Edge coherence in multiplex networks

TL;DR

This paper proposes a nonparametric framework to quantify linear dependence between layers of multiplex networks using a novel measure called edge coherence, applicable to non-Euclidean data like graphs.

Contribution

It introduces the concept of edge coherence for multiplex networks, providing a new way to model and analyze dependence across network layers.

Findings

Edge coherence effectively captures linear dependence between network layers.

The framework applies to non-Euclidean data such as graphs and shapes.

Illustrated with models like correlated stochastic blockmodels.

Abstract

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.