Network centrality analysis in management and accounting sciences

2.1 Co-authorship networks and the role of gender and seniority on scientific collaboration

The collaborative production of knowledge has become a dominant manner to produce high-quality research results (Ahrweiler & Keane, 2013). Collaboration involves complex problems, rapidly changing technology, dynamic growth of knowledge, highly specialized areas of expertise and is considered a critical issue of “big science” (Hara, Solomon, Kim, & Sonnenwald, 2003). According to Glänzel & Schubert (2004), almost every aspect of scientific collaboration can be tracked by analyzing co-authorship networks using bibliometric methods, and the most recent efforts in this tradition are extensively based on graph theory and SNA techniques (Breschi & Catalini, 2010).

In a social network, people or groups are called “actors” or “nodes” and the connections that express the relations between them are called “links” (Abbasi & Hossain, 2011). Empirical evidence suggests that co-authorship networks tend to present a small world configuration, which means that the nodes are highly connected and at the same time, there is a small average distance between the network regions (Stefano, Fuccella, Vitale, and Zaccarin, 2013). The redundancy of the links within local cliques ensures the formation of a common language and communication codes to promote reciprocal trust and knowledge sharing among actors. The short cuts linking local cliques to different and weakly connected parts of the network are essential to promote the diffusion and recombination of new ideas, serving as new sources of knowledge (Cowan & Jonard, 2004).

Besides the general properties of co-authorship networks, it is useful to compare the nodes’ importance in terms of their position. Thus, the idea of how central a node is can be essential. Jackson (2008) categorizes the measures of centrality into four groups:

1. degree – how connected a node is;

2. closeness – how easy a node can reach other nodes;

3. betweenness – how important a node is in terms of connecting other nodes and serving as a gatekeeper; and

4. neighbors’ characteristics indexes – how important, central or influential a node’s neighbors are.

Many studies relate demographic aspects of authors with their positions in the co-authorship network and gender has been widely adopted to explain differences in their positioning in the network. Compared to women, men were found to report higher degree and betweenness centralities (Koseoglu, King, & Rahimi, 2019) and closeness centrality (Karimi, Mayr & Momeni, 2019). Ozel, Kretschmer, & Kretscmer (2014) found that women were more likely to collaborate with other scientists irrespective of gender and to establish intergender (male-female) collaborations. Conversely, Araújo, Araújo, Moreira, Herrmann, and Andrade (2017) concluded that men collaborated more with other men than with women, across different fields and regardless of their number of collaborators. Such evidence sheds light on how men and women may adopt different collaboration strategies to produce knowledge, but they do not qualify the collaboration patterns and their impact on scientific outputs.

In this regard, Abramo et al. (2013) found that women, compared to men, collaborated more with researchers from the same university and with researchers from other national institutions, whereas men collaborated more with international researchers. Araújo, & Fontainha (2017) concluded that men were more likely to collaborate in interdisciplinary research than women. Dehdarirad and Nasini (2017) found that men and women had similar propensities to work collaboratively, but compared to those of men, papers signed by women tended to be cited less frequently. That is, even though men and women may share similar benefits in terms of their importance in the co-authorship network once both rely heavily on co-authorship ties to respond to publishing pressures (Badar et al., 2014), male authors seem to have an advantage over women when we qualify the types of collaboration established and the impact of the scientific production.

A critical perspective exposes several causes for gender asymmetry in science, highlighting that teaching jobs and administrative tasks available are not equally accessible to male and female PhD holders, male-dominated research fields occupy a better position in the global research market and are better paid, and female early career researchers face more struggles to obtain funding for their postdoctoral (Bozzon, Murgia, & Poggio, 2019). In sum, we draw attention to the fact that gender inequalities are partly the result of significant structural and systemic discriminatory practices (Aiston & Jung, 2015). To surpass barriers faced in male-dominated areas, Badar, Hite, and Badir (2013) suggest women strengthen their authorship ties, once they found a stronger positive relationship between their research performance and the degree and closeness centralities.

