Statistics > Methodology
[Submitted on 18 Feb 2022]
Title:Edge coherence in multiplex networks
View PDFAbstract: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.
Current browse context:
stat.ME
References & Citations
Bibliographic and Citation Tools
Bibliographic Explorer (What is the Explorer?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)
Demos
Recommenders and Search Tools
Influence Flower (What are Influence Flowers?)
Connected Papers (What is Connected Papers?)
CORE Recommender (What is CORE?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.