Advances in Network Clustering and Blockmodeling

6Blockmodeling of Valued Networks

Carl Nordlund^1,2, and Aleš Žiberna³

¹The Institute for Analytical Sociology, Linköping University, Sweden

²Center for Network Science, Central European University, Hungary

³Faculty of Social Sciences, University of Ljubljana

6.1 Introduction

In the wide variety of networks that connect and make up our worlds, relations not only either exist or not, but often carry a weight. Friendships can be ranked, interactions can be timed, and economic exchanges can be valued, details that provide us with a deeper, nuanced, and higher-resolution understanding of such networks than is provided by the mere existence of ties.

As with most methods and heuristics in network analysis, approaches for clustering¹ or blockmodeling are primarily geared to binary data [23, p. 25; 25]. For the set of indirect methods that do work with valued networks when determining clusters of equivalent actors, valued data still pose a dilemma when interpreting possible blockmodels derived from such approaches. Since the ideal blocks² of generalized blockmodeling (as well as density-based structural blockmodeling) are specified in terms of binary ties, these are not readily comparable with the intra- and inter-block patterns of valued relations. Valued networks are therefore often dichotomized, either prior to identifying equivalent sets of actors or when determining patterns within and between clusters using a statistically, theoretically or arbitrarily determined network-wide ...