Network Structure Influence on Tourism Industrial Performance: A Network Perspective to Explain the Global Tourism Development

Abstract

Global tourism development can be seen as a tourism network evolution; however, how the network structure influences the tourism industrial performance has not been clearly outlined. This paper utilizes complex network theory to understand the global tourism network changes and detect the global network structure effects on international tourism industrial performance, aiming to explain the tourism development from a network perspective and help to organize international tourism effectively. Using the data of 222 regions’ statistics from 1995 to 2019, this paper explores the influence of the global-level network structure on the tourism industry through Pearson’s correlations test and the individual-level effects through a combination of the gravity model with the mixed-effect model. At the global level, results indicate that a network structure with a higher density or clustering coefficient can improve the global tourism arrivals, but the high value of the network average path length and small-worldness characteristic have negative effects. At the individual level, the node’s characteristics including the high degree, closeness, and betweenness centrality of a region in the network positively improve its international tourism arrivals, while the eigenvector centrality and local clustering coefficient generate negative effects. Additionally, most network structure measurements of a region show stronger effects on its own tourism performance than the regions with which it connects. This paper verifies that the network structure has significant impacts on tourism performance and development, which can aid international tourism development both globally and individually.

1. Introduction

With the rapid development of globalization, countries in the world have gradually formed as an integration referring to economy, society, and culture [1]. Inside, tourism is admittedly a global phenomenon that relates to people from all over the world and has been regarded as one of the largest components of international industries [2,3]. Thus, each country and relative organization should carefully consider how to organize this global industry effectively [4].

As the tourists move from one country to another, the international tourists flow is formed. Considerable tourist flow constructs a complex network involving different parts and complicated relations in the world with multiple destinations connecting, in which, the countries/regions (where tourists leave or arrive) can be regarded as the nodes, and the tourist flow connecting with each pair of nodes represents an edge. This global network suggests an integral and systematic cognition of global tourism development and indicates that a network research view on global tourism organization is essential, which has not gained enough attention yet [5].

The research of the tourism network has undergone extensive development over the last three decades. Studying tourism from a network perspective is of growing importance due to three main catalysts: (i) tourism is a real-world network involving several quite different actors, activities, and connections, that make the field an ideal object of network science study [6]; (ii) network techniques provide a series of quantitative methods to describe various tourism phenomena [7]; and (iii) a combination of tourism and network science expands knowledge of systematic realities in human–nature connection [8]. Furthermore, the tourism network is recognized as a set of interacting elements that benefits tourism innovation, market expansion, information diffusion, local growth, and stimulating regional development from previous studies [9]. Saxena [10] and Cravens and Piercy concurred that tourism networks could result in flexibility, marketing information sharing, innovation, opportunity to enter other networks, resource development, and knowledge transfer between stakeholders [11]. Rotondo and Fadda provided evidence that a tourist network really improves hotels’ financial performance, which is mainly due to the improvement of relationships with other stakeholders [12]. However, research about the effects of tourism networks usually has been focused on a micro-perspective, specifically, exploring the advantages/disadvantages of being a part of a tourism network. The most important result of this interdisciplinary effort is recognizing that the structural (topological) characteristics of a network make the system measurable and strongly affect the system’s function [13,14,15].

The structure of networks is an important determinant that decides how the network organizes [16]. The topology of the network is formed by the different actors and explains the mechanisms of ideas, information, people, and knowledge traveling from one node to another in the system [6,17]. However, the effect of network structure on tourism industrial performance has rarely been considered in some quantitative discussions.

As the definition of industrial organizations in economics includes the effect of market structure on market performance [18], the global tourism development can be described as the effect of global tourism network structure on the tourism industrial performance. Moreover, the effects of network structure on other fields (e.g., research innovation, governance policies, knowledge spread, job search, and enterprise cooperation) have been identified, which gives meaningful implications for tourism research [19,20,21,22]. Thus, this paper proposes the hypothesis that network structure may be vitally important to the industrial performance of the tourism industry, which also needs to be verified. However, how the network structure generally changed the global tourism, and which characteristics may affect the tourism industry performance, have not been shown before.

To fill the research gap, this paper employs complex network theory to detect the law of the Global Tourism Network (GNT) structure working on international tourism performance based on the international tourism arrivals data of 222 regions during 1995 to 2019. From the network perspective, some tourism knowledge can be explained in a systematic and quantitative way.

The three leading contributions are: (i) understanding how the structure of GTN changes; (ii) exploring the relationship between international tourism industrial performance and network structure; and (iii) discussing how to effectively improve international tourism organization based on the network structure perspective. The remainder of this paper is organized as follows: Section 2 shows the progress of related works on the tourism network structure and global tourism network; Section 3 outlines the methodology of this research; Section 4 gives the analyzing outcomes; and the conclusion and discussion are in Section 5 and Section 6.

2. Literature Review

In this section, the related works of this study have been reviewed including tourism networks and network structure effects as well as the global tourism networks, which help to find the research gaps and give the foundation of hypotheses and research methods.

2.1. Tourism Networks and Network Structure Effects

The network organization gradually takes over traditional individual businesses and has been one of the most significant breakthroughs in management thinking recently [23], which also works on tourism. Hall has defined the tourism network as an arrangement of inter-organizational cooperation and collaboration, demonstrating the network structure as a corporative relationship among attendants [24].

