Temporal Analysis of Tourism Research Collaboration Network

Abstract

Network analysis is an effective tool for the study of collaboration relationships among researchers. Collaboration networks constructed from previous studies, and their changes over time have been studied. However, the impact of individual researchers in collaboration networks has not been investigated systematically. We introduce a new method of measuring the contribution of researchers to the connectivity of collaboration networks and evaluate the importance of researchers by considering both contribution and productivity. Betweenness centrality is found to be better than degree centrality in terms of reflecting the changes of importance of researchers. Accordingly, a method is further proposed to identify key researchers at certain periods. The performance of the identified researchers demonstrates the effectiveness of the proposed method.

Keywords

research collaboration network analysis centrality measure betweenness

Collaboration in scientific research is a common practice that enables researchers to share and exchange resources, knowledge, and ideas and, to achieve high-quality research outcomes. The investigation of the collaboration of researchers and the corresponding collaboration trends has a long history because collaboration is important for many research areas (Jogaratnam, Chon, McCleary, Mena, & Yoo, 2005; Katz & Hicks, 1997; Sheldon, 1991). In studying the collaboration relationships among researchers, better understanding of collaboration can be obtained to help promote the progress of research and to disseminate knowledge.

Two major approaches are used in the investigation of scientific research collaboration: traditional quantitative analysis (Sheldon, 1991) and network analysis (Newman, 2001a). With traditional quantitative analysis, researchers have investigated the scale of collaboration in the literature as well as the relationship between collaboration and the research influence. This approach provides information on the frequency of collaboration of researchers from different disciplines as well as the importance of researchers that can be measured by the number of citations. However, the approach provides no information on the paths where knowledge is spread. Without such information, understanding the spread of knowledge among researchers and the role of researchers in maintaining knowledge flow becomes difficult. To address this issue, network analysis approach has been recently exploited in studying the relationships among researchers. Scientific information and knowledge can be spread among researchers by, among others, collaboration and citation. Collaboration relationships (Newman, 2001a, 2001b) and citation relationships (Benckendorff & Zehrer, 2013) have been investigated in previous studies. In a co-citation network of researchers, a pair of researchers is connected if they are frequently cited together in the same article. In a collaboration network, two researchers are connected if they have collaborated in the same article. The focus of our work is the collaboration relationships among researchers. As such, we mainly concentrate on the dissemination of information and knowledge in terms of collaboration. In network analysis approach, researchers are represented as nodes, whereas the collaboration relationships among researchers are represented as edges. These nodes and edges form a collaboration network. Structural properties of a collaboration network can be used to measure the maturity of this network. Moreover, with graph visualization tools of network analysis, collaboration relationships among researchers become visible and easily understood. Recently, collaboration networks have been generated from published articles in many disciplines, including tourism research (Racherla & Hu, 2010; Ye, Li, & Law, 2013). One of biggest concerns of researchers is the evolution of collaboration networks. In existing studies, different collaboration networks have been constructed based on research articles published in different periods of time, and their structural properties have been calculated and compared (Franceschet, 2011; Huang, Zhuang, Li, & Giles, 2008).

However, most studies on the analysis of collaboration networks are hindered by two major limitations, especially in tourism research:

First, existing studies on the evolution of collaboration networks mainly focus on the changes of global properties of entire networks, such as the changes in the sizes of networks, clustering coefficients, percentages of the largest connected components, and other changes. The changes of these properties reflect the fast pace of the evolution as well as the global trend of collaboration. However, these studies overlook the changes of individual researchers, which can help explain the changes of global properties. For example, a researcher in a period may be essential in maintaining most knowledge flows because of the researcher’s heavy collaboration with researchers from different clusters. In studying the changes of the structural properties of individual researchers, explanations of global changes can be obtained, and key researchers of such global changes can be defined.

Second, in previous studies, productive researchers are considered important, and the rankings of these researchers in different periods have been compared (Racherla & Hu, 2010). However, in a collaboration network, an important researcher should also contribute to the connectivity of the network, whereas productive researchers do not necessarily contribute the most to effective knowledge dissemination in a collaboration network. Therefore, measuring the importance of researchers through productivity and the contribution to connectivity becomes necessary. The correlation between structural properties and importance should be investigated so that key researchers resulting in global changes of collaboration networks can be identified because the changes of researchers’ structural properties may reflect their changes of importance.

This study investigates the evolution of individual researchers in collaboration networks and identifies the key researchers who contribute significantly to the changes of collaboration networks. The outcomes of this study can be applied to further studies on the analysis of research topics. For example, by studying the evolution of research topics of individual researchers, especially key researchers, research trends can be understood and suggestions on selecting reviewers and collaborators can be provided. Moreover, the method proposed in this study can be applied in the analysis of other social relationships.

With advances in the structural analysis of social networks, the structural importance of individual nodes can now be quantified. This study will solve the problems overlooked in existing studies by systematically analyzing the changes of importance of individual researchers at different time periods and by studying the corresponding changes of centrality measures. In achieving these research objectives, two technical challenges should be addressed:

The importance of researchers is evaluated. From the perspective of knowledge dissemination, an important researcher should be critical in maintaining the connectivity of a collaboration network. However, previous studies mainly focus on researchers with high productivity. A measure that can assess the contribution of researchers to connectivity is in demand to evaluate the importance of researchers by both productivity and this measure.

Key researchers are identified. The importance of researchers in collaboration networks may change in different periods. A researcher with significant improvement in importance during a certain time period may be a key researcher critical in affecting the global properties of the collaboration network in this period. In network analysis, the importance of nodes can be reflected by centrality measures. A proper centrality measure should be suggested to identify key researchers with significant improvement in both productivity and contribution to connectivity.

The rest of this article is organized as follows. The next section reviews the literature on collaboration in research. Subsequently, the “Method” section presents the methodology used in this article. This is followed by the “Analysis and Results” section, which provides the results of the analysis in the study. The final section concludes this article and provides suggestions for future work.

Related Studies

Collaboration is a common research practice that can improve the influence and the quality of research articles in most areas (Franceschet & Costantini, 2010; Katz & Hicks, 1997). Therefore, the topic of research collaboration has attracted significant research interest in the past few decades. Investigating the collaboration among researchers or institutes explains the exchange and spread of knowledge and research resources.

Traditional Quantitative Analysis of Collaborations

Traditional quantitative analysis has been extensively used in the study of research collaboration. Typically, researchers have investigated collaboration frequency, collaboration distribution, and citation analysis. For example, in the study by Katz and Hicks (1997), the number of citations for each article is counted to measure the influence of the research articles. They have demonstrated that if the authors of an article are from institutions in different countries, the influence of the article can be improved.

