Social network analysis is well-known as a fundamental tool for structural assessment of relationships at scale. The overwhelming convention in this field is to model relations based on positive factors, often related to commonality between participants, such as mutual friendship, or other characteristics that may positively bind participants. However, this leaves undefined the meaning of absent links between agents, leaving open scope for alternative interpretations. For example, an absent link may be due to individuals being unfamiliar and irrelevant to each other, but it could also be due to negative relations. This context is particularly relevant to adversarial scenarios, where actors, or the groups that they represent, are the focus of analysis. Accordingly, in this paper we consider the importance of explicitly modelling so-called negative ties as a means to provide insight into conflict and adversarial interaction. This subtle redefinition of social network analysis provides an opportunity to gain new perspectives on the threats that can subvert traditional social network analysis due to negativity not being explicitly represented. In this paper we focus on the fundamental issue of how to define negative ties. Generally, these invoke or are the consequence of cognitive dissonance between conflicting parties. We distinguish further between these three domains of negative, network connections and provide illustrations of each type in the context of social conflict. We discuss implications of these various genres of negativity regarding their potential to be used as tools by adversaries and their ability to provide a deeper understanding of human conflict.