Networks containing negative ties

• We examine how standard methods can be applied to networks of negative ties.
• We extend cohesive subgroups to negative tie data.
• We propose a new centrality measure for negative tie data.
• We develop a centrality measure, PN centrality, for data with both positive and negative ties.

Social network analysts have often collected data on negative relations such as dislike, avoidance, and conflict. Most often, the ties are analyzed in such a way that the fact that they are negative is of no consequence. For example, they have often been used in blockmodeling analyses where many different kinds of ties are used together and all ties are treated the same, regardless of meaning. However, sometimes we may wish to apply other network analysis concepts, such as centrality or cohesive subgroups. The question arises whether all extant techniques are applicable to negative tie data. In this paper, we consider in a systematic way which standard techniques are applicable to negative ties and what changes in interpretation have to be made because of the nature of the ties. We also introduce some new techniques specifically designed for negative ties. Finally we show how one of these techniques for centrality can be extended to networks with both positive and negative ties to give a new centrality measure (PN centrality) that is applicable to directed valued data with both positive and negative ties.