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Evolutionary Dynamics of Scientific Collaboration Networks: Multi-Levels and Cross-time Analysis

Several studies exist which use scientific literature for comparing scientific activities (e.g., productivity, and collaboration). In this study, using co-authorship data over the last 40 years, we present the evolutionary dynamics of multi level (i.e., individual, institutional and national) collaboration networks for exploring the emergence of collaborations in the research field of"steel structures". The collaboration network of scientists in the field has been analyzed using author affiliations extracted from Scopus between 1970 and 2009. We have studied collaboration distribution networks at the micro-, meso- and macro-levels for the 40 years. We compared and analyzed a number of properties of these networks (i.e., density, centrality measures, the giant component and clustering coefficient) for presenting a longitudinal analysis and statistical validation of the evolutionary dynamics of"steel structures"collaboration networks. At all levels, the scientific collaborations network structures were central considering the closeness centralization while betweenness and degree centralization were much lower. In general networks density, connectedness, centralization and clustering coefficient were highest in marco-level and decreasing as the network size grow to the lowest in micro-level. We also find that the average distance between countries about two and institutes five and for authors eight meaning that only about eight steps are necessary to get from one randomly chosen author to another.


Introduction
In recent years, there has been a sharp increase in the number of collaborations between scholars. An explanation for the rapid growth of international scientific collaboration has been provided by Luukkonen and colleagues (1992;1993) as well as Wagner and Leydesdorff (2005). By jointly publishing a paper, researchers show their knowledge-sharing activities, which are essential for knowledge creation. "The rising awareness of collaborativeness in science has led to a sharpened focus on the collaboration issue" (Melin 2000). Scientific collaboration has even been called a "springboard for economic prosperity and sustainable development" (US Office of Science & Technology Policy 2000). As most scientific output is a result of group work and most research projects are too large for an individual researcher to perform,

Network Density:
Density describes the general level of linkage among the nodes in a network (Scott 1991). The more nodes are connected to one another, the denser the network is. Density describes the general level of cohesion in a network (Scott 1991). More specifically, density of a network is the proportion of exiting links to the maximum possible number of distinct links.

Network Centralization:
Another method used to understand networks and their participants is to evaluate the location of actors in the network. Measuring the network location is about determining the centrality of an actor. These measures help determine the importance of a node in the network. "Centralization describes the extent to which this cohesion is organized around particular focal nodes" (Scott 1991). Bavelas (1950) was the pioneer who initially investigates formal properties of centrality and proposed several centrality concepts.
Later, Freeman (1979) found that centrality is an important structural factor influencing leadership, satisfaction, and efficiency.
To examine if a whole network has a centralized structure, centralization can be used. It refers to "compactness" of a network. A network"s centralization indicates how tightly the network is organized around its most central nodes. The general view is finding differences between most central nodes" centrality scores and others". Then, centralization is calculated as the ratio of the sum of these differences to the maximum possible sum of differences. Therefore, to calculate a network centralization, the first step is to find all nodes measures and then find the whole network centralities measures. The important node centrality measures are:

 Degree Centrality
The degree centrality is simply the number of other nodes connected directly to a node. Necessarily, a central node is not physically in the centre of the network as degree of a node is calculated in terms of the number of its adjacent nodes.
 Closeness Centrality Freeman (1979;1980) proposed closeness in terms of the distance among various nodes. Extending the same concept Sabidussi (1966) used in his work the "sum distance", the sum of the "geodesic" distances (the shortest path between any particular pair of nodes in a network) to all other nodes in the network. A node is globally central if it lies at the shortest distance from many other nodes. However, simply calculating the sum of distances of a node to other nodes will produce a measure of "farness" and so we need to use the inverse of the "farness" measure as a measure of closeness. In unconnected networks, every node is at an infinite distance from at least one node, and closeness centrality of all nodes would be 0. Thus, in order to solve this problem to consider all nodes, Freeman proposed to calculate closeness of a node as the "sum of reciprocal distances" of a particular node to any other nodes.
 Betweenness Centrality Freeman (1979) also proposed a concept of centrality which measures the number of times a particular node lies "between" the various other nodes in the network. Betweenness centrality is defined more precisely as the number of shortest paths (between all pairs of nodes) that pass through a given node (Borgatti 1995).

