Knowledge and Networks by Johannes Glückler Emmanuel Lazega & Ingmar Hammer

Author:Johannes Glückler, Emmanuel Lazega & Ingmar Hammer
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Capturing Cluster’s Topology with Prespecified Block-Modeling

We used prespecified blockmodeling to gain a synthetic view of the structural evolution of IMAST collaboration network (Fig. 9.1). Blockmodeling is a type of clustering for relational data intended to reduce complex networks into simpler graphs, with nodes representing groups of equivalent actors (positions) and ties representing 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 pattern 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 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 algorithm 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 configurations compatible with that prespecified block model.

Figure 9.2 presents the prespecified block model used to reduce IMAST networks (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 collaboration 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.

Fig. 9.2An example of network reduction through prespecified blockmodeling. Panel A: A theoretical 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 partitioned matrix in Panel B is presented as a reduced graph (Source: Authors’ elaborations based on R&D collaboration within the technological district )

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.