复用网络中的边缘相干性
Edge coherence in multiplex networks
摘要：
本文介绍了一个非参数框架的设置，其中多个网络被观察到在同一组节点，也被称为多路复用网络。我们的目标是提供一个简单的参数化，明确捕捉网络的不同层之间的线性相关性。对于非欧几里德观测，如形状和图形，“线性”的概念必须适当定义。从随机过程的表示和类比的多变量谱表示的随机过程与联合交换的伯努利阵列的灵感，我们引入边相干的概念，作为一种措施的线性依赖在图极限空间。边缘相干性定义为来自任意两个网络层的边缘对，并且是关键的新参数。我们通过引出简单的模型，如相关的随机块模型和相关的非齐次图极限模型来说明我们的方法的实用性。
英文摘要：
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.
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