The concept of research seniority is also adopted to explain differences in the collaboration patterns. Seniority is related to the status that an individual has in the hierarchy of a social network (Stvilia et al., 2011), and it can be understood as an expression of the scientist’s research experience. One can expect that over time, researchers will enjoy greater importance in the network because they had more time to develop and strengthen their collaborative links. Bordons, Morillo, Fernández, and Gómez (2003) found that scientific productivity increased as scientists’ professional category improved and that research professors had more collaborators than their counterparts with lower academic ranks. Abramo et al. (2014) concluded that lower-ranking academics tended to construct their collaborations with colleagues at their home university, as at this stage they were less able to activate external collaborations with the same intensity as higher-ranking colleagues. Jeong et al. (2011) showed that researchers with superior academic records preferred collaboration to sole research and that the superior researchers strongly preferred inter-organizational collaboration. Pina, Barać, Buljan, Grimaldo, and Marusić (2019) analyzed the role of grants in collaboration networks of junior and senior researchers and found that while grants were important to position the former within their scientific communities, they had a positive effect for the expansion of scientific communities of senior researchers. Despite the evidence produced, there is a lack of comprehension of how the research experience relates to distinct centrality measures.

2.2 Collaboration networks in management and accounting sciences

Although scarce, literature provides some evidence regarding the researchers’ collaborative networks in management and accounting sciences and more broadly, in the applied social sciences. Nikzad, Jamali, and Hariri (2011) found that the average number of authors per article has increased in all disciplines in the social sciences. In the management field, the growing number of co-authors was attributed not only to the need for complementary skills but also to the expectation of increasing the chances of the manuscript’s acceptance and of being reciprocated by the favor later (Liu, Olivola, & Kovács, 2017).

Evidence on gender inequalities is inconclusive. Pacheco, Pinedo, Ditta, Ruiz, and Varela (2018) found that female authors signed only 2 per cent of the papers in top journals in the fields of operations research and management sciences between 2008 and 2013, stressing that papers with at least one female author accounted for only 33 per cent of the sample. Conversely, Corley and Sabharwal (2010) concluded that top male scholars in public administration were more likely than their female counterparts to publish sole-authored articles and those female authors were more likely to publish in high-quality journals, which shows that they benefit from the degree centrality to produce impactful research. Nielsen (2017) showed that the women’s share of authorship was considerably lower than men’s, although differences in citation-rates appeared to be negligible for a sample of 65,436 authors in management research.

Acedo et al. (2006) found that the networks obtained from publications in leading American and European journals dedicated to organizational studies were relatively cohesive and that prominent positions were occupied by authors who played an essential role in connecting the network and disseminating information. Behara et al. (2014) concluded that while specific authors, institutions and countries ranked high in terms of direct connections, others played an important role as gatekeepers and bridge builders in the network. Authors with more publications and more considerable influence tended to be interconnected through multiple direct links. In the accounting sciences, Endenich, and Trapp (2016) found a significant negative relationship between a researcher’s proportion of co-authored papers and his or her research output.

Koseoglu (2016) observed an increase in international collaborations in the Strategic Management Journal between 1980 and 2014. It was found an increase in density and connectivity and a decrease in fragmentation, indicating that the network was in the process of consolidation. The results also indicated that while few institutions presented low degree centrality, they had high betweenness scores. Institutions located in small and developing or undeveloped countries tended to build international collaborations with institutions located in developed countries to grow and join the network. In this sense, Ronda-Pupo, Díaz-Contreras, Ronda-Velázquez, and Ronda-Pupo (2015) concluded that articles published through international collaboration in Latin American and Caribbean research in management had 1.59 times more impact than those published through domestic collaboration.

In Brazil, Ferreira, Canela, Pinto and Falaster (2018) concluded that the increasing challenge in publishing in higher quality journals and the perception of pressure to publish had induced the scientific collaboration in the management field. Empirical evidence showed a growth in the percentage of co-authored papers (Espartel et al., 2013), a high level of fragmentation in the network (Cruz et al., 2011) and a predominance of well-defined clusters interconnected through few intermediaries (Rossoni, & Guarido Filho, 2009). Moreover, most co-authors belonged to the same institution (Espartel et al., 2013), which is alarming, once heterogeneous networks were determinant in achieving better scientific production in business schools (Orozco & Villaveces, 2015).

