Reciprocity, or the tendency of individuals to mirror behavior, is a key measure that describes information exchange in a social network. Users in social networks tend to engage in different levels of reciprocal behavior. Differences in such behavior may indicate the existence of communities that reciprocate links at varying rates. In this paper, we develop methodology to model the diverse reciprocal behavior in growing social networks. In particular, we present a preferential attachment model with heterogeneous reciprocity that imitates the attraction users have for popular users, plus the heterogeneous nature by which they reciprocate links. We compare Bayesian and frequentist model fitting techniques for large networks, as well as computationally efficient variational alternatives. Cases where the number of communities are known and unknown are both considered. We apply the presented methods to the analysis of a Facebook wallpost network where users have non-uniform reciprocal behavior patterns. The fitted model captures the heavy-tailed nature of the empirical degree distributions in the Facebook data and identifies multiple groups of users that differ in their tendency to reply to and receive responses to wallposts.

翻译：互惠性，即个体模仿他人行为的倾向，是描述社交网络中信息交换的关键指标。社交网络中的用户往往表现出不同程度的互惠行为，这种行为的差异可能暗示着存在以不同速率互相关联的社区。本文提出了一种方法，用于模拟成长型社交网络中的多元互惠行为。具体而言，我们提出了一种具有异质互惠性的优先依附模型，该模型模仿了用户对热门用户的吸引力，以及他们互相关联的异质性特点。我们比较了针对大型网络的贝叶斯与频率学派模型拟合技术，以及计算高效的变分替代方案。同时讨论了社区数量已知与未知两种情况。我们将所提出的方法应用于Facebook留言墙网络的分析，其中用户具有非均匀的互惠行为模式。拟合模型捕捉到了Facebook数据中经验度分布的重尾特征，并识别出多个在回复及接收留言墙帖子的倾向性上存在差异的用户群体。