# Inference of Edge Correlations in Multilayer Networks

## TL;DR

This paper introduces a correlated multilayer stochastic block model that captures edge dependencies across layers, improving community detection and edge prediction in complex multilayer networks.

## Contribution

It relaxes the independence assumption in multilayer SBMs by incorporating edge correlations, providing maximum-likelihood estimation and a new layer correlation measure.

## Key findings

- Edge correlation modeling enhances prediction accuracy.
- Method outperforms independent models on synthetic and real data.
- Provides a new framework for analyzing multilayer network structures.

## Abstract

Many recent developments in network analysis have focused on multilayer networks, which one can use to encode time-dependent interactions, multiple types of interactions, and other complications that arise in complex systems. Like their monolayer counterparts, multilayer networks in applications often have mesoscale features, such as community structure. A prominent type of method for inferring such structures is the employment of multilayer stochastic block models (SBMs). A common (but {potentially} inadequate) assumption of these models is the sampling of edges in different layers independently, conditioned on the community labels of the nodes. In this paper, we relax this assumption of independence by incorporating edge correlations into an SBM-like model. We derive maximum-likelihood estimates of the key parameters of our model, and we propose a measure of layer correlation that reflects the similarity between connectivity patterns in different layers. Finally, we explain how to use correlated models for edge "prediction" (i.e., inference) in multilayer networks. By taking into account edge correlations, prediction accuracy improves both in synthetic networks and in a temporal network of shoppers who are connected to previously-purchased grocery products.