Of the 1700 organizations, 1543 were connected through at least 1 collaboration. The overall network comprised of 6000 collaborative links. Figure 1 shows 2 extreme examples of ego-centered network, 1 characterized by a closed structure (cc org = 1) rich in third-party relationships (Figure 1A), and the other by an open structure (cc org = 0), rich in brokerage opportunities (Figure 1B).
Illustrative examples of the 2 extreme cases of a closed ego-centered network (A) and an open ego-centered network (B). The closed network is rich in third-party relationships and closed triangles: all nodes connected to ego (yellow node) are also connected with each other. The open network is rich in brokerage opportunities and open triads: ego (orange node) acts as the broker between all contacts that would otherwise be unable to reach one another. Ego in the closed network has therefore a clustering coefficient equal to one, while ego in the open network a clustering coefficient equal to zero.
The collaboration network among organizations is shown in Figure 2. While the highest-performing organizations (eg, University of Pittsburgh and Yonsei University) achieved the largest research impact (node size) and innovation value (node color), Figure 2A suggests that the correlation between the 2 performance measures is far from perfect. Successful organizations (Figure 2C) appear to be better connected than less successful ones (Figure 2B), which are more sparsely connected.
The global robotic surgery collaboration network. The size of each node is proportional to the average normalized citations of the corresponding organization, while the color is proportional to the innovation index. The weight of each link (ie, the thickness of the line connecting any 2 nodes) is proportional to the normalized count of collaborations between the connected pair of organizations. Panel A shows the largest connected component of the collaboration network. Panel B shows a subset of less successful organizations, more peripheral, and poorly connected. Panel C shows a subset of more successful organizations, highly connected and centrally located within the global network.
Table 1 shows the maximum-likelihood estimates of the coefficients and standard errors of the 2 hierarchical random-intercept models of research impact and innovation. The first 2 estimated parameters in both models suggest that both citations and innovation value at the organizational level were statistically significantly associated with the organization's position in the collaboration network. The local clustering coefficient at the organizational level was negatively associated with both performance measures, although only the association between clustering and innovation reached statistical significance. Both geographical entropy and industrial collaboration were positively and statistically significantly associated with both research impact and innovation. Estimates for all remaining fixed-effect and random-effect parameters are shown in Tables S3, https://links.lww.com/SLA/B554 and S5, https://links.lww.com/SLA/B554 (see also Tables S4, https://links.lww.com/SLA/B554 and S6–S8, https://links.lww.com/SLA/B554 for robustness checks).
Figure 3 shows the topology and properties of 4 ego-centered networks of selected organizations that differed in terms of both innovation index and clustering coefficient. For instance, Figure 3A suggests that Leiden University was characterized by a closed ego-centered network in which the collaborators tended to collaborate with one another, while Imperial College London (Figure 3C) was positioned in a more open network, rich in structural holes, and opportunities for brokerage between collaborators. In turn, Imperial College London was associated with a higher innovation index than Leiden University, which indicates that organizations can extract value from the structural cleavages separating their partners.
Ego-networks of 4 selected organizations, with decreasing values of clustering coefficient and increasing values of innovation index. In each panel, the ego-centered networks are identified by the yellow circles (above), and zoomed out (below).
Figure 4 shows the association between closure of ego-centered networks (node size) and both measures of performance (node color). Figure 4A does not suggest an unambiguous relationship between network closure and research impact, as both large and small nodes can be associated with high performance. Figure 4B, however, indicates that nodes within closer structures were associated with lower values of innovation index. Organizations that produced more innovative outcomes were those that spanned structural holes between collaborators.
The association between closure of ego-centered networks (ie, size of nodes) and both measures of performance (ie, color of nodes). In (A), the color is proportional to research impact, while in (B) to innovation index. In both panels, the size of each node is proportional to the number of closed triangles including the node. While there is no clear-cut relationship between network closure and research impact (ie, there are both large and small red nodes in (A)), nodes in closer structures are associated with lower values of innovation index (ie, most large nodes tend to be the blue ones in (B)).
Annals of Surgery. 2020;271(5):868-874. © 2020 Lippincott Williams & Wilkins