  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.