Analysis of Tourism and Hospitality Research

In the study by McKercher (2007), 25 prolific researchers in tourism and hospitality are investigated. Results show that these prolific researchers tend to take a leading role in research articles and do not collaborate with other prolific researchers frequently. In the study by Tsang and Hsu (2011), 119 articles on Chinese tourism and hospitality are analyzed. The results show that researchers usually collaborate with those from different universities or countries. Moreover, the authors study the trend of collaboration and find that the number of multi-authorship articles has grown since 1999. Leung and Law (2006) analyze 185 information and communication technology–related publications from six leading journals in tourism and hospitality. They find that multiple-authored articles increased from 1985 to 2004.

Analysis of Tourism Research Collaboration

Sheldon (1991) collects articles published on three tourism journals in the 1980s. The collaboration ratio for universities is calculated. The results show that the quality of research can be improved by cross-disciplinary and international collaboration. Jogaratnam et al. (2005) replicate the study of Sheldon (1991) with a collection of research articles published from 1992 to 2001. They follow the methodology of Sheldon (1991) stating that each author of multiauthored articles is given the same amount of credit as an author who has published an article independently. They analyze author affiliations, repeat contributions by authors, and repeat contributions by institutions and other bodies and find that the top 10 institutions identified in their work have changed significantly when compared with the work of Sheldon (1991). Moreover, Zhao and Ritchie (2007) investigate 57 leading researchers in tourism research. The authors provide the number of articles that these leading researchers have published in eight journals. Collaborations between these leading researchers are also studied. The results show that collaboration is a dominant theme, but leading researchers usually cooperate with only one collaborator. In the study of Hall (2011), journal influence and ranking are studied. The percentage of international collaboration is calculated to evaluate journal quality.

Traditional bibliometric methods can provide statistical information on the collaboration in different research areas as well as the trend of collaboration. However, patterns such as the way which knowledge is disseminated in the form of collaboration from a researcher to others or the paths that knowledge goes through cannot be obtained from these methods. Recently, researchers have introduced network analysis into the study of research collaboration.

Network Analysis of Research Collaboration

Network analysis has been proposed in the study of many real networks, such as social networks (Strogatz, 2001; Watts, 2004). In the study of social networks, individuals can be represented as a set of nodes, and the relationships between these individuals can be represented as a set of edges. Considering the fact that research collaboration is actually a kind of social relationship, network analysis can help understand the relationships in research collaboration. In the collaboration networks of existing studies, institutes, or researchers are represented as nodes, and the collaboration relationships between them are represented as edges. An example of a collaboration network is provided in Figure 1. In this figure, researchers are the nodes in the network. Researchers i, j, and k are connected to one another because they have published article A. Researchers k and l are connected because they have published article C. Similarly, researchers k and m are connected. The collaboration network in this figure is unweighted, so the edge between i and k has the same weight as the other edges, although i and k have published two articles together.

Figure 1

An Example of an Unweighted Collaboration Network

Collaboration Network Analysis

Network analysis has been used in the study of research collaboration for physics, biomedicine, and computer science (Newman, 2001a, 2001b). The structural properties of these networks, such as the average degree and the largest connected component, have been analyzed. Moody (2004) investigates a collaboration network of social science and analyzes its basic structural properties. Huang et al. (2008) build a collaboration network for computer and information sciences and compare it with those for biology and mathematics. They then study the evolution of the network. For each year between 1980 and 2005, a collaboration network is constructed from articles published on or before this year. Changes in global properties of the network are discussed, such as average degree, assortativity, component structure, and so on. Similarly, Franceschet (2011) constructs the collaboration networks for computer science. Both bibliometric properties and the structural properties of networks are investigated. A temporal analysis on the global properties of collaboration network is also given. Both the works of Huang et al. (2008) and Franceschet (2011) study the evolution of collaboration networks. However, both works do not provide details of the evolution of individual researchers. For instance, it is unknown whether the changes of researchers are similar and what the characteristics of researchers with significant changes are. These details are helpful in understanding the evolution of collaboration networks.

Collaboration Network Analysis for Tourism Research

In tourism research, collaboration networks have also been constructed in recent years. Ye, Song, and Li (2012) study the cross-institutional collaboration in tourism and hospitality. A collaboration network is created by defining a node as an institute. The authors evaluate the intensity of research collaboration among academic institutions and find that an institution with more collaborators has a higher probability of good research performance. Benckendorff (2010) constructs collaboration networks for both researchers and institutions. Articles in the data set of Benckendorff were published by Australian and New Zealand authors between 1999 and 2008. The average number of authors per article and the percentage of coauthored articles in each year show increasing trends. Unfortunately, the changes in the network properties are not provided. Characteristics of top 30 most collaborative researchers and institutions in these networks are studied. Examples of these characteristics include productivity and network centrality. The Spearman rho statistic is used to explore the correlations between the characteristics of researchers. It is found that researchers with high degree and betweenness centralities are likely to be productive. Benckendorff (2010) mentions that researchers with high degree play important roles in connecting colleagues, and the ones with high betweenness can control the communication flow in the collaboration network. However, the author does not define an evaluation method to measure the importance of the researchers or their ability to control communication flow. Racherla and Hu (2010) construct a collaboration network with articles published in three tourism journals from 1996 to 2005. They show the distribution of the number of collaborations in two 5-year periods and find that in both periods few researchers have high degree of connections. Racherla and Hu (2010) visualize the subgroups of a researcher in two periods and observe that a researcher is pivotal if he or she connects other researchers together. They investigate the top 10 most prolific researchers identified by Jogaratnam et al. (2005) and conclude that more publications would be produced if a researcher has more collaborations. However, this study is limited in terms of sample size and time span (Ye et al., 2013). Thus, the study of Ye et al. (2013) is based on a larger data set from both tourism and hospitality journals. The articles in their data set were published from 1991 to 2010. To study the development of the collaboration in tourism and hospitality research, the authors construct collaboration networks with articles published in every 4 years. Basic structural properties, such as average distance, clustering coefficient, and the largest connected component, are studied. In the work of Ye et al. (2013), two categories of critical researchers are defined: extroversive collaborating critical researchers and introversive collaborating critical researchers. Extroversive collaborating critical researchers are the ones with relatively large difference between degree in the original collaboration network and in the largest component of the pruned network (comprising nodes with degree 2 or higher). Introversive collaborating critical researchers are the ones with relatively low degree difference. The definition for extroversive collaborating critical researchers can reflect researchers’ ability to link nodes with low degrees to the largest component. The definition for introversive collaborating critical researchers reflects researchers’ contribution to the largest component. The critical researchers can be identified by calculating the ratio of degree difference to degree in the original collaboration network. However, Ye et al. (2013) neither provide the definition for critical researchers in smaller components nor discuss how researchers with such ability perform in productivity. The authors also investigate the relationship between the degree and productivity of researchers with a regression model. Their results show that collaborations are associated with research outputs of researchers. Zhong, Wu, and Morrison (2015) study articles on China’s tourism and provide an example to show a researcher is important if he or she plays a “connector” in a collaboration network. However, they do not provide a definition for “connector” and the structural properties of such a researcher.

