Positive and Negative Relationships

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 on-line 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 ...

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