Combinatorial characterizations and impossibilities for higher-order homophily.

Area of Science:

• Social Network Analysis
• Sociology
• Data Science

Background:

• Homophily, the tendency to associate with similar individuals, is fundamental to social organization.
• Traditional homophily measures use graph models, focusing only on pairwise interactions.
• Group interactions, prevalent in society, are not fully captured by pairwise models.

Purpose of the Study:

• To develop a framework using hypergraphs to quantify homophily in group interactions.
• To reveal higher-order social patterns of homophily beyond pairwise connections.
• To identify and address potential pitfalls in defining group homophily.

Main Methods:

• Developed a hypergraph framework to model group interactions.
• Applied the framework to analyze gender homophily in scientific collaboration.
• Examined political affiliation homophily in legislative bill cosponsorship.
• Investigated gender distributions in group photographs.

Main Results:

• Hypergraph analysis revealed group homophily patterns in gender and political affiliation, not fully captured by pairwise measures.
• Distinctive gender distributions were observed in group photographs using the hypergraph model.
• Demonstrated that some intuitive definitions of group homophily are combinatorially impossible.

Conclusions:

• Hypergraphs provide a more comprehensive method for quantifying group homophily.
• Higher-order homophily patterns are influenced by combinatorial constraints, independent of human behavior.
• Careful consideration of combinatorial properties is crucial when defining and interpreting group homophily.