This newer type of organizational structure is always seen as a more effective and flexible structure with less hierarchy than others, which determines how it operates and performs. As clarification from Zach and Racherla, network organization can bring benefits for the participating tourism firms, enhance destinations’ tourism performance, and help form a memorable experience for visitors [25]. Lynch et al. summarized three benefits of the tourism network including learning and exchange, business activity, and community, which highlighted the network’s value and left a lack of quantitative description [26]. For the tourism firms, participating in a collaborative tourism network could produce merits through inter-organizational learning, improving knowledge exchange, supporting the innovation process, and constructing a sense of collective common purposes [27]. In the destination system, a variety of local stakeholders involved in tourism development have been bound up in both business networks and service provider networks to balance the competition and collaboration [28], which allows these actors to understand interdependence, reciprocity, mutual interest, trust, representativeness, and leadership [29]. In the context of the tourism policy network, the effects of networks are focused on policy-making and understanding public–private relations with a goal of how network concepts can be used as an organizing method to cooperate in massive relationships [30].

No matter which scenario or sector, the network concept can be used; the core value of the network described is the relationship and how these interactions constitute a framework or structure [31]. For the individual, the network determines whom they will meet and what they will acquire, which must impact the outcome. For parts of the integration, the network contributes to recognizing mutual interdependence, more openly sharing knowledge and information, engaging in more significant future planning, and tending to take a more constructive problem-solving approach to conflict resolution.

Moreover, some factors that contribute to a thriving tourism network also have been detected, for instance, structure and leadership, resourcing, member engagement, and lifecycle stage [32], where the network structure usually determines the network’s ability to explicate knowledge and facilitate the creation of sustainability outcomes [33]. Thus, Bullmore and Sporns have pointed out that the most essential network recognition is “a network’s structural features are the system’s fundamental characteristic, which can be measured and significantly impact its function” [34].

The effects of network structure have been discussed in many fields. For example, Sandström and Carlsson found an efficient and innovative policy network consisting of a series of central and dense actors, and the level of centralized integration network promotes the function of prioritizing in the progress of policy making [34]. Zaheer and Bell posited that the firms with superior network structures were better able to exploit their internal capabilities and enhance their performance [35]. Grund suggested that high intensity and low centralization networks encourage collaboration with better soccer team performance [36]. Kim and Lee used an SEM method to detect the network density and found centrality positively affecting perceived convergence and the overall performance of Small and Medium-Sized Enterprises (SMEs) [37]. Volgger and Pechlaner reviewed the benefits and strategies of a governing network structure working on tourism development [38].

Thus, it can be inferred that both the whole network structure and nodal structure characteristics should affect the related performance. However, there is little evidence for how the tourism network structure affects the tourism performance. Some research provided knowledge on understanding the relationship between the tourism network structure and tourism industry performance. Pavlovich observes that high network density (more accounts of ties linking stakeholders) forces organizations to perform well because institutional values diffuse through the network [39]. Aarstad, Ness, and Haugland pointed out that the small-world network structure can help form an efficient inter-firm coproduction in the tourism industry, which is typically characterized by a high clustering coefficient but a relatively low connection path between actors [40]. Zach and Hill gave evidence that network structure characteristics can identify the most successful innovative partners, especially for betweenness centrality that shows strong positive effects on innovation [41]. The question is whether these conclusions work in other sectors, which needs more testimonies. On the other hand, since various levels (the global level, the meso level, and the individual level) of structure metrics are commonly used [42,43,44], different levels’ characteristics may bring unequal impact but need to be proven by real-world evidence. Above all, the past literature provides a research gap and a good foundation for this study.

2.2. The Global Tourism Networks

Global tourism boosted by globalization has become a popular global leisure activity currently. Overall, 1.5 billion international tourist arrivals were recorded and donated US $8.9 trillion contributions to the world’s GDP with a 10.3% occupation in 2019 [45], confirming tourism as a leading sector in the world economic industry. Simultaneously, the global tourism rapid expansion calls for a responsibly managed way to best grasp the developing opportunities for every participant around the world [46]. Obviously, the international tourism can generate benefits, including increasing business and trading opportunities, increasing the nation’s foreign exchange earnings, raising governmental tax revenues, diversifying industry structure, and promoting the destination country economic development [47]; thus, almost every country wants to engage in booming international tourism [48].

Improvement of international tourism performance is regarded as one of the essential objectives of tourism development. Some studies assessed destinations’ performance usually focusing on items such as tourists’ perception and satisfaction [49,50], destinations’ competitiveness [51,52], or just a single indicator such as tourism arrivals, tourism expenditures, and overnight visitors to show the differences in measurements [53]. Some creative approaches borrowed from other fields such as technical efficiency [54], and ecologic footprint [55] also have been accepted due to developing sustainably. Assaf and Josiassen have concluded eight broad drivers of tourism performance, including related infrastructure; economic conditions; security, safety, and health; price competitiveness; government policies; environmental sustainability; labor skills and training; and natural and cultural resources [56].

From a network perspective, Matthews has concluded that the international tourism performance reflects international relationships that were shaped through people (from origins to transnational destinations), governmental negotiations, and the corresponding political relationship [57]. Therefore, international tourism development highly relies on cooperation and collaboration, which means whom they contact and how to link are the prerequisites for performance.

