Page - (000186) - in Knowledge and Networks

180 esis formally by specifying that diagonal blocks are complete. In our specific case, these diagonal cores can be interpreted as research units or project partnerships. In keeping with Kronegger et al. (2011), these cores are hereafter referred to as simple cores. Furthermore, the blockmodel allows simple cores either to be connected to each other through bridging blocks or to stay disjointed. In our specification, off- diagonal blocks can be either null or complete. The former condition is the case when no overlapping exists between two research groups, whereas the latter condition sig- nals brokerage. The final block (5,5) of the blockmodel representing the periphery of this multiple- core blockmodel is left unspecified so that it can be either complete or null. The network will have a periphery if the last block is null, implying that the actors in the respective cluster 5 will have no relations among themselves. Pajek software for social network analysis was used to fit IMAST project networks to this block model at each time point. Panel B of Fig. 9.2 reports how the blockmodel fits the IMAST collaboration network in the year 2006. As mentioned, the observed network was permuted using structural equivalence so that organizations (rows and columns of the network matrix) formed either complete or null clusters (identified by blue lines in Panel B). The cells of the network report the number of times actors collaborated with each other. The higher the number of collaorations, the more intense the color. Inconsistencies between the observed network and the blockmodel hypothesis are reported in red. The location and pattern of inconsistencies can be examined to arrive at a substantive interpretation of blockmodeling solutions (Prota & Doreian, 2016). More specifically, in this study inconsistencies are used to operationalize the key concepts of cohesive cores and structural variations as discussed in the first section as follows: 1. Complete diagonal blocks with no inconsistencies refer to clusters whose mem- bers collaborated on exactly the same research projects or on a single research project. All the organizations participating in the same R&D project are, by defi- nition, collaborating with one another and form a complete clique or a 1-covered block. 2. Complete diagonal blocks with inconsistencies indicate effective cohesive cores. Through the use of structural equivalence, inconsistencies in a complete diago- nal block imply nonidentical patterns of ties between a cluster’s organizations. In other words, organizations recursively collaborate in slightly different partnerships. 3. A diagonal core is a bridging core when all the off-diagonal blocks associated with it are complete. This operationalization applies to block (1;1) in Panel B of Fig. 9.2, whose associated columns and rows are all complete. In our example the two research institutions in cluster 1 collaborated on all the projects under- taken by the district. By identifying a specific group of organizations participat- ing in all research projects, bridging cores can be taken as a measure of local brokerage as discussed by Glückler (2007). L. Prota et al.