Limitations of Existing Studies

On one hand, previous studies on research collaboration networks have focused mainly on the structural properties of collaboration networks, collaboration trends discovery, and key researcher identification in these networks. However, most of the studies in collaboration trend discovery only studied the global structural changes of collaboration networks, such as the changes of the average number of collaborators. The changes of individual researchers are overlooked, which are necessary information that explains the evolution of collaboration networks. For example, the value of a structural property may increase significantly in a period, whereas the change of the value was trivial before that. By studying the changes of individual researchers in this period, we can determine whether this change is attributed to some key researchers.

On the other hand, existing studies on key researchers consider the most productive researchers in the whole collaboration network as important. However, if a productive researcher only collaborates limitedly with researchers, then his or her contribution to the connectivity of this collaboration network is limited. Supposing that information disseminates though paths of this collaboration network, a large connected component in the network is a desirable property (Franceschet, 2011). Considering this, important researchers in a collaboration network should be the productive ones who also contribute significantly to the connectivity of the network. Such researchers and their changes over time have not been studied systematically.

Summary

Traditional quantitative analysis can provide statistical information on research collaboration, such as the average number of authors per article. However, the way knowledge is disseminated from a researcher to others cannot be answered by this approach. Network analysis is a better way to provide such information. As a result, network analysis has been extensively used in recent years, and its effectiveness has been shown in existing studies. In this study, collaboration networks for tourism research are investigated with the network analysis approach. To fill the gap of existing studies on collaboration networks, this study focuses on the changes of individual researchers in collaboration networks. Two major differences are found between our work and existing papers on collaboration networks, especially in the area of tourism research:

Apart from the global changes in structural properties of collaboration networks, the property changes of individual researchers are also considered so that we can verify whether the global changes are due to key researchers. Thus, we can explain the reason for the global changes of collaboration network, and we can possibly promote future research collaboration.

The importance of researchers and key researchers are defined differently in this study. In the investigation of the importance of researchers, their contributions to productivity and the connectivity of collaboration networks are both considered. Moreover, the correlation between the changes of the importance of researchers and their changes of centrality measures is studied. A method is proposed to identify key researchers who are critical in the evolution of collaboration networks. Such a method can be applied in studies on research collaboration.

Method

Preliminary in Network Analysis

A collaboration network is an undirected graph in which the nodes are researchers and the edges between nodes indicate whether the corresponding authors have jointly published an article. This study investigates the changes of collaboration of tourism research in different periods through network analysis. The structure of collaboration networks has been investigated by researchers because the structure of a network can affect the spread of information (Barabási et al., 2002; Franceschet, 2011; Newman, 2001c). In this section, the basic structural properties in network analysis are introduced, and a method to measure the importance of nodes is presented.

Terms

Adjacency matrix

A network can be formally represented as adjacency matrix A . Element A_ij is the weight of the edge between nodes i and j. In this study, the research collaboration networks are unweighted networks. A_ij = 1 if researchers i and j have at least one jointly published article; otherwise, A_ii = 0. The adjacency matrix for the network in Figure 2a with nodes {i, j, k} is

A = [\begin{matrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{matrix}] .

Figure 2

Three Sample Networks. (a) Density D = 1, clustering coefficient C_i = 1, degree k _i = 2, betweenness B _i = 0. (b) Density D = 0.667, clustering coefficient C _i = 0, degree k _i = 2, betweenness B _i = 2. (c) A network with two connected components.

The number of rows of an adjacency matrix is the size n of the corresponding network, and the number of edges in this network is m = (∑_ijA_ij)/2.

Network density

Density is an important characteristic of a network, which is the ratio of the number of edges to the maximum possible number of edges. Given n nodes and m edges in a network, the density of the network can be written as the following:

D = \frac{m}{n (n - 1) / 2} .

Nodes in a higher density network have more interactions. The network density in Figure 2a is 1, whereas the density in Figure 2b is 0.667. Racherla and Hu (2010) calculate the density of collaboration networks in tourism research to measure the cohesion of networks. They have found that the network density from 2001 to 2005 is lower than the one from 1996 to 2000.

Degree centrality and degree distribution

In network analysis, an important characteristic of a node is its degree (Wang & Chen, 2003), which is the number of its direct neighbors:

k_{i} = \sum_{j} A_{i j} .

In Figure 2a, the degree of node i is k_i = 2. Considering that degree reflects the number of edges connected to a node, it is a centrality measure that indicates the importance of a node. In research collaboration networks, degree is the number of collaborators of researchers. Degree centrality has been used to identify important researchers as a centrality measure (Racherla & Hu, 2010; Ye et al., 2013). Degree distribution P(k) is the probability of any node in a network with a degree of k, which has been studied in collaboration networks (Barabási et al., 2002; Franceschet, 2011; Racherla & Hu, 2010). Many collaboration networks are found to be heterogeneous, and the range of possible degree values is large.

Clustering coefficient

Clustering is an important concept in network analysis, describing the connection of the neighbors of a node i. If node i has connections with nodes j and k, then an edge possibly exists between j and k. This phenomenon can be described by clustering coefficient (Watts & Strogatz, 1998). The local clustering coefficient of a node i can be defined as the following:

C_{i} = \frac{E_{i}}{k_{i} (k_{i} - 1) / 2} a .

In the equation for clustering coefficient, k_i is the number of neighbors of node i. Among these k_i neighbors, the maximum number of possible edges is k_i(k_i − 1)2. E_i is the number of actual edges among these neighbors. Therefore, the clustering coefficient of node i is the fraction of actual edges between its neighbors. For example, in Figure 2a, the local clustering coefficient of node i is 1. In Figure 2b, C_i = 0 for node i.

The clustering coefficient of a network is the mean of the local clustering coefficients for all nodes in this network:

C = \frac{1}{n} \sum_{i} C_{i} .

