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.

翻译：相形之下 -- -- 结点与同类的其他人连接的倾向 -- -- 是网络研究中的一个中心问题。这里,我们从当地的角度来看待单点问题,定义第一阶点(其个人倾向于与类似其他对象连接)和第二阶点(其邻居的总一阶同系)的概念。通过这种观点,我们发现一个令人惊讶的结果,即单极点的数值只适用图形表层的最小假设。最简单的表述方式可以是 " 在红和蓝结点的图表中,红结点的红友平均比蓝结点的红友更具有同性。 " 平均而言,这种差距是简单的直觉解释,适用于全球的异性理论和同性理论网络,与友谊Paradox有不同的结构。这种差距的存在表明各组之间在同性测量中的内在偏差,因此与网络中的同性经验研究有关。