Rossoni & Guarido Filho (2007) asserted that the location of Brazilian institutions was a significant factor in the determination of collaborative relationships. In terms of geography, the institutions in the south and southeast of the country stand out (Espartel et al., 2013; Sidone, Haddad, & Mena-Chalco, 2016; Wood, & Chueke, 2008). Thus, we emphasize the importance of considering geographical peculiarities in the analysis of collaboration networks in Brazil, as the Brazilian scientific production is not equally distributed.

4.1 Characterization of network properties and authors’ importance

The connectivity statistics of the co-authorship network are presented in Table II. The network consists of 3,387 nodes, which have an average number of connections of 2.65 and is formed by 731 connected components. The largest connected component consists of 22.91 per cent of nodes. Despite this grouping, the low connectivity of the network is demonstrated by the density of 0.001, indicating that only a small portion of the possible connections has been completed. Evidence gathered by Jackson (2008) showed that the fraction of nodes in the largest component represented 41 per cent in economics, which gives an impression of the small-world nature of the network analyzed. Broadly speaking, the statistics allow us to conclude that the network is sparsely connected with many small and disconnected components, in which the knowledge flow is not evenly distributed within it.

In Figure 1, we highlight the 10 largest communities reported by the modularity analysis. By increasing the analysis resolution, we obtained a minimum of 731 communities, that is, the network clustering produced a large number of clusters, which does not appear to characterize the small-world properties common to scientific collaboration networks (Fleming, King, & Juda, 2007). We also found that about four per cent of the authors published alone. They appear in the most peripheral regions of the network. Small groups of connected authors suggest that knowledge sharing is restricted mainly to isolated communities. In this sense, our findings expose the low connectivity of Brazilian research groups compared to the advances reported in international collaboration networks in the disciplines analyzed (Acedo et al., 2006; Koseoglu, 2016).

Figure 2 presents the ranking of the node centralities for those authors with at least one connection. Degree, eigenvector and closeness centralities are the main indexes by which the authors’ positions can be distinguished. We found a substantial overlap trend between the degree and eigenvector centralities. However, we emphasize the importance of the adjacent nodes, which is noticeable when weighting the nodes by the eigenvector centrality because of their connections with influent nodes linked to several actors.

When considering the betweenness centrality, we found only a small group of authors who exercised minimal control over the knowledge flow. The mean of this index is close to zero and even those authors who appear highlighted have low scores. The shortage of nodes that serve the function of gatekeeper can be considered a determining factor for the low connectivity of the network and contributes to narrow the knowledge into small communities. We also found that the most central nodes concerning the closeness centrality were predominantly located in larger communities.

4.2 Analysis of gender, research experience and geography in the co-authorship network

Table III presents the descriptive statistics of the centrality indexes according to the three dimensions of our analysis. We used a sample clipping composed of nodes with at least one connection, whose classification of academic degree was equal to or higher than the master’s degree in progress and linked to Brazilian institutions, resulting in 2,470 nodes. The betweenness centrality was neglected for this stage because of its low capacity of nodes distinction. The unconditional means show that men have a higher degree score (2.96) than women (2.66), whereas the other centrality indexes do not indicate significant differences between both genders. In terms of academic degrees, PhDs report a higher number of connections (3.22) and closeness scores (0.61). Master’s degree holders are systematically associated with the smallest means and report 2.15, 0.03 and 0.49 for the degree, eigenvector and closeness centralities, respectively. Concerning the geography, the degree statistics are higher for the north-eastern (2.96) and southern (2.90) regions, whereas the northern region reports the highest closeness score (0.85).

In our modeling, the binary dependent variables were defined based on the nodes’ centrality scores. We defined the nodes with strong centrality based on the distributions of the indexes (Table IV). We considered the most central nodes to be those with degree and eigenvector scores from the 90th percentile, which corresponded to the mean of each index plus one standard deviation. For the closeness centrality, we found a cut-off from the 25th percentile, below which we defined the most central nodes. Figure 3 shows the distributional graphs, which corroborate our decision. For the degree and eigenvector centralities, we found a concentration of highest scores among the last portion of approximately 10 per cent of authors. In turn, about 25 per cent of them presented the lowest closeness scores.

