and Dongguan. However, Guangzhou, the capital city of Guangdong Province, is experiencing a decline in such influence and development. Second, there is a counter-trend growth in the number of tourism-related economic links among the 21 cities. Although Guangdong's tourism economic network intensity is strong, there is still room for further optimisation. Third, the results of the overall network indicators show that there is a need for further improvement in network density, grade and efficiency to help reduce the relative development gap of the cities' tourism and effectively improve the overall development of Guangdong's tourism economy. Finally, based on the core–periphery structure, this study proposes relevant suggestions for the sustainable development of Guangdong's tourism industry.

resources, prominent industrial clusters, a high degree of marketisation, a relatively sound public service system and a sound foundation and conditions for the integrated development of culture and tourism. In 2020, Guangdong Province received 231 million overnight tourists (226 million domestic and 4.7 million overseas, including 804,600 foreigners and 2.8 million Hong Kong citizens). A total of 587,100 people came from Macau and 470,900 from Taiwan. Guangdong Province's total tourism revenue in 2020 was 469.1 billion yuan, of which US$2.3 billion was foreign exchange earnings from international tourism and 452.8 billion yuan was domestic tourism revenue (from the 2020 Guangdong Province National Economic and Social Development Statistical Bulletin).

Methods
The British scholar Brown first proposed the concept of social network [24], which was later adopted and widely used in many fields, including innovation, urbanisation, tourism and economy. Social network analysis was used in this study because it is considered a strong paradigm for spatial research in tourism [25]. This research method can help to understand the spatial correlation of the tourism economy, examine the structural characteristics and temporal and spatial evolution trends of the tourism economic network, analyse the status and role of each city and understand the current situation of the tourism economy in Guangdong Province.

Gravity model of tourism economic linkage
Gravity models in economics are derived from the law of universal gravitation [26]. Universal gravitation describes the interaction and mutual influence relationships between objects. Taaffe proposed that the strength of economic ties is proportional to the product of the population between cities and inversely proportional to the square of the distance between cities [27]. Since then, the gravity model has been widely used to study regional economic interactions [28]. The gravitational model means that there is an attractive force between objects, and the strength of the gravitational force is proportional to the mass (scale) of the two objects and inversely proportional to the square of the distance between the two objects. Scholars generally use the factors of total tourism revenue, the number of tourists and the shortest road distance between cities to reflect the strength of regional tourism economic correlation [29]. However, as cities of different sizes and grades contribute differently to the tourism economic correlation between two cities, the tourism economic correlation should be directional and the gravity model should be corrected according to the different contributions of the two cities.
The total GDP is the most direct factor for measuring a city. Therefore, based on the original gravity model, this study adds the factor of total GDP, expresses the 'quality' of the tourism economy by the total number of tourists, total tourism income and total GDP and represents the 'scale' by the total number of tourists × total tourism income × total GDP data. The 'shortest road distance' is adopted as the 'distance' data. The ratio of the total GDP to the sum of the total GDP of the two cities is used as the correction coefficient to conform to the directional characteristics of the attractiveness of the tourism economy between cities [30].
where Kij is the gravitational coefficient and Yij is the tourism economic linkage intensity between two cities. Pi and Pj are the number of tourists in the year, Ti and Tj are the tourism income of the two cities in the year, Gi and Gj are the total GDP of the two cities in the year and Dij is the distance between two cities.