The global tourism network is a comprehensive system to show how tourists move among countries and explain the various phenomena in international tourism [58]. A larger volume of flow connecting between two countries in the network always demonstrates a closer relationship, which may be affected by population, economy, cultural context, international policies, environment, transportation, employees in tourism, travel services, and others [59,60]. Depending on econometric and geographic modeling (e.g., linear or non-linear regression analysis, panel data, meta-analysis, gravity model, artificial neural network), plenty of works on the influential factors, tourists’ demands, and arrivals forecasting according to the international tourists’ flow have appeared in past three decades [61,62,63,64,65], while relatively little has been published with a global network perspective.

Previous studies have shown some characteristics of the global tourism network. Miguéns et al. firstly used the complex networks method to clarify the free-scale and small-world structure of the worldwide tourist arrival network, which also showed a degree-correlation feature [66]; Lozano and Gutiérrez found that the global tourism network with the most important ties among countries has a scale-free distribution with some occurrence of reciprocity, large transitivity, and high-degree centralization inside the formation of tourism clusters determined by geographical, trade and cultural factors [67]. Similarly, in the work of Chung et al., the social network method has been applied to identify the global tourism cluster changes and showed the factors (including language, distance, attractions, crisis events and visa policies) affecting tourists flows [5]. Recently, Seok et al. adopted social network analysis to find that global outbound and inbound tourism have decentralized gradually from 2002 to 2014, where the nodal degree, betweenness, and eigenvector centrality were correlated with each other as well as significantly affected by GDP and population [8]. Undeniably, these research studies brought contributions to understand the GNT evolution and help clear the tourism relationship in the world, but some limitations also remain.

First, what does the GNT really mean to the participating countries? As a network can raise the transferring efficiency of information and knowledge, it is deemed to speed up the tourist’s travel frequencies and raise the number of international tourists’ arrivals. Thus, as the GNT expansion, global tourism’s performance may be changed by the unique structural characteristics, which needs a long period of observation but has not been born out.

Second, the network brings both cooperation and competition to each actor with a decentralized path; however, the impacts of the GNT on different individuals are various. What these impacts are and how they work are also the issues that need to be explored and explained.

Third, the international travel market is characterized by uncertainties; as Morrison et al. suggested, resources should be targeted at the careful formulation of networks guided by the identified success factors [27]. As a member of the tourism network, the rule of choosing the best cooperators to improve the tourism industrial performance is essential for participants. The application of social network research shows an approach to detect the targets’ characteristics, which can be considered available on the GNT and is expected to provide more practical implications for international tourism management.

3. Materials and Methods

This section describes the proposed approach for this research. The aim of this research is to detect the influence of the GNT structure on the tourism industry, and the research framework is shown in Figure 1. Firstly, through statistics data, all 222 regions can be seen as nodes, and the tourist flow from one country to another can be seen as an edge (which means the edge has a certain direction); thus, the GNT can be constructed. Secondly, the GNT structural characteristics should be calculated; some metrics are chosen from both the global level and individual level to reflect the network structure and network evolution. Thirdly, how the GNT structure work on the tourism industrial performance is identified. In order to recognize the influential law among different structural characteristics (variables), the authors propose the hypotheses model and employ two research methods from the global and individual level, respectively. From the global level, the Pearson correlation test is used, since it can indicate the relationship among variables easily, and then, some simple fit-ting models are used to help to find the influential rules. From the individual level, the gravity model with mixed-effect regression is applied, considering the relationship between pairs of nodes (the gravity model can reflect the source and target nodes’ characteristics) and the impact of other noises on the results (the mixed-effect model can strip other uncertain factors and conduct stratified analysis easily). Above all, the impacts of network structure on the tourism industry can be indicated and used to organize the international tourism development effectively.

3.1. Data Source

Data on international tourists’ flow were all gained from the UN World Tourism Organization (UNWTO) (https://www.e-unwto.org/toc/unwtotfb/current, accessed on 10 December 2021). The database refers to the tourism arrivals of 222 regions from 1995 to 2019 (all the regions’ names can be gained in the database, where China Mainland, China Hongkong, China Macao, and China Taiwan are classified as different regions). Since the data are not available in this database, this paper did not consider the change during the COVID-19 period. The statistics of the regions’ outbound and inbound tourists are shown as how many tourists move from one region to another, and some different indicators also exist for each country, including, (i) the “TFR” represents “arrivals of non-resident tourists at national borders”; (ii) the “VFN” represents “arrivals of non-resident visitors at national borders”; (iii) the “TCER” represents “arrivals of non-resident tourists in all types of accommodation establishments”; and (iv) the “THSR” represents “arrivals of non-resident tourists in hotels and similar establishments”. For the sake of data unification, the research chooses the data of “TFR” and “VFN” firstly, and if there are no “TFR” or “VFN” indicators, the “TCER” and “THSR” will be substituted. All the data of the 222 listed regions in the UNWTO database from 1995 to 2019 have been obtained, and the number of data is more than 300,000.

What is more, the distances between different countries are needed to help modeling, which are shown as the straight-line distances and can be calculated by the geodetic coordinates of geometric center in each.