The value of clustering coefficient is in the range of 0 to 1. The clustering coefficient for the network in Figure 2a is 1. This value for the network in Figure 2b is 0. The high value of clustering coefficient of a collaboration network indicates that the researchers in this network have strong relationships with one another. In previous studies on collaboration networks (Barabási et al., 2002; Huang et al., 2008; Newman, 2004a; Ye et al., 2013), the value of the clustering coefficient is in the range of 0.3 to 0.8. Moreover, Ye et al. (2013) have found that for collaboration networks of hospitality and tourism research, the clustering coefficient has increased from 1991 to 2010.

Betweenness centrality

Betweenness centrality B_i is a measure of node i, defined as the number of the shortest paths passing through the node (Freeman, 1977):

B_{i} = \sum_{s \neq i \neq t} \frac{g_{s t} (i)}{g_{s t}} .

Here, g_st is the number of the shortest paths from node s to node t, and g_st(i) is the number of the shortest paths from node s to node t passing through node i. In Figure 2B, node i is on two shortest paths, namely, path j → i → k and path k → i → j. Thus, the betweenness of node i is B_i = 2. In collaboration networks, knowledge and research resources spread through paths. A researcher with a higher betweenness means that more shortest paths in a collaboration network pass through this researcher, and this researcher is considered important in this collaboration network. Therefore, in the studies of Ye et al. (2013), Racherla and Hu (2010), as well as Newman (2004b), betweenness centrality has been used to measure the importance of researchers in collaboration networks.

Connected component

In an undirected network, a connected component is a subnetwork that a path exists between any pair of nodes in this component. For example, the network in Figure 2c has two connected components: {i, j, k} and {l, m}. The size or the percentage of the largest connected component measures the maturity of a collaboration network (Franceschet, 2011). In a collaboration network with a high percentage of large connected components, knowledge can be disseminated to more researchers (Barabási et al., 2002; Moody, 2004; Newman, 2004a).

Robustness of Networks

For a connected network, a path exists between any pair of nodes. Thus, knowledge from any node can be spread to all other nodes in the connected collaboration network. If some nodes and their associated edges are removed, then the whole network may break down into several separated components. However, if most nodes in this network remain connected, this network is considered to be robust. The collaboration network in the study of Franceschet (2011) is found to be robust if some random selected nodes are removed, but it is fragile if nodes with high degrees are removed. Thus, a robustness test can measure the importance of nodes in maintaining the structure of a network. In other words, the contribution of a node to the connectivity of a network can be measured by removing this node and checking the connected components of the remaining network.

Analysis of Phase Collaboration Networks

In this subsection, we first introduce the methods for data collection and data processing for our analysis and then present the structural properties to be calculated in the study. We provide a definition of key researcher in this article because the structural changes of collaboration networks may be due to some key researchers. To measure the importance of researchers and to identify key researchers, we consider both the productivity of researchers and their contribution to the structure of collaboration networks, which can be measured by a method proposed in this section. We discuss the way to find a centrality measure to reflect the importance of researchers so that a method for identifying key researchers can be proposed. In addition, we discuss the evaluation process for our identification method:

Data Collection

Following previous studies on authorship in tourism research (Jogaratnam et al., 2005; Leung & Law, 2006; Sheldon, 1991; Ye et al., 2013), our data set includes articles published in one research journal. The data collected for analysis are sourced from a first-tier tourism research journal that has published thousands of articles. Even though the methods are applicable to any repository of publications, we focus on one single source in this study because of two reasons. First, this journal is one of the top tourism journals, which has published articles with broad topics (Benckendorff & Zehrer, 2013; Racherla & Hu, 2010). This indicates that this journal is representative. Second, the time span of our data set is longer than related ones in existing studies on collaboration in tourism research. For example, articles published in three journals during 10 years were collected in the work of Racherla and Hu (2010). Our data set comprises 2,193 articles and 3,225 authors, which is much larger than the repository of Racherla and Hu’s (2010) work. It would be very difficult to process the data if multiple journals are included. A total of 2,193 research articles and research notes published from 1982 to 2014 are collected. However, the name problem should be addressed before constructing the collaboration networks. Two name problems in the present study are as follows: a researcher with several names and several researchers with the same name. We process the data using the methods mentioned in the study of Franceschet (2011). We analyze each pair of researchers for the case of the researcher with several names. If two researchers with similar names have no common articles but have at least one common collaborator, then they may actually be the same person; thus, we manually check such pairs of researchers. For the case of several researchers having the same name, we first obtain a list comprising the collaborators of each researcher i. If these collaborators can be divided into two or more clusters, and the collaborations within these clusters are dense but no collaboration between the different clusters, then the name of the researcher i may actually be shared by two or more researchers. A manual check is also conducted for this case.

A total of 3,225 researchers are included in this data set after the name processing. In previous studies on the evolution of collaboration networks, there are two ways to construct phase networks. One is the method used in Huang et al.’s (2008) study, in which a phase network is constructed from all articles published until a certain year. The other has been used in the studies of Racherla and Hu (2010) as well as Ye et al. (2013), in which a phase network for a certain period is constructed with the articles published in this period. We use the second method because articles published a long time ago could not effectively reflect recent collaboration statuses. For every 3 years, a phase collaboration network is constructed from the articles published in these 3 years, thereby resulting in 11 phase collaboration networks.

Basic Structural Property Analysis

The basic structural properties of a network provide its basic information. Previous studies on collaboration networks provide the basic structural properties, such as network size, network density, clustering coefficient, and size of the largest connected component (Franceschet, 2011; Racherla & Hu, 2010; Ye et al., 2013).

The current study also provides the basic structural properties for each phase collaboration network. Changes in different phases of these properties are investigated to discover the global trend in tourism research collaboration. The individual researchers’ average properties are also analyzed in the present study. Moreover, the changes of the networks’ global properties and the researchers’ properties are compared to verify the hypothesis that global changes are caused by a few key researchers.

Measuring the Researchers’ Importance

In this study, the researchers who make observable contributions to the global changes in collaboration networks during a certain period are called “key researchers” of this period. It seems that key researchers should be the most important researchers in connecting their peers to collaboration networks. However, if a researcher is of extreme importance in two adjacent periods, then this researcher is only essential in maintaining the previous period’s structure and not the primary reason for the global changes in the recent one. Thus, key researchers are researchers with significant improvement in importance. We measure the changes of the researchers’ importance in a collaboration network by analyzing the changes in both their contribution to the network’s connectivity and their productivity. Therefore, we propose to use a revised robustness test to measure the researchers’ contribution to the collaboration networks’ connectivity.

