The Paradox of Second-Order Homophily in Networks

Abstract

Homophily -- the tendency of nodes to connect to others of the same type -- is a central issue in the study of networks. Here we take a local view of homophily, defining notions of first-order homophily of a node (its individual tendency to link to similar others) and second-order homophily of a node (the aggregate first-order homophily of its neighbors). Through this view, we find a surprising result for homophily values that applies with only minimal assumptions on the graph topology. It can be phrased most simply as "in a graph of red and blue nodes, red friends of red nodes are on average more homophilous than red friends of blue nodes." This gap in averages defies simple intuitive explanations, applies to globally heterophilous and homophilous networks and is reminiscent of but structurally distinct from the Friendship Paradox. The existence of this gap suggests intrinsic biases in homophily measurements between groups, and hence is relevant to empirical studies of homophily in networks.

arXiv comment26 pages, 4 figures

References in corpus (11)

• The structure and function of complex networks
• Assortative mixing in networks
• Mixing patterns in networks
• The Anatomy of the Facebook Social Graph
• Social Structure of Facebook Networks
• The Majority Illusion in Social Networks
• Homophily and minority size explain perception biases in social networks
• Visibility of minorities in social networks
• Cumulative effects of triadic closure and homophily in social networks
• Gender homophily from spatial behavior in a primary school: a sociometric study
• Generalized friendship paradox in complex networks: The case of scientific collaboration

Cited by in corpus (3)

• Inequality and Inequity in Network-based Ranking and Recommendation Algorithms
• Strength of minority ties: the role of homophily and group composition in a weighted social network
• Towards Understanding Link Predictor Generalizability Under Distribution Shifts