3.2. Method

3.2.1. Network Structure and Performance Measurements

The network structure is usually described from three levels: the global level, the meso level, and the individual level. Measurements from the three levels reflect the various features of whole, subgroups, and single nodes in a network, respectively [43,68]. The global-level metrics reflect the topological characteristics and the whole function, the meso-level metrics indicate the degree of hierarchy within the network, while the individual-level metrics demonstrate the degree of centralization and density, the strength of ties and the extent of structural equivalence between different segments of the network [68,69,70]. The two dimensions of network structure, the global level and the individual level, are regarded as the fundamentals that determine the network’s efficiency; thus, this paper only focuses on the two-level structural metrics’ impact. The measurements this paper adopts are listed in

Table 1. The measurements of network structures and international tourism performance.

Metric	Abbreviation	Means	Formula
Network Structure on Global Level f(G)
Density	DE	The density of edges between nodes in a network.	$DE=\frac{L}{2N\left(N - 1\right)}$
Clustering Coefficient	CLC	The degree of clustering between vertices.	$CLC=\frac{\mathrm{number} \mathrm{of} \mathrm{closed} \mathrm{triplet}}{\mathrm{number} \mathrm{of} \mathrm{triplet}\left(\mathrm{closed} + \mathrm{open}\right)}$
The Average Path Length	APL	The average shortest distance between all pairs of nodes.	$APL=\frac{2}{N\left(N+1\right)}{\displaystyle \sum }_{i\ne j}{d}_{ij}$
Small-Worldness	SW	The degree of small-world nature.	$SW =\frac{CLC/CL{C}_{random}}{APL/AP{L}_{random}}$
Network Structure on Individual Level
Degree Centrality	DC	The number of other nodes in the network directly tie with a referred one.	$D{C}_i=\frac{{{\displaystyle \sum }}_j(w_{ij}+w_{ji})}{2\left(N-1\right)}$
Closeness Centrality	CC	The degree of a node is close to all others.	$C{C}_i=\frac{1}{{{\displaystyle \sum }}_{j=1}^N{d}_{ij}}$
Betweenness Centrality	BC	The frequency of a node which is just in the path of other pairs in the network.	$B{C}_i={\displaystyle \sum }_{j,k\in I}\frac{\sigma \left(j,k\mid i\right)}{\sigma \left(j,k\right)}$
Eigenvector Centrality	EC	Based on connections to high-scoring nodes contribute more to the score of the node to measure a node’s influence.	$E{C}_i={\lambda }^{-1}{\displaystyle \sum }_{j=1}^N{A}_{ij}{e}_j$
The Local Clustering Coefficient	LCLC	The extent of the neighbors of a referred point, which are also interconnected.	$LCL{C}_i=\frac{E_i}{m_i\left(m_i-1\right)}$
International Tourism Performance
The Amount of Average International Tourism Arrivals	AITA	The average number of international tourism arrivals of all countries in the GNT	The amount of all international tourism arrivals in the world divided by the number of countries
The Number of International Tourism Arrivals From a Country	ITA	The international tourism arrivals from j country to i country	Directly gain from statistics

Note. In the above formula, G means a definite network, which has N members and L edges. i and j represent the two nodes i and j, respectively, if there is a direct tie from i and j, and the edge is shown as e_ij. Notice that the network is directed, the edge from i to j is different from the edge from j to i. L(i) is the set of nodes directly connected to vertex i. d_ij represents the path length of a pair node i and j. $A_{ij}$ is the adjacent matrix of the network, where A_ij is 1 if i directly contacts with j; otherwise, $A_{ij}$ is 0. w_ij is the weight of edge from i to j. $\sigma \left(j,k\right)$ is the sum of the shortest path between a given pair of nodes i and j, which can be counted by the distance $d_{ij}$.$\sigma \left(j,k\mid i\right)$ denotes the weighted shortest paths from node j to k that pass-through vertex i. $\lambda$ and $e_j$ are the largest eigenvalues of the adjacent matrix and its eigenvector. E_i is the number of edges in a subgraph, which only contains all the nodes that directly contact with the node i.

. All the structural metrics are commonly mentioned in the complex network research and used to reflect the network structure comprehensively [68,71].

Since the metrics of two levels show the network structure in different scales, we take two indicators to reflect the international tourism industrial performance (Table 1): at the global level, the amount of average international tourism arrivals is considered (because the number of participants is dynamic); at the individual level, the international visitors from different regions are employed (to show the tourism industrial performance between each two regions).

The previous research foundation in Section 2.1 has shown that different metrics generate different impacts. Considering the mean of each metric and others’ relative research results, this paper proposes hypotheses as shown in Figure 2. Firstly, the influences of the global-level structure of GNT on tourism industrial performance are recognized from Hypothesis 1.

Hypothesis 1.

The global tourism network structure will affect the overall international tourism performance.

Furthermore, from the measurements above, this paper lists the following detailed hypotheses:

Hypothesis 1a (H1a).

The density (DE) of GNT can positively affect the overall tourism performance.

Hypothesis 1b (H1b).

The degree of clustering between regions (CLC) of GNT can positively affect the overall tourism performance.

Hypothesis 1c (H1c).

The average shortest distance between all pairs of regions (APL) of GNT can negatively affect the overall tourism performance.

Hypothesis 1d (H1d).

The degree of small-world nature (SW) of GNT can positively affect the overall tourism performance.

Secondly, the influences of the individual-level structure of GNT on tourism industrial performance are recognized from Hypothesis 2.

Hypothesis 2.

The individual structure of regions in the tourism network will affect individual tourism performance.