Overall network characteristic indicators
This study uses the social network analysis method to analyse the overall network spatial correlation characteristics of the tourism economic development of Guangdong Province comprising 21 cities by calculating the values of network density, correlation degree, grade degree and efficiency.
The network density is the ratio between the number of own relationships and the maximum possible in the entire network. Its value reflects the density of tourism economic relationships between cities [31].
where D is the network density, L is the number of actual relationships and N is the number of regional cities. Network connectedness reflects the robustness and vulnerability of the tourism economic development cyberspace association itself. When many lines in the urban tourism economic development cyberspace association pass through a certain point (city), the network has a lower degree of correlation and therefore weaker robustness. In contrast, when the spatial correlation network line is not distributed around a single point, the network will have a greater correlation, making it more robust [32].
where C is the correlation degree, V is the logarithm of unreachable points in the network and N is the number of regional cities. Network hierarchy measures the degree of asymmetric arrival between cities in the network. The higher and stricter the network level, the more dependent and marginal the cities are in the network space structure [33].
where H is the degree of hierarchy, K is the logarithm of symmetrically reachable points in the network and max (K) is the logarithm of the maximum possible reachable point. Network efficiency reflects the efficiency of connections between cities in the cyberspace connection of tourism economic development. The lower the network efficiency, the more the strengthening of connections and the reinforcing of tourism economic links needed between cities [34]. A stabler spatial connection network for tourism economic development makes it easier to promote the development of the economy through the spatial connection network [35].
where E is the network efficiency, M is the number of redundant lines in the network and max (M) is the maximum possible number of redundant lines.

Individual network characteristic indicators
The analysis of individual network structure features mainly adopts the centrality of the social network midpoint analysis [36]. Point centrality analysis includes the centrality of the point and its middle and near centrality [37]. Pointwise centrality measures the degree of contact between two participants [38]. The higher the centrality of the point, the closer the actor is to other actors and the greater the actor's power. In a directed graph, the pointwise centrality is divided into 'point-in degree' and 'point-out degree'. Intermediate centrality measures the ability of participants to control other participants [39]. If a point is located on the connection path of the other two points, it has a high intermediate centrality, meaning that the point plays the role of a communication bridge in the connection [40]. Near centrality is the opposite of middle centrality. It measures the ease of contact between participants, i.e. the ability to resist being controlled by other participants. The closer the centrality the less controlled the point. The calculation formula for each centrality is as follows [41]: CAD = Degree of point. CRD=(Point penetration + Point out)/(2n-2) C − 1 APi = ∑ n j=1 d ij ,d ij is the shortcut path between points i and j.
where C AD is the absolute degree centrality of a point, C RD is the relative degree centrality of a point and n is the scale of the network. C ABi is the absolute middle centrality of point i and C RBi is the relative middle centrality of point i. C − 1 APi is the absolute approach centrality of point i and C − 1 RPi is the relative approach centrality of point i.

Core edge model
We adopt core edge analysis to scientifically and extensively examine its internal spatial structure [42,43]. Using the Ucinet6 software, this model can be employed to show the position of each city node clearly and intuitively in the tourism economic network, indicate the spatial characteristics of the tourism economic network of 21 cities in Guangdong Province and provide relevant development countermeasures [44,45].

Data source
The dataset consists of panel data from 2000 to 2020 for the number of tourists (1000 persons), tourism income (100 million yuan), gross domestic product (100 million yuan) and per capita gross domestic product (100 million yuan) in 21 cities in Guangdong Province. The above data are obtained from the statistical bulletins concerning the national economic and social development of each city in the corresponding year, the China Tourism Statistical Yearbook, the websites of the Guangdong provincial and municipal tourism bureaus, the websites of the National Bureau of Statistics and the China Statistical Yearbook. Considering the difficulty and representativeness of data acquisition, the years 2000, 2005, 2010, 2015 and 2020 are selected as time sections, with time nodes evenly selected every 5 years.

