In our discussion of networks thus far, we have generally viewed the relationships contained in these networks as having positive connotations – links have typically indicated such things as friendship, collaboration, sharing of information, or membership in a group. The terminology of online social networks reflects a largely similar view, through its emphasis on the connections one forms with friends, fans, followers, and so forth. But in most network settings, there are also negative effects at work. Some relations are friendly, but others are antagonistic or hostile; interactions between people or groups are regularly beset by controversy, disagreement, and sometimes outright conflict. How should we reason about the mix of positive and negative relationships that take place within a network?

Here we describe a rich part of social network theory that involves taking a network and annotating its links (i.e., its edges) with positive and negative signs. Positive links represent friendship while negative links represent antagonism, and an important problem in the study of social networks is to understand the tension between these two forces. The notion of structural balance that we discuss in this chapter is one of the basic frameworks for doing this.

In addition to introducing some of the basics of structural balance, our discussion in this chapter serves a second, methodological purpose: it illustrates a nice connection between local and global network properties. A recurring issue in the analysis of networked systems is the way in which local effects – phenomena involving only a few nodes at a time – can have global consequences that are observable at the level of the network as a whole.