The details of Hypothesis 2 are shown as follows:

Hypothesis 2a (H2a).

The number of other nodes in the network directly tied with a region (DC) in the tourism network has a positive effect on its tourism performance.

Hypothesis 2b (H2b).

The degree that a region is close to all others (CC) in the tourism network has a positive effect on its tourism performance.

Hypothesis 2c (H2c).

The frequency of a region that is in the path of other pairs (BC) in the tourism network has a positive effect on its tourism performance.

Hypothesis 2d (H2d).

The high structural influence of a region (EC) in the tourism network has a positive effect on its tourism performance.

Hypothesis 2e (H2e).

The neighbors of regions also being interconnected (LCLC) in the tourism network has a positive effect on its tourism performance.

Additionally, all the individual indicators can be expressed in a standardized form, ranging from 0 (lowest value) to 1 (highest value), which is used to measure different facets of the same node’s features in the network. These metrics may not be enough to describe the network structure comprehensively; however, they still reflect the basic network structural characteristics to some extent.

3.2.2. The Correlation Tests

The correlation test can find associations in variables and performance to address research questions about how the network structure influences tourism performance at a global level. In this study, the Pearson correlation test is applied for calculating the correlation coefficients, which is a common method to measure variable relationships numerically and easily. The Pearson correlation test is conducted based on the software SPSS v21.0.

3.2.3. Gravity Model Building

The gravity model is one of the widely used methods to study the tourists travel from one place to another, which belongs to the family of spatial interaction models. Its significant advantages rely on its simply used and good ability to produce accurate results, which are easily explained by the spatial relationship and demonstrate the relationship between two entities considering their different characteristics.

The gravity model assumes the trade flow (tourist flow can be regarded as a type of trade flow) transferring from the origin to destination is positively affected by the reciprocal of the distance between the two and positively affected by the characteristics of the two regions (e.g., population, income, GDP) [72,73]. In addition, these concepts allow for different interpretations. For instance, spatial separation, which is always regarded as physical distance, can be expressed by political or cultural distance. Just as Morley said, the traditional gravity model also needs to consider more variables to statistically show the potential relationship and provide more theoretical and practical implications [74]. Thus, this research takes the gravity model as the basic statistic theory to analyze the effects of tourism network structure on tourism performance.

Here, the tourist flow from one country is shown as the dependent variable in this study, representing the international performance; meanwhile, the node’s characteristics can be seen as the influencing characteristics, and the global measurements of the GTN’s structure are shown as mediator variables in the equation as follows:

$$IT{A}_{ijt}=\frac{C_{it}{}^{{\beta }_{1t}}{C}_{jt}{}^{{\beta }_{2t}}}{d_{ij}{}^{{\beta }_3}}·E_{ijt}$$

(1)

where $IT{A}_{ijt}$ represents the tourist flow from i to j in the year of t, and d_ij is the spatial distance between the two, which can be calculated from the latitude and longitude of each region’ s geographical center and then transformed into a geodetic coordinate system; $C_{it}$ and $C_{jt}$ represent the measurement of the node i and j in the year of t, respectively; and E_ij is a normal distributed error.

The gravity model can be converted as a linear model to estimate all these factors’ impacts. This research applies the mixed-effect multi-level regression model considering different countries’ features. The mixed-effect model is developed to account for both network and temporal dependencies [75]. The results provide means and regression estimates of the factors affecting global tourism networks as well as evidence of statistical dependencies [5]. The mixed-effect regression model from the gravity model conversation is displayed as Equation (2), and it is calculated based on the mixed-effect modular of software State v16.0.

$$\begin{array}{lll}\ln IT{A}_{ijt}& =& {\beta }_{1t}\ln D{C}_{it} + {\beta }_{2t}\ln D{C}_{jt}\\ & & + {\beta }_{3t}\ln C{C}_{it} + {\beta }_{4t}\ln C{C}_{jt} + {\beta }_{5t}\ln B{C}_{it} + {\beta }_{6t}\ln B{C}_{jt} + {\beta }_{7t}\ln E{C}_{it} + {\beta }_{8t}\ln E{C}_{jt}\\ & & + {\beta }_{9t}\ln LCL{C}_{it} + {\beta }_{10t}\ln LCL{C}_{jt} + {\beta }_{11t}lndi{s}_{ij} + s_{it} + t_{jt} + {\epsilon }_{ijt}\end{array}$$

(2)

where β_1t to ${\beta }_{11t}$ represent the coefficients of all the variables we selected in the year of t; s_it shows the effect of the source country i; t_jt is the effect of target country j; and ${\epsilon }_{ij}$ is a residual error in regression model.

For an objective estimation, this research firstly arranges the model as longitudinal panel data to obtain the effects of all the variables overhaul; then, it calculates the coefficients between 222 regions for each year from 1995 to 2019, which can help to understand the changes of GNT. Additionally, owing to the possible multicollinearity among variables, before calculating the coefficients, the multicollinearity test must be conducted first.

4. Results

4.1. The Structure Characteristics of GTN from 1995 to 2019

During the 24 years, Figure 2 shows that the members of nodes in GNT have increased from 215 to 222, the number of GNT’s edges has risen from 7163 to 15,701 with an average rate of 4.76% (Figure 3).