Overall network structure indicators of the cities
Using the panel data of 21 cities in Guangdong Province and the modified gravity model, the spatial relationship matrix of tourism economic development between cities is constructed. Netdraw, the visualisation tool of the Ucinet software, is used to draw the data for five separate time points of the network structure: 2000 (92 relationships), 2005 (114 relationships), 2010 (106 relationships), 2015 (91 relationships) and 2020 (97 relationships), as seen in Figs. 1-5, respectively. Figs. 1-5 show that the overall spatial connection network structure of the Guangdong tourism economy is obvious, with Guangzhou, Shenzhen, Zhuhai and Foshan at the core of the network. In 2005 and 2010, based on the original network core of Guangzhou, Shenzhen, Zhuhai and Foshan, Shaoguan and Heyuan were integrated into the network core, with the shape of 'one core and two wings'. In 2015 and 2020, Shaoguan and Heyuan migrated from the core network centre circle. The reasons for the above changes lie in the following point: Guangzhou, Shenzhen and Foshan have strong tourism potential.
The Pearl River Delta region has a relatively high intensity of tourism economic correlation and total gravitational force of each city. It is the hinterland of the tourism economy in Guangdong Province. This conclusion is incontestable for the following reasons: first, Guangzhou is the capital city of Guangdong Province and is certainly impacted by factors such as transportation and economy. Second, Foshan is spatially closer to Guangzhou, offering convenient transportation and rich tourism resources. Third, Shenzhen and Zhuhai are the second and third largest cities in Guangdong Province. Fourth, in 2017, the Guangdong-Hong Kong-Macao Greater Bay Area policy was proposed. The nine cities (Guangzhou, Shenzhen, Zhuhai, Dongguan, Zhongshan, Foshan, Jiangmen, Huizhou and Zhaoqing) in the Pearl River Delta of Guangdong Province are all a part of the Bay Area. The rapid development of regional integration in the Pearl River Delta has improved its interaction with Shaoguan and Heyuan, two major cities in Northern Guangdong. In 2005, the tourism economic network of 21 cities in Guangdong Province expanded significantly (from 92 to 114). The tourism economic network intensity decreased between 2010 and 2015, reaching the lowest level in history in 2015, before marginally improving in 2020.

Network density
Using the above formula, the tourism economic spatial network density of Guangdong Province in 2000, 2005, 2010, 2015 and 2020 is calculated along the network/density path in the Ucinet6 software. Table 1 shows that the tourism economic network density of the province in 2000, 2005, 2010, 2015 and 2020 was 0.219, 0.271, 0.222, 0.217 and 0.231, respectively. The network density is always lower than 0.5, indicating that the tourism economic ties in Guangdong Province are weak with a big potential for improvement, thus cooperation should be strengthened. In 2015, the tourism economic network density of Guangdong Province reached the lowest level in history. In 2020, the tourism economic ties rose by 64.5%, meaning that after the outbreak of the COVID-19 pandemic, the tourism economic network showed a counter-trend growth in 2020.

Network relevance, network grade and network efficiency
Using the above formula and following the network/connectedness path in the Ucinet6 software, we find that the spatial network correlation degree of the tourism economy in the Guangdong Province in 2000, 2005, 2010, 2015 and 2020 is 1. This shows that the spatial network of the tourism economy in the region is not developed only around one city. Instead, the economy is well developed, and the network has a clear spatial correlation and spillover effects.
Cities have both direct and indirect tourism economic relationships, and the network structure is stable. Fig. 6 shows the changing . The connection of tourism economic development among cities in Guangdong Province is increasing, the stability of the network is gradually improving and the cities participating in the coordination and cooperation of tourism development in the region are developing.

Analysis of intermediate centrality The intermediate centrality index measures how far a city is located between two other cities and is an intermediate coordination and leading index.
In the tourism economic network structure, cities with high middle centrality usually have more inbound and outbound tourists. The findings in Table 5    factors that are closely related to tourism resources, traffic location, consumption capacity and other factors. The middle centrality index of other cities is generally low, indicating that Guangdong is in a marginal position in the entire tourism economic network structure and is highly controlled by the central cities.

Proximity centrality analysis
The proximity centrality is opposite to the middle centrality. It measures the convenience of a city's connection with other cities, i. e. the ability of not being under their control. The higher the proximity to the centre, the less controlled by others. Shaoguan, Heyuan, Meizhou, Shanwei, Yangjiang, Zhanjiang, Maoming, Yunfu, Chaozhou, Shantou and Jieyang are near the top of the centrality index (see Table 6). A comparative analysis of the middle centrality index and the near neutrality index of the 21 cities of the Guangdong Province shows that the tourism economic network of these 11 cities is relatively scattered, with no strong participation in the tourism economic network structure.

