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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 structually 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.

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In many countries, the representation of women on corporate boards of directors has become a topic of intense political debate. Social networking plays a crucial role in the appointment to a board so that an informed debate requires knowing where women are located in the network of directors. One way to quantify the network is by studying the links created by serving on the same board and by joint appointments on multiple boards. We analyse a network of ≈ 320 000 board members of 36 000 companies traded on stock exchanges all over the world, focusing specifically on the position of women in the network. Women only have ≈ 9 − 13% of all seats, but they are not marginalised. Applying metrics from social network analysis, we find that their influence is close to that of men. We do not find evidence to support previous claims that women play the role of "queen bees" that exclude other women from similar positions.