From the result of global network structure statistics (Figure 4), the APL is increasing, while the CLC is decreasing. Simultaneously, the GNT has small-world characteristics, but when removing with the effect of the network’s scale, the degree of small-worldness (SW) is declined.

The global performance indicates that AITA changes from 1995 to 2019. From Figure 5, the result demonstrates that its trend is fluctuating upward.

Based on ArcGIS visualization, Figure 6 shows the global international tourist flows distribution in 1995, 2003, 2011 and 2019, which are selected in a similar interval to reflect the changes directly. We can find that only the tourists flow of Poland to Germany, US to Mexico, and China Hong Kong to China Mainland ranked on the first level in 1995 based on the natural breaking classification method. Then, the tourist flow of UK to Spain and US to Canada came into the first level in and after 2003, which represents the top attractive routes for international tourists.

Then, this research calculates each of the individual measurements’ average value as the formulas in Section 3.2.1 of all the countries, and we list the top three and last three countries according to each metric in

Table 2. The average descriptive statistic of all individual metrics during 1995−2019.

Metric	Value Range	Std. Error	Top 3 Countries	Last 3 Countries
DC	[1.728 × 10−5, 0.877]	0.133	China Mainland, United States, Germany	Tuvalu, Equatorial Guinea, Nauru
CC	[0.467, 0.946]	0.086	United States, Canada, Germany	Sint Maarten, Aruba, Palau
BC	[0, 0.067]	0.008	United States, Canada, Italy	Equatorial Guinea, Nauru, Guinea-Bissau
EC	[0, 0.971]	0.294	Belgium, United States, Hong Kong (China)	Equatorial Guinea, Nauru, Guinea-Bissau
LCLC	[0, 0.975]	0.182	South Sudan, Eritrea, Burundi	United States, Belgium, Canada

. The value frequency distribution of each metric is shown in Figure 7 through MATLAB v7.0. The distribution of weighted degree centrality shows as a power law, which is same as that with the research from Miguéns et al. [66] and Lozano et al. [67], and it indicates that the GNT has a significant small-world nature. The power law distribution can be seen in BC’s distribution as well, meaning only few countries with a very high level of BC. The distributions of EC, CC and LCLC appear as skew distributions but with different shapes (Figure 5).

4.2. The Effects of Global Network Structure on Tourism Industrial Performances

The results of Pearson’s correlation coefficients based on SPSS v21.0 are shown in

Table 3. The correlation coefficients between the global measurements and performance indicator.

	DE	CLC	APL	SW	AITA
DE	1
CLC	0.928 **	1
APL	−0.975 **	−0.951 **	1
SW	−0.977 **	−0.919 **	0.972 **	1
AITA	0.963 **	0.918 **	−0.951 **	−0.909 **	1

Note. Here “ ** ” means the coefficient is significant in the level of 0.05.

, which suggest all these variables are correlated with each other.

There are positive and significant relationships between the global international tourism performance (AITA) and two metrics (DE and CLC), but APL and SW have significant negative impacts on AITA. That is to say, the higher the density of edges between nodes or the higher the degree of clustering between nodes in GNT, the higher the whole number of international arrivals. Contrarily, either a higher average shortest distance among all pairs of nodes or high small-world nature degree of GNT always indicates a lower number of tourists traveling overall. Meanwhile, different from the results from Aarstad et al. [40], Table 3 shows that a higher degree of small-worldness cannot contribute to improving global performance; thus, promoting rational global network structure construction is necessary for the whole world’s tourism development.

To explore how the network structure influence the global performance, this research applies some commonly used fitting models including linear model, exponential model, logarithmic model, and power model, respectively, to try to find the statistical relationship between global international tourism performance and these four indicators (DE, CLC, APL, and SW). All the calculation procedures are conducted in SPSS v21.0. From the results of R² (

Table 4. The fitting models test of different metrics and AITA.

	Linear Model		Exponential Model		Logarithmic Model		Power Model
Model	$\mathit{y}={\mathit{\beta }}_0+{\mathit{\beta }}_1\mathit{x}+\mathit{\epsilon }$		$\mathit{y}={\mathit{\beta }}_0\mathit{e}{ }^{{\mathit{\beta }}_1 \mathit{x}}\mathit{\epsilon }$		$\mathit{y}={\mathit{\beta }}_0+{\mathit{\beta }}_1\ln \left(\mathit{x}\right)+\mathit{\epsilon }$		$\mathit{y}={\mathit{\beta }}_0\mathit{x}{ }^{{\mathit{\beta }}_1}\mathit{\epsilon }$
	${\mathit{\beta }}_0$	${\mathit{\beta }}_1$	${\mathit{\beta }}_0$	${\mathit{\beta }}_1$	${\mathit{\beta }}_0$	${\mathit{\beta }}_1$	${\mathit{\beta }}_0$	${\mathit{\beta }}_1$
DE	1 × 106	2 × 107	1 × 106	5.288	1 × 107	5 × 106	2 × 107	1.277
R2	0.9267		0.9623		0.8926		0.9495
CLC	−3 × 107	6 × 107	503	13.952	2 × 107	4 × 107	2 × 108	8.899
R2	0.8428		0.8662		0.8338		0.8615
APL	3 × 107	−2 × 107	4E+9	−4.077	2 × 107	−3 × 107	2 × 108	−7.703
R2	0.9051		0.9483		0.9181		0.9562
SW	9 × 106	−2 × 106	1 × 107	−0.601	8 × 106	−5 × 106	1 × 107	−1.329
R2	0.8265		0.9071		0.8708		0.9348

), we can assume that the relationship between AITA and DE as well as the relationship between AITA and CLC tend to exponential models. At the same time, the relationship between AITA and APL as well as the relationship between AITA and SW look like an obeying power model. That means the different characteristics of a network structure require different influencing laws on tourism performance, which can help us to guide the global tourism performance from a network structure perspective.