The Giant Component:
In small networks (few nodes and connections), all individuals belong to a small group of collaborations or communications. As the total number of connections increases, however, there comes a point at which a "giant component" forms, i.e., "a large group of individuals who are all connected to one another by paths of intermediate acquaintances" . It is important to realize that a collaboration network is usually fragmented in many clusters (components). One of the reasons for this is that in every field there are scientists that do not collaborate at all, that is they are single authors of all papers on which their names appear. In most research fields, apart from a very small fraction of authors who do not collaborate, all authors belong to a single "giant component" (cluster) from the very early stages of the field (Barabási, Jeong et al. 2002).

Clustering Coefficients:
Networks are mostly clustered which means they possess local communities in which a higher than average number of people know one another. One way to check the existence of such clustering in network data is to measure the fraction of ""transitive triples"" (also called clustering coefficients) in a network . The clustering coefficients of a network is the fraction of ordered triples of nodes A, B, C in which edges AB and BC are present that have edge AC present. In other words, it is the probability that two neighbors of a vertex are adjacent to each other. Clustering coefficient is an important property of networks which is "the probability that two of a scientist"s collaborators have themselves collaborated" (Barabási, Jeong et al. 2002;Grossman 2002). Watts and Strogatz (1998) defined clustering coefficient as follows. Consider node i that has links to k i other nodes in the network. If these k i nodes form a fully connected sub-network (clique), there are k i (k i − 1)/2 links between them, but in reality we find much never. Let us denote by N i the number of links that connect the selected k i nodes to each other. The clustering coefficient for node i is then C i = 2N i / k i (k i − 1). In simple terms, the clustering coefficient of a node in the co-authorship network tells us how much a node"s collaborators are willing to collaborate with each other, and it represents the probability that two of its collaborators wrote a paper together (Barabási, Jeong et al. 2002). Thus, authors" low clustering coefficients value means less probability of collaboration among the non-connected co-authors of the author. This gives power to the author by brokering new collaborations between their co-authors. The clustering coefficient for the whole network is obtained by averaging C i over all nodes in the system.

Data Sources
Scopus (www.scopus.com) is one of the main sources of bibliometric data. To construct the database for this study, publications were extracted using the string "steel structure" in the titles or keywords or abstracts in the top 15 specified journals of the field (shortlisted by one of authors as an expert of the field) and restricting the search to publications in English. After extracting the publications" meta-data from Scopus and importing the information (i.e., title, publication date, author names, affiliations, publisher, number of citations, etc), we used an application program, AcaSoNet (Abbasi and Altmann 2010), for extracting relationships (e.g., co-authorships) between researchers, and stored the data in tables in a local relational database. Four different types of information were extracted from each publication meta-data: Publications information (i.e., title, publication date, journal name, etc); authors" names; affiliations of authors (including country, institute and department name, etc); and keywords.
As we are interested in different macro-, meso-and micro-levels of analysis (i.e., country, institute, author), affiliation data is so important for our research. We found affiliation information, in our original extracted data, especially for older publications messy (the order and even different written name for the country, institute and department, etc) and also for some publications some fields (e.g., country) were missing. So, in our second step we undertook manual checks (using Google) to fill the missing fields using other existing fields (e.g., we used institute names to find country). Also manually we merged the universities and departments which had different names (e.g., misspellings or using abbreviations) in our original extracted.
After the cleansing of the publication data, the resulting database contained 2,226 papers reflecting the contributions of 5,201 authors (117 of authors had no affiliation data that we ignored them in our analysis) from 1,324 institutes (i.e., universities and private companies) of 76 countries. We found 447 multi-affiliation authors who for 411 of them just two affiliations have been recorded. While it is possible to have different authors with similar academic names, but since we are focusing on a specific discipline, it is more reasonable to regard the ones that have similar academic name as an author with multiaffiliations. To validate that we checked manually for some of them and find them as an author who was graduated in one institute and then has been worked as researcher or a professor in other institutes.  Although the publications dataset that we have extracted are not representative of the world production in the "steel structures" field (as there is the possibility of significant biases: evolving list of relevant journals, publications in other journals, same field using other words in a 40 years period) but the database does not pretend to represent the field, and is just to illustrate the use of the indicators to analyse this field. Therefore, the biases are not a problem for our analysis. authors, of whom one is from an institute (or country) different from the others, it is considered as an inter-institute (or international) collaboration.

Macro-Level Analysis
The distribution of international collaborations over the last 40 years is now analyzed in order to identify the countries collaboration activity. Figure    In order to identify the strongest collaborations (links), we evaluated the frequency of collaboration between each pair of countries.

