During the formation process of stochastic networks, nodes tend to establish edges based on selective linkage mechanisms. In general, these mechanisms involve probability distributions that underlie the selection of target nodes. In social networks, edges are often associated to relationships that are homophilic with respect to individual traits. Such traits include, for example, gender and age, and are referred to as node types . Our work considers an affinity-weighted preferential attachment model that characterizes the tendency of two group of nodes to connect to other nodes of the same type. We derive mathematical expressions for the dynamics and convergence of homophily measures at the node, group, and network level. Furthermore, we characterize the convergence of network modularity and show that the formation of community structures can be expressed as a function of network homophily.

中文翻译：

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亲和加权优先依恋网络中的动力学

在随机网络的形成过程中，节点倾向于基于选择性链接机制建立边。通常，这些机制涉及作为目标节点选择基础的概率分布。在社交网络中，边缘通常与在个人特征方面具有同质性的关系相关联。这些特征包括例如性别和年龄，并且被称为节点类型。我们的工作考虑了一个亲和度加权的优先连接模型，该模型表征了两组节点连接到相同类型的其他节点的趋势。我们推导出节点、组和网络级别的同质性度量的动态和收敛的数学表达式。此外，