We introduce a new family of network models, called hierarchical network models, that allow us to represent in an explicit manner the stochastic dependence among the dyads (random ties) of the network. In particular, each member of this family can be associated with a graphical model defining conditional independence clauses among the dyads of the network, called the dependency graph. Every network model with dyadic independence assumption can be generalized to construct members of this new family. Using this new framework, we generalize the Erd\"os-R\'enyi and beta-models to create hierarchical Erd\"os-R\'enyi and beta-models. We describe various methods for parameter estimation as well as simulation studies for models with sparse dependency graphs.

中文翻译：

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网络独立结构的层次模型

我们引入了一个新的网络模型系列，称为分层网络模型，它允许我们以明确的方式表示网络的二元组（随机关系）之间的随机依赖性。特别是，这个家族的每个成员都可以与一个图形模型相关联，该模型定义了网络二元组之间的条件独立子句，称为依赖图。每个具有二元独立性假设的网络模型都可以推广到构建这个新家族的成员。使用这个新框架，我们概括了 Erd\"os-R\'enyi 和 beta 模型，以创建分层的 Erd\"os-R\'enyi 和 beta 模型。我们描述了参数估计的各种方法以及具有稀疏依赖图的模型的模拟研究。