How characteristics outside the nodes.

Homophily

Intrinsic and Contextual

For example, the principle of triadic closure — that triangles in the network tend to “close” as links form between friends of friends — is supported by a range of mechanisms that range from the intrinsic to the contextual.

In Strength of Weak Ties we motivated triadic closure by hypothesizing intrinsic mechanisms: when individuals B and C have a common friend A, then there are increased opportunities and sources of trust on which to base their interactions, and A will also have incentives to facilitate their friendship.

However, social contexts also provide natural bases for triadic closure: since we know that A-B and A-C friendships already exist, the principle of homophily suggests that B and C are each likely to be similar to A in a number of dimensions, and hence quite possibly similar to each other as well. As a result, based purely on this similarity, there is an elevated chance that a B-C friendship will form; and this is true even if neither of them is aware that the other one knows A.

Principle of Homophily

Homophily: “birds of a feather flock together”.

Measuring Homophily

We say that an edge is heterogeneous if it connects two nodes that are different according to the characteristic in question. We then ask how the number of heterogeneous edges compares to what we’d see if we were to randomly assign values for the characteristic to all nodes in the network — using the proportions from the real data as probabilities.

when people tend to be similar to their neighbors in a social network, it may not be clear why.

The tendency of people to form friendships with others who are like them is often termed selection, in that people are selecting friends with similar characteristics. For immutable characteristics such as race or ethnicity, this is definitely the case.

With characteristics that are more mutable - behaviors, activities, interests, beliefs, and opinions - another process comes into play as well. People may modify their behaviors to bring them more closely into alignment with the behaviors of their friends. This process has been variously described as socialization and social influence.

In a word, social influence can be viewed as the reverse of selection in terms of causality. With selection, the individual characteristics drive the formation of links, while with social influence, the existing links in the network serve to shape people’s (mutable) characteristics.

Longitudinal Studies

Affiliation Network

We can include contextual factors as nodes in a graph,

and triadic closure.