Page - (000189) - in Knowledge and Networks

183 clusters to one another. In 2012 a third bridging cluster emerged (cluster 3), whereas in 2013 the institutional bridging function seemed to have lost out to increasingly diffused bridging ties captured by the model as inconsistencies. In the next section the pattern and location of inconsistencies are examined to aid in understanding what types of variations occurred and what types of actors were involved in this process of recombination. Inconsistency Analysis and Structural Variations This section includes an in-depth analysis of inconsistencies to aid in understanding (a) what types of variations shifted the IMAST development trajectory from a core– periphery to a multiple cores topology as discussed in the immediately preceding section (Results) and (b) what types of actors were involved in terms of knowledge bases and geographical location. Inconsistencies in blockmodeling do not have a straightforward interpretation. A blockmodel solution cannot be accepted or discarded based on the number of incon- sistencies it produces (Doreian et al., 2005). The number of inconsistencies depends mostly upon the shape of the block (Prota & Doreian, 2016). Rather, inconsistencies need to be interpreted in the light of the equivalence chosen for the reduction. From this perspective, inconsistencies indicate where and how the observed network devi- ates from the specified block model. With this consideration in mind, we have used blockmodel inconsistencies in this study to operationalize structural variations such as local and global bridging. To explore the location of the inconsistencies the data produced, we examine the inconsistencies matrices as reported in Fig. 9.4. The matrices offer an alternative visu- alization of the reduced graph presented in Fig. 9.3 and highlight different aspects of the solutions. Although graphs provide an immediate idea of the evolutionary trajec- tory of the network, matrices allow a more detailed analysis of inconsistencies’ loca- tions. In each reduced matrix of Fig. 9.4, rows and columns represent clusters of similar organizations (nodes in the graphs of Fig. 9.3), and cells represent relations between clusters representing ties in the graphs of Fig. 9.3. Matirx’s cells are hereafter referred to as blocks (row #; column #). Black cells indicate complete blocks, and white cells represent null blocks. Numbers indicate inconsistencies. As expected, complete diagonal blocks without inconsistencies identify organi- zations collaborating on a single project. We refer to these project groups as simple cores. Simple cores are, for instance, all diagonal blocks in year 2006; block (1;1) in 2009; and all diagonal blocks but blocks 3;3 and 5;5 in 2013. We defined cohesive cores as complete blocks on the main diagonal with incon- sistencies. Examples include block (3;3) in 2007, blocks (2;2), (3;3), and (5;5) in 2011, and blocks (3;3) and (5;5) in 2013, as in Fig. 9.4. Beyond simple and cohesive cores, the blockmodel also identified bridging cores. Particularly central to the system of collaboration are block (4;4) in 2007, block (5;5) in 2009, and block (6;6) in 2010. These clusters are peculiar insofar as 9 Topology and Evolution of Collaboration Networks