4.3. The Effects of Individual Network Structure on Tourism Performances

Firstly, before the coefficient calculation, the variance inflation factor (VIF) is applied to test the multicollinearity, and the result is shown in

Table 5. The estimation of variables’ effect.

Variables	Coefficient	Std. Err.	t	95% Confidence		VIF	Revised VIF
				Lower	Upper
Constant	42.8090	0.0838	511.08 ***	42.6448	42.9732	-	-
ln dis	−1.7354	0.0049	−356.15 ***	−1.7449	−1.7258	1.154	1.154
ln DCi	0.7068	0.0148	47.83 ***	0.6778	0.7357	8.784	6.836
ln DCj	-	-	-	-	-	11.331	-
ln CCi	8.9563	0.0380	235.52 ***	8.8818	9.0308	2.468	2.311
ln CCj	9.3708	0.0394	238.02 ***	9.2936	9.4479	3.068	2.165
ln BCi	-	-	-	-	-	12.853	-
ln BCj	0.1994	0.0040	49.82 ***	0.1916	0.2072	6.431	6.145
ln ECi	−0.0017	0.0016	−1.08 ***	−0.0048	0.0014	7.782	2.181
ln ECj	−1.0637	0.0124	−85.46 ***	−1.0880	−1.0393	5.942	3.204
ln LCLCi	−1.4942	0.0262	−57.05 ***	−1.5455	−1.4428	4.600	3.401
ln LCLCj	−1.6121	0.0282	−57.08 ***	−1.6674	−1.5567	4.557	4.049

Note. Here “***” means the coefficient is significant in the level of 0.01.

. The VIFs of DC_j and BC_j are all greater than 10, which means the multicollinearity problems exist and the two variables need to be deleted [76]. Then, the revised VIFs have been calculated and shown in Table 5; all the variables’ VIFs are below 10, which means the multicollinearity has disappeared. Then, the effect of sources and targets are added as random effects, and other variables are shown as fixed effects. From the significance testing of t (Table 5), all the variables can significantly influence the dependent of ITA. The impacts of dis, EC_i, EC_j, LCLC_i, and LCLC_j are negative, while other variables generate a positive impact on ITA.

By comparison, expect for the DC and BC, all the degrees of impact from the variables of target countries are higher than the sources, which means if a country wants to improve their international tourism performance, it would be better to optimize its own network characteristics (e.g., increase the value of centrality).

The coefficients of variables indicate how much the expected international tourism arrivals from a country are multiplied through a unit increase in the independent variable (the degree is exp(β_i) − 1). Due to all the nodal measurements being normalized, we can easily find that the measurement of CC_j has the highest degree of impact on international tourism performance. The coefficient shows that when increasing one unit of CC_i, the percentage of international arrivals from a definite origin will rise ([exp(9.3708) − 1] × 100%). That means how many regions one can connect with will most positively impact one’s international arrivals. The CC of the source has the second rank of positive effect, and then the DC of the source is the third. Furthermore, no matter the coefficients of DC from the source and target, the values are higher than other coefficients with the positive impacts, which means that DC is the most important metric for individual performance improvement.

The variable dis shows the negative effect as we assumed, which indicates that a higher distance between two countries causes fewer visitors from one to another. The EC_i, EC_j, LCLC_i and LCLC_j also negatively impact international tourism arrivals, which have not been detected ever and deny H2f and H2g. The higher score of eigenvector centrality of a node means that this node relates to many others with a higher score, which may cause the individual region’s international tourists’ loss, and that is similar to the research from Abbasi, et al. [77].

Then, we analyze the effect of all the variables each year to detect the changes of impact yearly. All the degrees of variables’ impact have been converted to the direct effect on ITA for each year from 1995 to 2019 based on visualization in MATLAB v7.0 (Figure 8).

The result indicates that the influence of CC has been changing considerably in both target and source. The effects of CC from the source are the most changeable with 7414.14% between the lowest (1995) and the highest (2018), and the highest (2000) of CC from the target is higher with 1148.41% more than the lowest (1997).

Before 2000 and in the years of 2002, 2004, and 2008, the coefficients for LCLC of the target are positive, but in other years, the coefficients are negative, demonstrating that the influence of targets’ LCLC is uncertain.

The negative effect of EC and LCLC from the target as well as the distance have been amplified, whereas the coefficients of CCi are gradually more positive.

5. Discussion

The global tourism development has made the world tourism industry a network. The network structure significantly influences the dynamical characteristics of tourism under the perspective of networks [78], but the impact characteristics are not clear yet.

In order to improve the achievement of international tourism and ensure that it is well-performing, this study applies the complex network theory to detect how the GNT changes and how the GNT structure affects the international tourism industrial performance.