In most existing studies using a robustness test, the size of the largest connected component evaluates a network’s connectivity status (Franceschet, 2011). A node’s contribution to a network’s connectivity can be evaluated by this node’s contribution on the largest connected component. For example, if the change in the largest connected component’s size is considerable after removing a node, then this node is considered critical. However, the nodes in the other components are also parts of the entire network. These nodes contribute to their own components despite having no contribution to the largest connected component. Therefore, modifying the robustness test is necessary, and the contribution of a researcher to a network is his or her contribution to the component where he or she belongs. For example, if the component where a researcher i belongs to is cⁱ, then this component’s size is |cⁱ|. After excluding researcher i, the component cⁱ is divided into k components {c₁ⁱ, c₂ⁱ, . . . c_kⁱ}. Therefore, the contribution of researcher i to the network’s connectivity is the change of the component |cⁱ|, that is,

C o n n_{i} = | c^{i} | - \max (| c_{1}^{i} |, | c_{2}^{i} |, ... | c_{k}^{i} |) .

Analysis of Correlation Between Changes in Importance and Centrality

Although key researchers are defined as researchers with significant improvement in importance, combining the researchers’ contribution to connectivity and productivity is difficult. Nevertheless, nodes with high centrality in a network are considered important in this network. For example, Wang and Chen (2003) discussed that the nodes with a large degree are more important in a network. Newman (2004b) demonstrated that by collaborating with one or two researchers with high betweenness, one can obtain a short path to a considerable portion of other researchers. Thus, changes in the researchers’ importance may be reflected by their centrality changes.

To find a proper centrality measure to identify the key researchers, we investigate the correlation between the researchers’ changes in importance and centrality. The different types of centrality measures include degree centrality, betweenness centrality, closeness centrality, and eigenvector centrality (Bonacich, 1987; Freeman, 1978). Eigenvector centrality has been demonstrated to be less effective than degree centrality in reflecting the researchers’ importance (Franceschet, 2011). The closeness centrality of a node i is defined by the mean distance from this node to all other nodes in the network. However, no path exists between most pairs of researchers in our collaboration networks; thus, the closeness centrality is an unsuitable centrality measure for the current study. Degree centrality and betweenness centrality are popular in existing studies (Newman, 2004b; Racherla & Hu, 2010; Ye et al., 2013). Degree centrality has been determined to be correlated to researchers’ productivity (Racherla & Hu, 2010), and researchers with high betweenness centrality are information hubs (Ye et al., 2013). Therefore, both degree centrality and betweenness centrality are analyzed in the present study.

Identifying Key Researchers

With the result of the correlation analysis between the changes in importance and centrality, we can identify which centrality measure can better reflect the changes of importance for a researcher, particularly the significant changes. Thereafter, we introduce a method to identify the key researchers in each phase collaboration network, and evaluate the method by studying their performance. If the identified researchers have significant improvement in their contribution to connectivity, as well as a significant increment in productivity, then the identification process is considered effective.

Analysis and Results

This section presents the analysis and results of the current study. First, the basic structural properties of the different phase collaboration networks and the average properties of the researchers are investigated. The global and individual properties trends are then compared. Thereafter, we analyze the correlation between the researchers’ changes in importance and centrality. A centrality measure that reflects the change in importance can be concluded. Moreover, we propose a method to identify key researchers who contribute to the global changes in collaboration networks. Finally, the proposed method is evaluated by investigating the performance of the identified key researchers.

Changes in the Phase Collaboration Networks’ Basic Properties

Figure 3 provides both the number of published articles and the number of corresponding researchers for each phase collaboration network. The number of both articles and researchers in each phase gradually increased before 2006. Two phases where the number of articles significantly increased are the 2006-2008 and 2012-2014 phases. Consequently, the number of researchers also increased considerably in these two phases. This result is similar to the observation in Ye et al.’s (2013) work that in the interval 2003-2010, the scale of tourism research community expanded significantly.

Figure 3

Number of Articles and Researchers in the Phase Collaboration Networks

Table 1 provides the size, density, clustering coefficient, and size of the largest connected component for each phase collaboration network. Our observations are as follows.

Table 1

Basic Properties of Phase Collaboration Networks

Phase	Network Size	Density	Clustering Coefficient	Largest Component	Average Degree	Average Betweenness	Average Productivity
1982-1984	96	0.0053	0.0851	5	0.5000	0.1042	1.1250
1985-1987	100	0.0051	0.0900	5	0.5000	0.2000	1.1300
1988-1990	121	0.0065	0.1956	5	0.7769	0.1653	1.1157
1991-1993	154	0.0053	0.1786	5	0.8182	0.1039	1.1169
1994-1996	205	0.0047	0.2317	7	0.9659	0.2634	1.1268
1997-1999	257	0.0049	0.3372	5	1.2529	0.1556	1.1167
2000-2002	275	0.0053	0.4001	6	1.4473	0.3782	1.1236
2003-2005	385	0.0044	0.4826	31	1.6883	5.5481	1.1273
2006-2008	646	0.0032	0.5237	51	2.0557	15.2074	1.2090
2009-2011	713	0.0029	0.5927	25	2.0533	2.4488	1.1164
2012-2014	1,039	0.0025	0.6941	17	2.5717	1.5188	1.1540

The phase collaboration network’s size is constantly increasing. The increasing trend of network size means the number of researchers involved in tourism research has grown in the past 33 years. The increments in the 2006-2008 and 2012-2014 phases are significant. The network size has a 68% increment in the 2006-2008 phase and 46% in the 2012-2014 phase.

The phase collaboration network’s density generally shows a decreasing trend, which is consistent with the conclusion of Racherla and Hu (2010). A collaboration network with high density means the researchers in this network interact with others frequently. But the decreasing trend of density here does not imply a decreasing tendency of research collaboration. From Equation (2), network density is inversely related to network size. The decreasing density is because of the increasing network size.

The clustering coefficient of the phase collaboration networks increases over time. Therefore, researchers tend to form clusters with high densities. The changes in the clustering coefficient demonstrate an increasing collaboration trend in tourism research.

From 1982 to 2002, the largest connected component’s size is within the range of 5 to 7. This observation means that although the phase collaboration network’s size is constantly increasing, the connected components’ sizes remain small. In the 2006-2008 phase, the largest connected component’s size peaks at 51. However, this value remains low compared with the size of this phase’s entire network. This result indicates that although researchers show tendency to form clusters, the collaboration in tourism research is still limited.

