Homophily

graph-theory sociology

Definition

Homophily

Homophily is the tendency of individuals or entities to form connections with others who are similar to them. In graph-theoretic terms, it is the propensity for nodes to link to other nodes that share attributes, labels, or characteristics.

A graph exhibiting homophily is called a homophilic graph; one exhibiting the opposite tendency is called a heterophilic graph.

Sociological Origin

The term originates in sociology, where it describes the observation that “birds of a feather flock together.” Individuals tend to associate and bond with similar others across dimensions such as age, gender, education, and social class.

Graph-Theoretic Formulation

For a graph $G=(V,E)$ with node labels $y:V\to \mathcal{Y}$:

$$\underset{\text{neighbour agreement}}{\underbrace{\mathbb{P}(y_u=y_v\mid (u,v)\in E)}}\{\begin{array}{l}\gg \\ \ll \end{array}\underset{\text{prior agreement}}{\underbrace{\mathbb{P}(y_u=y_v)}}$$

• Homophily (left $\gg$ right): neighbours are more likely to share labels than random pairs.
• Heterophily (left $\ll$ right): neighbours are less likely to share labels than random pairs.