Firstly, the GNT based on international tourism arrivals of 222 regions from 1995 to 2019 has been constructed. In terms of the GNT evolution, the results show that the size of the GNT has been gradually expanding both from the numbers of nodes and edges as well as the total number of tourists. The APL increased, while the CLC and SW decreased at the global level, which are partly similar with the findings of Chuang [5] and Lozano [67], which also indicate that the network structure may affect the number of tourists.

Then, the work of the GNT structure’s influence analyses is divided into two parts. The study employs the AITA (the amount of average international tourism arrivals) as the overall performance indicator and global network structure measurements (density, average path length, clustering coefficient, and small-worldness) as the variables to show how they affect each other through Pearson’s correlations test. The results indicate that each pair among them has a significant correlation, and the effect of density and clustering coefficient on the AITA is significantly positive, while the average path length and small-worldness have a significantly negative impact. That means if the global tourism network has either a higher density of edges between the nodes (regions) or a high degree of clustering, it will generate a larger amount of tourists overhaul. However, if the network has a high average shortest distance between all pairs of nodes or a high degree of small-world nature, the overall number of tourists will be lower. The similar outcomes are shown in other fields of research, e.g., team–game network [37], knowledge diffusion network [79] and policy network [35], which demonstrates that these real-world networks have general characters in the structures. What is more, from the fitting model test, the exponential models can well fit with the relationship of DE and CLC between AITA, respectively. Simultaneously, the relationship between AITA with APL and SW shows a power model, which means they have different influencing degrees, and this can be helpful for predicting the global tourism performance from a network structure.

Secondly, we explore how the individual’s network structure characteristic affects an individual’s tourism performance through the gravity model and mixed-effect model. The results reflect the individual’s weighted degree centrality, the closeness centrality, and the betweenness centrality, which positively influence the individual’s international tourism arrivals with significance at the level of 0.001. Meanwhile, the eigenvector centrality and local clustering coefficient work negatively on individuals’ performance. That is to say, if a region is connected with more other regions, that means it is close to others and helps link to other pairs of regions, which can bring more international arrivals. However, if the region only relies on some more influential regions’ connections or has some competitive neighbors, its attraction for international tourists will decrease. Additionally, all the impact degrees from the same variable of target countries are higher than those of the sources. That means that a region needs to change its own roles in the global tourism network to gain more arrivals instead of only relying on cooperative partners. These results may look like common sense for scholars, but they are firstly explained from a network perspective in a quantitative way. However, uncertainties that originated from the models and data also exist. For example, the lack of meso-level analysis may generate bias, and the yearly changes variables need long-time observation.

6. Conclusions

The findings of this research have supported the argument that the tourism network structure can affect the tourism performance significantly. However, the different influential characteristics are shown from different structural metrics from the global and individual level. The results indicate the network structure can change the global international tourism arrivals, which means the global tourism development can be described as the effect of the global tourism network structure on the tourism industrial performance. The methodology gives a useful application of network theory in the tourism field by a long-time period statistic and a new quantitative way to explain how the global network influences global and individual tourism development.

The work demonstrates the various effects of the network structure from nine hypotheses divided into the global and individual levels. The different characteristics of tourism network structure can reflect different levels of tourism industrial development status, which helps researchers further understand each measurement’s means and impacts as well as contributes to the network theory.

What is more, the differences between the measurements of the sources and targets explain that a pair node (region) in the tourism network have different effects on each other, where the target’s structural characteristics have the larger impact, which has not been considered before.

According to these findings, some practical suggestions and implications can be proposed for global tourism development. Such efforts are believed to bring tourism economic developments and increase countries’ awareness of screened cooperators in the global context.

For a country that wants to increase their international performance, the most important thing is to improve its own network structural characteristics, such as raising the degree centrality (contact with more countries), closeness centrality (direct contact with other countries not based on others’ links), and betweenness centrality (help more region pairs construct the shortest path to each other), as well as declining its eigenvector centrality (decrease the attachment with regions that have a higher connection and influence to others) and decreasing the local clustering coefficient (establish association with some end-point regions). By comparison among coefficients, in global tourism networks, the closeness centrality, especially from the source, is the most important in international tourism performance. Thus, keeping a close tie with high closeness countries is an effective strategy for attracting international tourists.

Secondly, from the targets, some countries (such as the United States, China mainland, and Canada) with higher degree/closeness/betweenness centralities and lower eigenvector centralities and clustering coefficients will be popular for those who want to increase their own tourism performance.

Certainly, strengthening ties between regions to raise the global tourism network’s density and clustering coefficient can increase global tourism and bring benefits to all the regions, which need international cooperation and close coordination.

Meanwhile, this research also has some limitations that need to be further researched. First, we only set the tourism network within global tourism, as we know that the tourism network can be divided into many types, and the network effects should be discussed in other issues to help to solve complex tasks. Second, we use longitudinal quantitative methods to analyze the effect of network structure; why the coefficients are changeable and how they are affected by other conditions are covered. Third, we separate the overall performance and individual performance in this study, but they work simultaneously and must influence each other in reality. We divided the two levels into different models and discussed them, respectively, which can cause bias in the effect estimation. Fourth, this research only considers the indicators of the global and individual level of network structure, and they cannot conclude all the details of the tourism network. More metrics should be further analyzed and distinguished. Moreover, the mixed effect includes the effects from sources and targets; thus, more countries’ profiles need to be considered in effects such as population, economy, political stability, accessibility, and resources, which may affect the location of the country in a network and cause the difference in performance.