Page - (000187) - in Knowledge and Networks

181 4. Inconsistencies in null off-diagonal blocks identify brokerage. An example of this pattern of collaboration is shown by the red ties in block (2;5) and (4;5). These inconsistencies show that individual organizations in clusters 2 and 4 are also taking part in the projects undertaken by the organizations in cluster 5. These organizations cross a structural hole. Note that all the inconsistencies reported in Panel B involve the peripheral block (5;5), which happens to be null for that year. In other words, the network in 2006 indeed took a classic core–periphery structure with a bridging core (block (1;1)) and a disconnected periphery (block (5;5)). An increased number of inconsistencies involving actors in cluster 5 will ultimately have an impact on the core-periphery structure of the network by eliminating the periphery. In that eventuality, this local bridging would represent a structural variation (Glückler, 2007). Finally, Panel C of Fig. 9.2 illustrates an example of network reduction by which the rows and columns of the partitioned network matrix in Panel B are shrunk to single nodes if they are equivalent. The reduced graph represents the observed con- figuration consistent with the prespecified blockmodel. In the reduced graph, nodes with loops represent simple cores (complete diagonal blocks in Panel A), whereas ties indicate cross-cluster bridging. Dotted red lines indicate a discrepancy between the network observed and the ideal core-periphery model tested. Blockmodeling Results The blockmodel specified in the previous section is used to reduce the observed networks (as illustrated in Fig. 9.3) in each year from 2006 to 2013.7 The reduced graphs obtained are presented in Fig. 9.3. Empirical results confirm that a process of structural transition characterized the evolutionary trajectory of the IMAST collaboration network. Between 2006 and 2009, the network configured as a core–periphery model with few inconsistencies. In each year of that period, it was possible to identify a clear bridging core linking all the other clusters in a star configuration. Moreover, during those years, there were only a few cross-cutting ties connecting clusters beyond the bridging core, and they were all defined as inconsistencies (reported as red ties in Fig. 9.3). Lastly, from 2006 to 2008, a clear periphery was identified. Members of cluster 5 did not have collaborations among themselves (there was no loop on the cluster), but they did have systemic ties with the bridging core and sporadic ties with other clusters (inconsistencies). In 2009 there occurred a variation capable of shifting the network evolutionary path toward a new configuration. The shift is signaled, among the other things, by 7 An increasing number of clusters (from 4 to 10) were used for reduction. Only the best solutions are reported. The chosen solutions are those that minimize the number of clusters and inconsisten- cies and still provide stable results. One thousand repetitions were done for each fit. 9 Topology and Evolution of Collaboration Networks