Our friends' friends become our friends

Triadic closure denotes the fact that two people with a relationship in common have a high probability of connecting in turn. It was described in the founding work of network sociology. Georg Simmel was already analysing in 1908 what changes in a two-person relationship when a third is added.

Measurements on large graphs find a clustering coefficient markedly higher than that of a random graph of the same density, which is one of the defining properties of real social networks. Duncan Watts and Steven Strogatz made it in 1998 one of the two features of their small-world model, alongside the shortness of paths between any two points.

Three mechanisms produce the same effect: opportunity, since a common friend creates encounters; homophily, since two friends of the same person often resemble them; and risk reduction, the shared relationship serving as a guarantee. Mark Granovetter drew a consequence from this in 1973: two strong ties from the same person make it very unlikely that the other two remain strangers to each other.

Those mechanisms are hard to separate in observational data, and studies attempting to do so exploit unchosen opportunities to meet. They are not mutually exclusive, and most often act together.

A dense network facilitates social control and the rapid circulation of information within the group. James Coleman argued in the 1980s that this density produces a collective capacity, by making lapses visible. He developed the argument in a 1988 article on social capital.

Ronald Burt defended the opposite position from the same period: the most advantageous positions are those connecting poorly connected groups, which he calls structural holes, a notion systematised in a 1992 book.

The two theses concern different outcomes: density favours trust and coordination, openness favours access to new information. They contradict each other only if one seeks a single optimal property.

Later work sought to articulate the two, showing that the advantageous configuration depends on the task and the context, which is the most solid conclusion of this literature. The same structure may serve a group for one task and hinder it for another.

Relationship suggestion systems on platforms rely mainly on shared connections, which mechanically strengthens triadic closure. A suggestion based on a mutual friend is the most direct form of this mechanism, automated on a large scale.

The experiment published in 2022 on weak ties consisted precisely in varying that parameter, which indicates that the composition of online networks depends on a technical setting as much as on users' choices.