  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.