Analysis of the core-periphery model of the Guangdong tourism economic network structure
The core-periphery programme in Ucinet6 software is used to analyse the core edge structure of the Guangdong tourism economic network space. The distribution results are shown in Fig. 10 (a), (b), (c), (d) and (e), which indicate that in the tourism economic network structure of the Guangdong Province, from 2000 to 2020, five nodes have become members of the core area: Guangzhou, Shenzhen, Zhuhai, Foshan and Dongguan, with four other nodes moving in the structure of the core and edge areas, namely, Zhongshan, Jiangmen, Huizhou and Jieyang. The other 12 nodes are stable at the edge structure.
By comparing and analysing the data presented in Figs. 1-5, 7 and 8 using a detailed comparison of the index values and the results of the point-degree centrality, point-out degree, point-in degree, proximity centrality and betweenness centrality of each city (Figs. 7-9) using intuitive pictures in Figs. 1-5 and 10, we have added four levels to the original core edge two-level structure as follows (Fig. 11).

Discussion
Compared with the existing research, this study has the following advantages. First, based on the original gravitational model, this study added the factor of total GDP, expressing the 'quality' of the tourism economy as the total number of tourists, total tourism revenue and total GDP, making the research data and conclusions more rigorous. Second, this study selects panel data of up to 21 years from 2000 to 2020 and evenly selects time nodes every 5 years, addressing the lack of original research in the time dimension. Third, this research identifies and presents the status and role of each city in the tourism economic network structure of Guangdong Province with fine-grained city-level data, specifically for the future of several important cities in the Pearl River Delta. Forecasting the changing trend, there is need for in-depth research on the characteristics of spatiotemporal evolution and development trends. Fourth, we added four levels to the original core edge two-level structure.
The shortcomings of this study are as follows. First, we use a modified gravity model to determine the spatial correlation of the tourism economy in Guangdong Province. In the future, spatial autocorrelation analysis and vector autoregressive model can be used to establish spatial correlation and compare the results to obtain complete advantages of different methods. Second, owing to time and space limitations, this study did not identify the factors and degrees that affect the tourism economy network structure in Guangdong Province; therefore, some data conclusions have not been explained in depth.

