Dense networks with weighted connections often exhibit a community like structure, where although most nodes are connected to each other, different patterns of edge weights may emerge depending on each node's community membership. We propose a new framework for generating and estimating dense weighted networks with potentially different connectivity patterns across different communities. The proposed model relies on a particular class of functions which map individual node characteristics to the edges connecting those nodes, allowing for flexibility while requiring a small number of parameters relative to the number of edges. By leveraging the estimation techniques, we also develop a bootstrap methodology for generating new networks on the same set of vertices, which may be useful in circumstances where multiple data sets cannot be collected. Performance of these methods are analyzed in theory, simulations, and real data.

翻译：具有加权连接的密集网络往往呈现出类似结构的社区,尽管大多数节点相互连接,但根据每个节点的社区成员情况,可能会出现不同的边缘权重模式。我们提出了一个新的框架,用于生成和估计密集的加权网络,在不同社区之间可能存在不同的连接模式。拟议模式依赖于一种特定的功能类别,即绘制连接这些节点的边缘的单个节点特征,允许灵活性,同时要求与边缘数相对应的少数参数。通过利用估算技术,我们还开发了一种靴套方法,用于在同一套脊椎上创建新的网络,这在无法收集多个数据集的情况下可能是有用的。这些方法的绩效在理论、模拟和真实数据中进行了分析。