网络中的二阶同质性悖论
The Paradox of Second-Order Homophily in Networks
摘要：
同质性（Homophily）--节点与其他同类节点连接的倾向--是网络研究的核心问题。在这里，我们采取一个本地的同伦观，定义一阶同伦的节点（它的个人倾向于连接到类似的其他）和二阶同伦的节点（聚合一阶同伦的邻居）的概念。通过这种观点，我们发现了一个令人惊讶的结果同伦值，适用于只有最小的假设图的拓扑结构。它可以简单地表述为“在一个红色和蓝色节点的图中，红色节点的红色朋友平均比蓝色节点的红色朋友更亲同性。“这种平均值的差距违背了简单的直观解释，适用于全球异性恋和同性恋网络，让人想起但在结构上与友谊Parkway不同。这一差距的存在表明，在群体之间的同质性测量的内在偏见，因此是相关的同质性网络的实证研究。
英文摘要：
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.
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