Conclusion
Based on the data on tourism economic development, this study analyses the characteristics and development of the spatial correlation structure of the tourism economy in Guangdong Province by adopting the social network analysis method and Ucinet6 software. The main conclusions are as follows.
First, the tourism economic network of the 21 prefecture-level cities in Guangdong Province has been gradually strengthened, showing a fluctuating upward trend. In general, the network layout structure of the Pearl River Delta is dense around the region. From 2000 to 2020, the province has seen a weak network density, with values lower than 0.5, indicating the need for further improvement and strengthened cooperation. In 2015, the tourism economic network density of Guangdong Province reached the lowest level in history. In 2020, however, the tourism economic ties indicated a growth rate of 64.5%, thus showing a counter-trend growth after the pandemic outbreak in 2020. The tourism economic network in Guangdong Province is maintained at a level above 0.5, which indicates obvious level characteristics, and the network structure should be further optimised.
Second, Guangdong's tourism economic network structure has a clear core and limitations. The core area is the Pearl River Delta (except Zhaoqing), followed by Jieyang in eastern Guangdong. Obvious differences exist in tourism development among regions in Guangdong Province; however, in recent years, these differences have gradually decreased. Third, obvious differences exist in the active degree of tourism economic network structure among different regions in the province. The Pearl River Delta region is more willing to travel, even higher than its own tourism attraction, and its tourism economy is developing more actively. However, Guangdong's eastern, western and northern regions are more attractive, with lower willingness to travel; thus, they are not active in the overall tourism economic network structure.
Lastly, in the spatial connection network, Zhuhai has the greatest influence and development potential in the future tourism economic network, followed by Shenzhen, Huizhou, Zhaoqing, Zhongshan, Jiangmen and Dongguan. The influence of the tourism economic network of Foshan, Guangzhou and Qingyuan is declining.
From the node centrality (point, proximity and intermediary centrality), the spatial distribution characteristics and role positioning of the tourism economy in various regions of Guangdong Province are explored in detail, and the following development countermeasures are proposed.
First, focusing on the regional connotation and consolidating the characteristic industries is necessary. The economy in the region has developed rapidly, and various elements between and within regions have been continuously linked, developed and evolved. The distribution of administrative regions, the degree of planning tendency, the feelings about tourism and the popularity of tourist destinations differ greatly. Each region should focus on its regional characteristics, focus on its strengths and combine 'culture + industry' to further promote the long-term connotation and practical benefits. Tourism culture based on local characteristics and the traditional characteristics of Guangdong, such as the cultural Han Opera and the Chaoshan Kung Fu Tea, will be injected into the brand connotation to form an industrial chain, and clusters will provide practical benefits. The culture of Guangfu, Hakka, Chaoshan and Leizhou will continue to be inherited and carried forward. Further, it is essential to develop the online promotion of tourist destinations in Guangdong to promote regional culture and create multiple benefits in addition to economic benefits.
Second, the radiation role of central cities should be fully utilised, and adhering to the mode of developing multicore tourism in Guangdong Province is necessary. Furthermore, it is crucial to strengthen the radiation and driving role of Shenzhen, Guangzhou, Foshan, Dongguan and other cities and continue to improve Guangzhou's leading position as the tourism economic network of the region.
Moreover, there is a need to develop the role of Shenzhen, Guangzhou, Zhuhai and Foshan as the province's tourist distribution centres in transferring tourists to the surrounding cities and counties. The impact of one trillion cities, such as Shenzhen, Guangzhou, Foshan and Dongguan, on the tourism economy of Guangdong's marginal cities should be strengthened, which is not limited to developing their own tourism. For example, the focus should be on holiday short-distance leisure tourism in conjunction with surrounding cities and counties; the development of intercity transportation and tourism routes; the enhancement of transportation accessibility in Yunfu, Chaozhou, Heyuan and other cities and the promotion of tourism facilities.
Third, it is necessary to understand the degree of spatial correlation and promote the coordinated development of regions. The core development area of the Guangdong-Hong Kong-Macao Greater Bay Area should be fully utilised, considering the coordinated development of other regions in Guangdong Province, which can help expand multiple core nodes, improve the traffic structure network of its surrounding and core nodes and strengthen mutual assistance and win-win results in the region and its surroundings. It is also essential to continue to develop the Metropolitan Circles of Guangzhou, Shenzhen, Pearl River West Coast, Zhan Mao and Chaoshan Jiedu and use the radiation power of megacities, including underdeveloped cities, such as Shaoguan, Qingyuan and Yunfu to closely combine core and sub-core cities to achieve integrated development.
This study comprehensively and systematically explored the spatiotemporal characteristics and evolution trends of the network structure of Guangdong's tourism economy from 2000 to 2020 using the gravity model and social network analysis method. The tourism economy of Guangdong Province is generally well developed, but individual cities differ significantly. This study can provide an empirical basis for the tourism departments of Guangdong Province and prefecture-level cities to develop policies for coordinating the development of tourism linkages. The spatial interaction theory is applied to study Guangdong Province's tourism economic network structure, which this case can further enrich.

Author contribution statement
Lijuan Zhang: Conceived and designed the experiments; Performed the experiments; Analyzed and interpreted the data; Contributed reagents, materials, analysis tools or data; Wrote the paper.
Zhenjie Liao: Contributed reagents, materials, analysis tools or data; Wrote the paper.

Data availability statement
Data will be made available on request.

Declaration of competing interest
The authors declare no conflict of interest.