Page - (000185) - in Knowledge and Networks

179 complete blocks (Batagelj, Ferligoj, & Doreian, 1992; Doreian et al., 2005). The term block refers to the ties linking equivalent actors to alters in this permuted matrix. In prespecified blockmodeling, a hypothesis on the overall configuration of the network is formulated a priori on theoretical grounds. Subsequently, this model configuration is fit to the data by means of a local optimization algorithm. The algo- rithm partitions the network to minimize the overall number of inconsistencies between the expected and observed ties. Lastly, the permuted matrix can be reduced to a simpler graph (the image), which represents an instance of all the possible con- figurations compatible with that prespecified block model. Figure 9.2 presents the prespecified block model used to reduce IMAST net- works (Panel A) and exemplifies the process of reduction (Panels B and C). Panel A reports, in a matrix format, the multiple-core blockmodel specified to fit the data. This particular blockmodel was introduced by Kronegger et al. (2011) to study col- laboration among Slovenian academics. The rows and the columns of the matrix in Panel A represent groups of organizations, whereas the cells of the matrix indicate how these groups are related to each other (i.e., the role they play in the system). As mentioned, we specified the groups to be formed according to the definition of structural equivalence. The topological hypothesis advanced by this blockmodel is that multiple cores of completely connected actors exist in the observed network. We express this hypoth- Fig. 9.2 An example of network reduction through prespecified blockmodeling. Panel A: A theo- retical multiple-core model. Panel B: The multiple-core model fit to data. Inconsistencies between observed and expected ties are marked in red. Panel C: An example of reduction where the parti- tioned matrix in Panel B is presented as a reduced graph (Source: Authors’ elaborations based on R&D collaboration within the technological district) 9 Topology and Evolution of Collaboration Networks