Network Inequality through Preferential Attachment, Triadic Closure and Homophily

Inequalities in social networks arise from simple linking preferences. Understanding how these preferences interact is essential for understanding observed group disparities and for designing effective interventions. PATCH is a growing network model that integrates three mechanisms. Preferential attachment increases the chance to connect to already well-connected nodes. Homophily increases the chance to connect to similar nodes based on any attribute and triadic closure increases the chance to connect to friends of friends. Nodes are assigned to a minority or majority group, arrive sequentially and create a fixed number of links. Each link forms either globally to any existing node or based on triadic closure via a common neighbor. Candidate targets can be chosen at random or biased by popularity and similarity, and these biases may differ between global and triadic closure linking. Homophily creates links within groups, segregating the network and favoring one group over the other in their network visibility. Preferential attachment steers links to already central nodes, which concentrates degree and elevates degree inequality. The effects of triadic closure are nuanced. When triadic closure selection among friends of friends is unbiased, closure reduces inequity. When closure selection favors popular and similar nodes, it exacerbates global and between group inequalities. With strong heterophily, closure can redirect links across groups and modestly lower disparities. Advantages for one group always coincide with higher degree inequality in the advantaged group, indicating that benefits concentrate among few members. To interpret five decades of gender inequalities in academia, we calibrate PATCH on three networks: collaborations and citations in Physics, and collaborations in Computer Science. We identify persistent popularity bias, moderate similarity bias, and common closure. These forces are sufficient to generate the observed combination of segregation, degree concentration, and group gaps, clarifying how routine linking behavior accumulates into durable inequalities. PATCH shows that reducing similarity bias lowers segregation and narrows group differences but can heighten concentration within the advantaged group. Substantial reductions in overall degree inequality require tempering popularity bias and limiting biased friends-of-friends recommendations. Because outcomes depend on joint mechanism settings, tuning them together is crucial to avoid trading one inequality for another.