Analyzing the Network of Collaboration Countries
From total 76 countries which had at least one publication, 10 countries (Albania; Bulgaria; Croatia; Estonia; Iraq; Latvia; Lithuania; Republic of Macedonia; Ukraine; Venezuela) did not have any international collaboration while even some of them like Lithuania and Ukraine have 12 and 7 publications respectively. The network of 1,076 international collaborations with 188 links (pair of countries) has been analyzed using UCINET (Borgatti, Everett et al. 2002). Table 3 shows results of the analysis. The network can be considered as a dense network as almost half of the possible links among all nodes (countries) exist. The network is fully connected and all nodes belong to a component (a group of nodes that are all connected to one another by paths of intermediate acquaintances) whereby the whole network is the "giant component". The clustering coefficients value for the network shows that the probability that any two unconnected collaborators of a country, collaborates (wrote a paper) together is just 8% which is very low. The international network is decentralized considering the degree centrality of the nodes but the network is centralized around a few countries close to all others on average (having high closeness centrality). Average distance among any country to reach any other one in the network is 2.38 meaning that just by two steps (on average) each country reaches another one.

Meso-Level Analysis
Here we focus on collaborations between institutes (e.g., university, research institutes and corporations). Figure 6 shows the evolution over time of inter-institutional collaborations (meso-level) for the "steel structures" field having distinct collaborators (

Identifying the Top Collaborative Institutes and Strong Links
Evaluating the 2,583 collaborations for 1,514 links among 907 intuitions, we ranked the institutes in terms of total collaborations they have. Table 4 shows the top collaborative institutes in the "steel structures" field and their sum of collaborations and number of collaborators (number of unique institutes which have at least one co-authored paper with the institute. "Tsinghua University" from China is ranked first followed by "Imperial College London" from United Kingdom and "University of Sydney" from Australia with 115, 82 and 65 inter-institute collaborations respectively over the last 40 years. Interestingly while United States is the most collaborative country but the first institute from United States in the list is ranked 5 th and there are just three institutes from United States in top 10 collaborative institutes. This shows that overall huge numbers of institute are active in this field in United States but none of them (individually) is not in top 4 collaborative institutes. On the other hand, "University of Coimbra" from Portugal is ranked 11 th but Portugal is not among in the top 20 collaborative countries. Table 5 shows the top 10 strongest inter-institutional collaborations links among institutes which have nine or more collaborations. Two Chinese universities have the strongest inter-institutional collaborations followed by two universities from Brazil and Italy. Among the 10 collaborations, two Chinese institutes have international collaborations with an institute in US and Egypt. Thus, data shows 80% of the top 10 strong collaboration links are intra-national collaborations (i.e., two institutes are located in the same country). The data also shows that most of the institutes in this table are not among the top collaborative institutes in Table 4 which means that the institutes listed in Table 5 have strong links with only a few number of institutes (collaborators). The clustering coefficients for the network demonstrate a very low probability that any two collaborators of an institute are collaborating. The inter-institutional network may be described as a ring network as its degree centralization value is very low but the network is somehow centralized around a few institutes having high closeness centrality. By five steps (on average) an institutes can reach any other institutes in their collaboration network.      Table 7 shows the top collaborative authors in this field of study, each with more than 28

Identifying the Top Collaborative Authors and Strong Links
collaborations. They are in order of the total number of collaborations but numbers of co-authors (number of unique authors which have at least one co-authored publication) is also shown for each author.
Although "L-H. Han", from Tsinghua University is ranked first followed by "B. Young" from University of Hong Kong, but "Nakashiman" from Kyoto University has more collaborators.  Table 8 shows the top strongest co-authors collaborations with seven or more collaborations (joint-publications). The strongest co-authorship collaborations are among two authors from the "University of Sheffield" following by two authors from the "University of Sydney" and two authors from "Nagoya University". As the data shows, only five of the top co-authorship collaborations (about 34%) are inter-institutional collaborations and only three (20%) are international collaborations. High intrainstitutional collaborations indicate that the co-authors may have advisor-student relationship. The data also shows that most of the authors are not among the top collaborative authors.  We extract 1,116 cliques with at least 3 nodes. The largest cliques includes one clique of 15 fully connected authors, one clique of 9 authors and two cliques including 8 fully interconnected authors (to all other 7 authors) as shows below. As shown in Figure 10, none of the authors from above cliques are connected to other cliques that lead cliques to be fragmented from each other.   1970-1982 and 1983-1997. On the other hand, the Scopus-listed publications pre-1983 is very small while the pre-1983 frequency of publication was higher than shown in Figure 1 due to the fact that the electronic publication of research on "steel structures" started around 1982 and hence. Therefore, we will have a macro-level cross-time analysis for the two periods: 1983-1997 and 1998-2009. Table 10 shows the top 20 collaborating countries (in order of the sum of collaboration) for each three periods of times. There were only 33 countries during 1983-1997 that had at least one collaboration through 50 distinct pairs of collaborations (links) over the 15 years but 163 pairs of collaborations have extracted among 55 countries for the following 11 years (during 1998-2009). In addition, sum of collaborations had a sharp increase from 159 during 1983-1997 to 911 during 1998-2009. Studying the evolution of the scientific collaboration activity amongst countries, United States has the majority of collaborations followed by China and United. Interestingly France, South Korea, Singapore and Portugal among are the top 10 collaborating countries in the second period (1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)), but were not in the top 10 ranked countries in the first period. very weak intra-region links. European countries not only had collaborations with other regions but also had a strong collaboration among them especially between Luxembourg and Belgium and Netherlands.   has more nodes and links than the 1983-1997 period, the average path between countries was lower.

