Page - (000184) - in Knowledge and Networks

178 Capturing Cluster’s Topology with Prespecified Block-Modeling We used prespecified blockmodeling to gain a synthetic view of the structural evo- lution of IMAST collaboration network (Fig. 9.1). Blockmodeling is a type of clus- tering for relational data intended to reduce complex networks into simpler graphs, with nodes representing groups of equivalent actors (positions) and ties represent- ing the relation between positions (roles) (see Ferligoj, Doreian, & Batagelj, 2011; Wasserman & Faust, 1994). These reduced graphs (also called images) are used in this study to facilitate synthetic visualization of the overall topology of the IMAST collaboration network and its evolution. To reduce a complex network into its image, a single node subsumes similar actors if they are equivalent. This study uses the definition of structural equivalence to reduce IMAST collaboration networks. Actors are considered equivalent if their pat- tern of ties to and from alters is identical (Lorrain & White, 1971). In practice, when structural equivalence is used, the network matrix is permuted to form either null or Fig. 9.1 Energized graphs by structural-hole measures of collaboration networks in selected years (2006, 2009, 2011, 2013). Nodes represent the IMAST’s associated members and external part- ners; line lengths = dyadic constraint; node size = aggregate constraint; node shape = IMAST’s associated member (circle), partner (triangle); node color: firm (gray), research institution (black), other organizations (white), and external partner (yellow) (Source: Authors’ elaborations based on R&D collaboration within the technological district) L. Prota et al.