Friend of a friend

Balance theory

The tendency of a friend of a friend to become a friend was noted by Fritz Heider, though he also considered the possibility that one of the friendships might breakdown, according to balance theory, which his view of human triangles is called. According to Heider, the friend of a friend contact could be stressful enough to undermine one or another of the friendships. Extending the study of social dynamics caused by such friend-of-a-friend tensions to social networks beyond triangles, Dorwin Cartwright and Frank Harary used signed graphs to indicate positive or negative sentiments between persons. In 1963 Anatol Rapoport summarized the theory: "The hypothesis implies roughly that attitudes of the group members will change in such a way that one's friends' friends will tend to become one's friends, ..." In September 1975 Dartmouth College offered a symposium on these dynamics.

Bo Anderson made an analysis of the friend-of-a-friend relationship in connection with his criticism of balance theory.

We have all encountered cases in which somebody has said, "You should meet so-and-so", only to find that we have little in common with that person, even though he or she was introduced to us by a mutual friend...In some friendships the persons value the exclusiveness of their relationship and are therefore not likely to let others into it. Friends differ from acquaintances in that they are not merely slots in a grid of social network relationships, but are valued for their personal, unique qualities. Hence, when I relate to a friend of a friend, I need to know something about the perceptions and exchanges that make up this friendship. My reaction to my friend's friend (or spouse) may even be unfavorable, although I may also well understand and sympathize with my friend’s affection for her, given his needs, perceptions, interests and so on.

Considering friendship between people to be a binary relation, the connection to a friend of a friend is a composition of the relationship with itself. Composed relations are used to describe kinship, so it may be natural to apply composition to friendship. One consequence is that frequently a person's friends have more friends than him (the friendship paradox), which accents the reach of the compound connection. But the fact that friendship is not automatically a transitive relation produces some social dynamics.