The Paradox of Second-Order Homophily in Networks

TL;DR

This paper reveals a paradoxical phenomenon in network homophily, showing that nodes tend to have neighbors with higher same-type homophily than expected, which impacts how homophily is measured and interpreted.

Contribution

It introduces a novel local perspective on homophily, defining first- and second-order homophily, and uncovers a surprising, minimal-assumption-based paradoxical gap in homophily measurements.

Findings

Red friends of red nodes are more homophilous than red friends of blue nodes.

The gap exists in both heterophilous and homophilous networks.

This phenomenon affects empirical homophily measurements and interpretations.

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.