From the perspective of knowledge dissemination via collaboration, high percentage of large connected components in a collaboration network is expected. Figure 4 shows the distribution of the connected components’ sizes. We also calculate the percentage of the separated researchers without collaborator in the collaboration networks. Figure 4 also shows the percentage of these researchers. It is found that the sizes of the components are small, especially in earlier phases. In Ye et al.’s (2013) work it was mentioned that some small components may be due to the geographical isolation and the lack of collaboration between research institutions or groups. In Figure 4, the percentage of the separated researchers has decreased significantly since the 1988-1990 phase. However, the percentage of the small components, with a size range of [2, 10], increased. From the 2003-2005 phase, large components with more than 10 researchers have emerged. Although only a few large components exist, an increasing trend in their percentage can be observed. This result indicates that collaboration has become a common trend in tourism research over time.

Figure 4

Distribution of Connected Components’ Sizes

Table 1 shows that the largest connected component’s size is small from 1982 to 2002. In the 2003-2005 and 2006-2008 phases, the size of the largest connected component increased significantly. However, the largest connected component’s size decreased in the 2009-2010 and 2012-2014 phases. To explore this result, we plot parts of the phase collaboration networks in the 2000-2002, 2003-2005, and 2006-2008 phases in Figure 5a-c, respectively. Only 50 common researchers are included in the 2000-2002 and 2003-2005 phase networks. This result indicates that most researchers in the 2000-2002 phase have no publication in the 2003-2005 phase in our data set. Only 82 common researchers are included in the 2003-2005 and 2006-2008 phase networks. This observation means that in the evolution of collaboration networks, most researchers leave the networks and new researchers emerge. The global evolution of collaboration networks may occur because of the significant changes in the composition of these networks.

Figure 5

Researchers 356, 549, 586, and 594 in Figure 5a still exist in Figure 5b, which shows a component of the 2003-2005 phase. Figure 5B also shows that Researcher 594 is the center of the component; this component will become fragmented if Researcher 594 is removed. By collaborating with new Researcher 894, Researcher 594 connects to the cluster of Researchers 893, 894, 895, 896, and 897. By collaborating with Researcher 586, Researcher 594 connects to Researchers 510, 945, 946, 947, 919, and 1116. Similarly, collaborating with Researcher 549 also makes the connected component large. Researcher 594 is still in the center of the connected component in Figure 5c. However, most researchers in this component can maintain their connections without Researcher 594. Instead, Researchers 294, 589, and 1789 become important in the 2006-2008 phase; Researchers 294 and 1789 do not exist in the collaboration network of the 2003-2005 phase. Note that researchers who act as connectors are able to link small clusters to form a large component and vital in maintaining a collaboration network’s connectivity. The importance of researchers may also considerably change in different phase collaboration networks.

Table 1 also lists the average values of the individual researcher’s properties, including degree, betweenness, and productivity. The average degree in the phase collaboration networks is constantly increasing since 1988; the exception is the 2009-2011 phase in which the average degree slightly decreased. Both the average betweenness and productivity reach their respective peaks in the 2006-2008 phase, where the largest connected component’s size is also the largest. The reason for this increase may also be related to the preceding discussion on key researchers. For example, for Node 594 in Figure 5a, k₅₉₄ = 4 and B₅₉₄ = 12. In Figure 5b, k₅₉₄ = 12 and B₅₉₄ = 689. Both degree and betweenness of Node 594 considerably increased, particularly the latter. This observation indicates that the changes in the researchers’ centrality may be able to reflect their changes in importance. In the following section, we study the evolution of individual researchers by measuring the researchers’ importance and investigate which centrality measure can better reflect their changes in importance.

Correlation Between Changes in Importance and Centrality

Previous works on the evolution of collaboration networks mainly focused on the changes in properties of the overall networks. In this section, change of importance of each researcher in our data set is measured. By reviewing the researchers, we can explore whether the importance of researchers can be reflected by their network centrality. From the previous analysis, we can observe that certain researchers play a bridging role between different network components. These researchers are significant because of their contributions to the collaboration networks’ connectivity. Researchers with numerous publications are also important to their research community. Therefore, important researchers are defined in the present study as those individuals who have both structural importance and high productivity. Different from Ye et al.’s (2013) work, which identified critical researchers by measuring their ability to link nodes with low degrees to the largest component or their contribution to the largest component, we define the impact of a researcher in the collaboration network as the combination of his or her productivity and contribution to the connectivity of the whole network, including both small and large components.

The importance of nodes in a network can be reflected by centrality measures; degree and betweenness are two commonly used centrality measures. Existing studies (Racherla & Hu, 2010; Ye et al., 2013) consider researchers with high degree or betweenness as important researchers. Therefore, we calculate both the degree centrality and betweenness centrality in each phase network for every researcher. Among the 3,225 researchers in our data set, 440 have a degree of 0 in all the phase collaboration networks. A total of 3,041 researchers have a betweenness of 0 in all the phase collaboration networks. Table 1 shows that the increment of the average degree is nearly linear; however, the average betweenness has no significant increment before 2003. The average betweenness peak is determined in the 2006-2008 phase. The largest component’s size and average productivity also reach their corresponding peaks in the 2006-2008 phase. Therefore, betweenness centrality can evidently reflect the productivity trend better. The largest connected component’s size can reflect a network’s connectivity; thus, this observation also indicates that a researcher with a higher betweenness centrality is more important in maintaining a network’s connectivity.

A detailed study of each researcher is necessary to verify the aforementioned observations. Therefore, we assess how the researchers’ importance changes when the two centrality measures have differences in two adjacent phases. Our objective is to determine an appropriate centrality measure to identify the researchers who have increasing importance.

For any two adjacent phases, if the centrality of a researcher increases, then this researcher’s contribution to the collaboration networks’ connectivity possibly increases. To verify this assumption, we calculate the changes in degree and betweenness of each researcher in every two adjacent phases, and the corresponding change in contribution to connectivity. Equation (7) can be used to estimate the researchers’ contribution to connectivity. Figure 6 shows the correlation between the changes in degree and contribution to connectivity, while Figure 7 shows the correlation between the change in betweenness and the change in contribution to connectivity. The size of a circle in the aforementioned two figures is determined by the number of researchers with the corresponding changes in centrality and contribution. For example, the circle in the center of Figure 6 has the largest size, which indicates that numerous researchers have no changes in both degree and contribution to connectivity in most phase collaboration networks. It is found that the circles near the center have relatively large sizes, which means most researchers have slight changes in degree, betweenness, and contribution to connectivity. In Figures 6 and 7, most researchers with positive changes in degree or betweenness have an increment in their contribution to connectivity and vice versa. However, if we focus on the researchers with significant increment in degree, then only a few such researchers are determined to have a considerable increment in contribution to connectivity. However, Figure 7 shows that most researchers with significant increment in betweenness also have a relatively considerable change in contribution to connectivity. Therefore, a significant change in betweenness centrality is a better indicator of the increment in importance. The reason is that degree centrality is the number of immediate neighbors of a node, which merely provides the local structural information of this node. With betweenness centrality, more information on the other nodes can be obtained; betweenness is a better choice than other centrality measures from the communication control perspective (Freeman, 1978).

