Page - (000190) - in Knowledge and Networks

184 Fig. 9.4 Image matrices of IMAST collaboration networks over time. Black cells represent com- plete blocks; white cells represent null blocks; numbers indicate inconsistencies between observed and expected ties (Source: Authors’ elaborations based on patterns of R&D collaboration within the technological district) they included only a few organizations linked by strong collaborative ties involving all other clusters (all the blocks on the associated rows and columns are complete). These key bridging cores had ties spanning all the other research units and played the role of pivots for the whole collaboration network. Finally, the number of positive ties in null blocks signals that individual broker- age was occurring. Figure 9.4 shows that there was a systemic and generalized increase in this type of inconsistency over time. In 2013, inconsistencies spread across full rows and columns in correspondence with cores. This pattern suggests that a single organization acted as a broker linking more cores, as if it were a bridg- ing core embedded within another type of core. Examples are provided by blocks (1;1), (2;2) and (3;3) in 2013 whose associated rows and columns present a signifi- cant number of inconsistencies. To verify this substantive interpretation of the results further, blockmodeling par- titions are fitted onto the original network data. In Fig. 9.5, the observed collabora- tion networks in selected years (2007, 2009, 2011, 2013) are shown by means of blockmodeling partitions. The changes that occurred within the main cohesive core can be appreciated in Fig. 9.5. Whereas in 2007 all cores were exclusively connected to the bridging core (block (4;4)), in 2013 a large group of local organizations was right in the middle of the graph (red nodes in Figure 9.5, diagonal block 3;3 in Figure 9.4) and was linked to a number of other cores. This group fully represented the heterogeneity of knowl- edge bases in IMAST: firms from the defense, aeronautics, maritime, transport, aerospace, and automotive industries, and public universities were all embedded within this cluster along with private research centers and universities. L. Prota et al.