Blockmodelling and role analysis in multi-relational networks
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ORIGINAL ARTICLE
Blockmodelling and role analysis in multi-relational networks Andreas Harrer • Alona Schmidt
Received: 6 December 2012 / Revised: 22 April 2013 / Accepted: 27 April 2013 / Published online: 11 May 2013 Springer-Verlag Wien 2013
Abstract In this paper we introduce an approach for the analysis of multi-relational networks based on blockmodelling, investigation of role systems within these relations and an integrated visualisation to show all the analysis results in one representation. Our direct Blockmodellingmethod is inspired by the Pajek-Approach generalised for two-relational networks and evaluated statistically against current indirect approaches. Based on the resulting blocks the interrelations between different relations are considered and represented as inclusion and equivalence dependencies. For better interpretation of these methods, we present a visualisation that presents actors, positions they belong, roles, and group concepts integrated and at one glimpse. Finally, we apply our methods to the ‘‘Krackhardt’s Hightech Managers’’ dataset to show the feasibility of the approach and present a different interpretation proposal for this well-known data set. Keywords Blockmodelling Role analysis Network visualisations
1 Introduction The widespread use of computer-based networks, e.g. in social networking systems and co-constructive knowledge spaces (like Wikis), for communication or knowledge production creates a research demand on methods for the A. Harrer (&) A. Schmidt Catholic University Eichsta¨tt-Ingolstadt, Ostenstr. 14, 85072 Eichstaett, Germany e-mail: [email protected] A. Schmidt e-mail: [email protected]
analysis of complex social networks. This is caused by the fact that the data of these networks is usually multi-mode, multi-relational, and/or dynamic (Kazienko et al. 2010). For example, Wikis consist of authors, pages, and versions; networking systems and social software like Facebook allow different kinds of relations like friendship, group membership, etc.; usually these networks have also interesting temporal evolution and dynamics to research in, such as changes in group structures over time (Gilbert et al. 2011). The difficulty of the analysis of complex networks thus lies not only in a possible colossal size of the network, but rather in the complexity of the structure of the networks which can include different kinds of relations (Peters et al. 2012), different types of actors as well as the dynamic of the network (Davis et al. 2012). In recent years several methods have been proposed for the analysis of specific types of complex networks, e.g. multislice networks (multirelational, multiscale, and/or time-dependent networks) (Mucha and Porter 2010) or multidimensional networks (multi-relational networks with time windows and group hierarchy) (Kazienko et al. 2011). A network where several possible connections (edges) exist between the same pair of entities (nodes) is called in the literature a multi-relational network (Wasserman and Faust 1994
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