Figure 6

Correlation Between the Changes in Degree and Contribution to Connectivity

Figure 7

Correlation Between the Changes in Betweenness and Contribution to Connectivity

Existing studies show that researchers are more productive if they have more collaborators (Racherla & Hu, 2010). Therefore, a positive change in degree implies that a researcher’s productivity may increase. For every researcher, we calculate the change in productivity for every two adjacent phases.

Figure 8 illustrates the correlation between the changes in degree and productivity and Figure 9 shows the correlation between the changes in betweenness and productivity. Similar to Figures 6 and 7, the circles near the center have relatively large sizes. This result implies that only a few researchers have significant changes in productivity. We can observe from Figure 8 that most researchers with positive changes in degree have positive changes in productivity; however, the number of researchers who have a positive change in degree and a negative change in productivity is not negligible. Figure 9 shows that researchers who have an increment in betweenness have an increment in productivity in most cases. Moreover, researchers with significant increment in betweenness often have relatively large increment in productivity. Compared with change in degree, the change in betweenness more accurately reflects the change in productivity of a researcher in a collaboration network. This result seems to be different from the study by Racherla and Hu (2010). However, the current study focuses on the researchers’ changes in centrality, whereas Racherla and Hu (2010) analyzed the actual values of the degree. Moreover, betweenness can measure whether a researcher is at the core of the collaboration networks in terms of knowledge exchange (Ye et al., 2013). Therefore, if a researcher has improved betweenness, then more paths for academic resources and knowledge dissemination pass through this researcher. Research collaboration accelerates knowledge exchange and promotes research outcomes; thus, this result is reasonable (Franceschet & Costantini, 2010; Katz & Hicks, 1997).

Figure 8

Correlation Between the Changes in Degree and Contribution to Productivity

Figure 9

Correlation Between the Changes in Betweenness and Contribution to Productivity

Identifying Key Researchers Using Betweenness

In the analysis presented in the previous section, we conclude that the key researchers with significant changes in their importance can be identified by the extent of their changes in betweenness.

Therefore, we propose a method to identify the key researchers of a given period k based on the aforementioned result. The necessary steps are as follows:

For each researcher i in the collaboration network, the betweenness centrality in the period B_i^k is calculated.

For each researcher i in the collaboration network, the betweenness centrality in last period B_i^k ⁻ 1 is calculated.

For each researcher i in the collaboration network, the change of betweenness centrality ΔB_i^k = B_i^k − B_i^k ⁻ 1 is calculated.

{ΔB₁k, ΔB₂^k, . . . ΔB_i^k, . . .} is sorted in descending order; the key researchers of period k are the ones with the largest ΔB^k.

To evaluate our identification method for each phase after 1984, we list the researchers with the largest increment in betweenness and the corresponding rankings of their changes in importance in Table 2. Except for Researcher 561 in the 2000-2002 phase, almost all researchers have the largest positive changes in contribution to connectivity. Most researchers listed in Table 2 also have relatively high rankings for their changes in productivity, with the exception of Researcher 1789 in the 2006-2008 phase.

Table 2

Researchers With the Largest Increment in Betweenness in Each Phase

Phase	Researcher ID	Ranking of Changes
Phase	Researcher ID	Betweenness	Contribution to Connectivity	Contribution to Productivity
1985-1987	182	1	1	2
1988-1990	140	1	1	1
1991-1993	428	1	1	2
1994-1996	294	1	1	3
1997-1999	627	1	1	4
2000-2002	561	1	6	2
2003-2005	594	1	1	1
2006-2008	1789	1	1	7
2009-2011	874	1	1	3
2012-2014	1439	1	1	4

For comparison, Table 3 provides the information on researchers with the largest changes in degree. On average, the researchers listed in Table 2 have better performance in their contributions to both connectivity and productivity.

Table 3

Researchers With the Largest Increment in Degree in Each Phase

Phase	Researcher ID	Ranking of Changes
Phase	Researcher ID	Degree	Contribution to Connectivity	Contribution to Productivity
1985-1987	153	1	4	9
1988-1990	101	1	2	1
1991-1993	428	1	1	2
1994-1996	286	1	1	2
1997-1999	441	1	8	18
2000-2002	1276	1	1	6
2003-2005	586	1	4	3
2006-2008	1860	1	6	3
2009-2011	1465	1	4	3
2012-2014	2777	1	39	81

Table 2 shows that no researcher retains the top position for two consecutive phases; however, a few researchers continuously have positive changes in betweenness. For example, Researcher 594 has positive changes in betweenness in the 2000-2002, 2003-2005, and 2006-2008 phases. Table 4 lists the aforementioned researcher’s changes in betweenness and importance. Researcher 594’s contribution to connectivity cannot continuously increase in the 2006-2008 phase because other researchers, such as Researcher 1789, have more significant contributions. Although the productivity of Researcher 594 decreases in the 2006-2008 phase, the net value of productivity is 6, which is the highest in this phase. Therefore, Researcher 594 remains a productive researcher in this phase; however, this researcher has lost the importance in connectivity of the collaboration network.

Table 4

Properties of a Researcher With Positive Changes in Betweenness in Three Continuous Phases

Changes of	2000-2002	2003-2005	2006-2008
Betweenness	12	677	159
Connectivity	3	19	−20
Productivity	2	7	−3

In summary, a key researcher in a certain phase should have a relatively large increment in betweenness than other researchers.