Growth Trend of Top Collaborative Countries
Considering network centralization measures to explore the structural change of the international network, as the size of the network increases, its degree centralization measures decreases while the closeness and betweenness centralization measures are increasing. This means that the network structure is becoming centralized around a few countries close to all other countries (having high closeness) and brokering more between others (high betweenness centrality).

Top Growing Collaborative Countries
In order to identify the fastest growing collaborating countries in "steel structures" research, we have compared average collaborations per year for the countries that has at least one collaboration during the two periods. We defined growth rate as the division of the average number of collaborations per year during the two periods.

Discussion and Conclusion
Using publication data and extracting co-authorship relations, we have presented an overview of collaboration efforts and collaborative networks in the "steel structures" research area. The collaboration networks of scientists in "steel structures" have been analyzed by using author affiliations from publications having "steel structures" in their "title" or "keywords" or "abstract" since 1970 to 2009 as extracted from Scopus. The publication dataset we have extracted does not support to represent the complete world production of research on "steel structures" (due to the possibility of significant biases: evolving list of relevant journals; publications in other journals and languages; and etc.). Hence, the database does not pretend to represent the complete field. Nevertheless, the paper presents a fairly accurate network of collaborations in the field of "steel structures", and illustrates the use of network theory indicators to analyse this field.
The frequency of publications shows that a few numbers of authors publish a large number of papers while the majority of authors publish a small number of papers. Thus, the distribution follows a scale-free power-law distribution. We have provided a methodological approach by applying known network and statistical measures to explore scientific collaboration networks at micro-(researcher), meso-(institute), and macro-(country) levels over the last 40 years. We find a number of interesting properties of these networks. By the growth of network size, density, connectedness, centralization measures and clustering coefficient are decreasing to the lowest values at micro-level. On the other hand, number of components and the average distance among nodes in the networks are increasing by the growth of network size.
Although the process of scientists introducing their collaborators to one another is an important one in the development of scientific communities but this had not applied in practice among weakly-clustered researchers in "steel structures" field. The low clustering coefficients values for all levels indicates that two randomly chosen authors (or institutes or countries) from the community are less likely to have collaborated if they have a third common collaborator.
Exploring average distance between countries indicate that a randomly chosen country can reach to another country just by two steps while average distance between institutes is five and authors is eight.
Therefore, any two authors in "steel structures" field are connected through about eight intermediate authors. While the authors" average distance for "steel structures" field is higher than some of other fields but still it reflect a "small-world" phenomena.
Network closeness centralization is the only measure which is almost significantly high in all levels of analysis though this value is much higher in marco-level and less in meso-level and the lowest in micro-level. This reflects that the scientific collaborations network structures are centralized around few authors with high closeness centrality. Networks are not centralized considering degree and betweenness centrality but they follow the same trend by having highest value in macro-level and go down for subsequent levels (i.e., meso-and micro-levels).
Investigating the network statistics during the growth of international collaboration networks over three periods of time (e.g., 1970-1982, 1983-1997, and 1998-2009) indicates increasing trend for international network"s density, connectedness, and clustering coefficients. While the closeness and betweenness centralization measure are increasing too but degree centralization was decreasing. It shows that by the growth of network size, the variance between nodes" (countries) degree centrality (number of directly connected nodes) decrease while the variance between nodes" closeness and betweenness centrality increase (a few of them having high measure but a large number of them, on the edge of the networks, with low measures. Interestingly, although countries" average distance increase during second period but again decrease during third period.