Table V presents the econometric results, which show that male authors are related to a higher proclivity to possess a strong degree centrality at a 1 per cent significance level. Despite the low explanatory power of the variables in the regression in which de dependent variable refers to the eigenvector centrality, men are also associated with a higher likelihood of having prominent positions at a 10 per cent significance level. These findings are consistent with those of Koseoglu et al. (2019) and Nielsen (2017). Our evidence corresponds to say that men tend to establish more links and although marginally, they are more prone to collaborate with well-connected and influential nodes compared to women. Apart from corroborating the female under-representation in science (Bordons et al., 2003), our evidence clearly shows an advantage in favor of male authors when it comes to their propensity in occupying central positions in the network. We cannot assert how much of this asymmetry is produced by a self-selection or social selection process (van den Besselar & Sandström, 2016). However, we should look deeper at the issue of gender inequality in management and accounting sciences, once it may be materialized through power dynamics by which women tend to be excluded from information and informal channels more often than their male peers (Bozzon et al., 2019).

We also found that lower academic degree holders, compared to PhDs, were less likely to occupy central positions in terms of the degree centrality. The master’s degree holders had the highest differential in the probability compared to the reference group, whereas PhD students had the lowest. In other words, the link with the research institution, still as a student, seems to be associated with a more significant number of collaboration links. Our findings support the assumption that senior researchers tend to enjoy greater importance in the network, showing that in the management and accounting sciences such importance seems to be heavily based on the additional number of connections that PhDs can establish.

The positive relationship between the academic degrees and the nodes’ importance was not sustained for the eigenvector and closeness centralities. Conversely, when weighting the nodes’ importance by the closeness centrality, authors with lower academic degrees presented a higher proclivity to occupy central positions compared to PhDs at a 1 per cent significance level. That is, we found a negative relationship between the academic degrees and the closeness centrality, and this evidence can be interpreted as synonymous with dependence (Brandes et al., 2016), once students depend on senior researchers to generate research outputs. This dependency systematically increases as academic degrees decrease. Thus, if the research seniority seems to be associated with a large number of collaborative links as also evidenced by Bordons et al. (2003), it makes researchers less dependent, therefore, more distant from other actors. Unlike the experimental sciences, research resources in the social sciences are substantially less sophisticated (Stephan, 2010), which can make senior researchers less sensitive to adopting collaborative strategies based on proximity simply because access to research resources is not so necessary as they are in the experimental sciences.

In terms of geography, our findings did not allow us to establish a relationship between the nodes’ importance and the development of Brazilian regions. We found that there was no difference in the probability of occupying central degree positions conditioned to the regions of authors’ institutions, despite the concentration of authors in the south and southeast regions. In turn, we found that authors from the southern region were more likely to occupy prominent positions in terms of the eigenvector centrality. It is interesting to note that among the most central nodes, there are 3 postgraduate students for each PhD in the southern region, whereas this ratio is 8, 6 and 11 in the midwestern, north-eastern and south-eastern regions, respectively. Proportionally, the authors’ collaboration network in the southern region consists of 31 per cent of PhD students, which is 8 times higher compared to the mean of the other regions. In this sense, our findings indicate that maintaining connections with researchers who hold higher academic degrees increases the likelihood of assuming a prominent position because of the benefits of their influence, which is consistent with the argument of Cimenler et al. (2014). An author can assume a relevant position in a network by favoring connections with other well-connected authors like those with higher academic degrees.

Except for the midwestern region, authors from other regions showed lower probabilities of occupying central closeness positions compared to those in the south-eastern region. We found that the proportion of master’s holders for each PhD was higher in the midwestern and south-eastern regions (3.5 and 2.7, respectively). This result may be related to a higher concentration of authors with a lower academic degree in the co-authorship groups in such regions, implying in higher closeness scores due to a higher dependence on senior researchers as mentioned before.