The investigation of collaborators and research topics of key researchers helps understand the changes in collaboration evolution better and provides suggestions on how to make collaboration networks better connected. In this study, we provide an example to explain a possible application of our identification method. In the 2003-2005 phase, the size of the largest connected component increased largely compared with the 2000-2002 phase. We select 10 researchers with the largest changes in betweenness in this phase and collect the titles of the articles published by these 10 researchers in this phase. Table 5 lists the words with relatively high frequency. For comparison, we also list the words in the titles of all articles in this phase. In this table, we exclude some prepositions with high frequency, such as “of,” and articles, such as “the.” In the titles of the top 10 key researchers, the words related to 2002 FIFA World Cup appear frequently, which cannot be observed in the titles of all researchers. Among the articles published by the top 10 key researchers, three articles related to this football competition were published by Researchers 586 and 919, 594 and 874, and 594 and 968, respectively. These five researchers are from five different universities located in three countries. We also notice that Researchers 586 and 594 are among the top 10 key researchers identified by the proposed methods, and these two researchers have been discussed in the analysis of Figure 5B in the “Changes in the Phase Collaboration Networks’ Basic Properties” section. In this example, key researchers show tendency to study the impact of a popular event just held. Moreover, they collaborate with researchers from universities in other countries. If we include the publication history of researchers, detailed information of collaborators, and the analysis of more text, such as abstract and keywords in the future, more characteristics of key researchers can be observed and suggestions on the development of tourism research can be concluded.

Table 5

Words in the Titles of the Articles Published in 2003-2005 Phase

Articles of Top 10 Key Researchers		Articles of All Researchers
Word	Percentage	Word	Percentage
Tourism	1.6	Tourism	2.64
Korean	1.28	Case	1.28
Case	1.28	Study	0.95
Analysis	0.96	Tourist	0.91
2002	0.96	Travel	0.87
FIFA	0.96	Analysis	0.74
World	0.96	Hotel	0.58
Perceptions	0.96	Management	0.5
Impacts	0.96	International	0.45
Positioning	0.64	Industry	0.45

Implications

The progress in tourism research can be improved with the method proposed in this study. Information about the evolution of collaboration network and the changes of each researcher can be provided. Furthermore, visualization of the collaboration network makes it easier to understand the evolution.

When there is change in the coauthorship of a researcher, the proposed method is able to identify whether this researcher has significant change in his or her contribution to the collaboration network of the tourism research community. With further research on topic analysis of the published articles, the corresponding changes in research topics that this researcher and his or her coauthors are interested in can also be discovered. When the proposed method is implemented in a web search engine, it represents an effective way to understand the trend of tourism research and identify possible reviewers and collaborators. Researchers in other fields have tried to provide a web search engine which enables users to find the articles and researchers related to a specific topic, and identify the research interests and coauthors of specific researchers (Chen & Zhao, 2015).

Furthermore, with the knowledge of coauthors and research topics of the researchers who have significant changes in contribution to the collaboration network, we can address the question of “how to make a collaboration network well connected,” which is a sign of a developed research community.

The method and findings in our work can be applied in further studies on research networks in tourism and hospitality. Besides collaboration networks of researchers, collaboration networks of universities, citation networks of researchers, and citation networks of journals can use the proposed method to explore the trends in tourism and hospitality research. For instance, it would be helpful in identifying publications which contribute the most to tourism and hospitality research in recent years. Progress of tourism and hospitality research can then be promoted with such results. Moreover, this work provides an alternative method to use centrality measure in network analysis. In recent years, network analysis has been applied to tourism research in different ways. For example, a network of destination stakeholders was constructed by Baggio, Scott, and Cooper (2010) to study information diffusion. In Baggio and Sainaghi’s (2016) work, a network based on a time series of observations is studied to identify turning points of tourism demand. In this article, the way of using betweenness provides a new method for tourism research using network analysis, which may lead to new discoveries.

Conclusion

Network analysis is a popular approach to research collaboration studies in recent years. Collaboration networks have been constructed with researchers and the collaboration relationships between/among them. However, most existing studies lack a detailed investigation on the effects of individual researchers on the evolution of collaboration networks. To fill this research gap, the present study focuses on the changes in individual researchers over time to explain the global changes in collaboration networks and to provide further benefits to studies on research collaboration.

We constructed 11 phase collaboration networks from research articles published in a leading tourism journal. The trends of the structural properties of these networks and the average properties of the researchers in these networks have been studied. We then defined that researchers who are important in making changes to the collaboration networks’ structure are called “key researchers”; they are also the ones who have the most significant improvement in importance in collaboration networks. A revised robustness test has been introduced to measure the researchers’ contributions to the collaboration networks’ connectivity. The importance of researchers can be measured by such contribution and productivity. Thereafter, we investigated which centrality measure can reflect the researchers’ changes in importance. By using the obtained results, a method has been proposed to identify the key researchers.

The contributions of this study are as follows:

Basic structural properties of phase collaboration networks: The size and clustering coefficient of phase collaboration networks exhibit increasing trends, which indicate that considerably more researchers are involved in tourism research, and collaboration has become a common practice. Moreover, we observed that the largest connected component’s size increases significantly in the 2003-2005 and 2006-2008 phases because of several key researchers.

Correlation between the researchers’ changes in importance and centrality. In the evolution of collaboration network, we found that researchers with significant changes in betweenness centrality often have significant changes in their contributions to connectivity of the network. Moreover, these researchers exhibit considerable changes in productivity. The performance of the degree centrality is limited in reflecting such relationships.

Identifying key researchers: A method to identify key researchers in a certain period has been proposed by calculating the researchers’ changes in betweenness. We evaluated the proposed method by studying the researcher with the most increment in betweenness for each phase collaboration network. All the researchers identified by our method have a significant improvement in their contribution to the connectivity of the corresponding phase collaboration networks. They also show relatively considerable increment in productivity. In summary, the proposed method based on betweenness centrality is effective.

This study explained the changes in collaboration networks during different periods by investigating an individual researcher’s changes. We also provided a method to identify key researchers in the collaboration networks’ evolution. The methods used in this study can be applied in the collaboration networks of other disciplines; thus, more journals can be included in the data set for cross-discipline collaboration research. Further studies can be carried out based on the key researchers identified by our method. For example, by investigating the research topics of key researchers in a given field at different periods, the trend of researcher topics in this field can be known with less effort. Moreover, results of our method can be used to find potential reviewers or collaborators, especially for cross-discipline studies.

Footnotes

Authors’ Note:

The work described in this article was supported by a grant funded by the Research Grants Council of The Hong Kong Special Administrative Region, China (GRF Project Number: 15503814, B-Q45Y), an international research grant funded by The Hong Kong Polytechnic University, and a research grant funded by the National Natural Science Foundation of China (71102097).

Wei Fan, PhD (e-mail: w.fan@polyu.edu.hk), is a research associate in the School of Hotel & Tourism Management at The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR. Gang Li, PhD (e-mail: gang.li@deakin.edu.au), is an associate professor in the School of Information Technology at Deakin University, Melbourne Burwood Campus, Victoria, Australia. Rob Law, PhD (e-mail: rob.law@polyu.edu.hk), is a professor in the School of Hotel & Tourism Management at The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR.

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