This paper introduces a nonparametric framework for the setting where multiple networks are observed on the same set of nodes, also known as multiplex networks. Our objective is to provide a simple parameterization which explicitly captures linear dependence between the different layers of networks. For non-Euclidean observations, such as shapes and graphs, the notion of "linear" must be defined appropriately. Taking inspiration from the representation of stochastic processes and the analogy of the multivariate spectral representation of a stochastic process with joint exchangeability of Bernoulli arrays, we introduce the notion of edge coherence as a measure of linear dependence in the graph limit space. Edge coherence is defined for pairs of edges from any two network layers and is the key novel parameter. We illustrate the utility of our approach by eliciting simple models such as a correlated stochastic blockmodel and a correlated inhomogeneous graph limit model.

中文翻译：

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多路复用网络中的边缘一致性

本文介绍了一种用于在同一组节点上观察多个网络的设置的非参数框架，也称为多路复用网络。我们的目标是提供一个简单的参数化，它明确地捕获不同网络层之间的线性依赖关系。对于非欧几里得观察，例如形状和图形，必须适当定义“线性”的概念。从随机过程的表示和具有伯努利阵列的联合可交换性的随机过程的多变量谱表示的类比中汲取灵感，我们引入了边相干性的概念作为图极限空间中线性相关性的度量。边缘相干性是为来自任何两个网络层的边缘对定义的，并且是关键的新参数。