Multilayer stochastic block models reveal the multilayer structure of complex networks

TL;DR

This paper introduces multilayer stochastic block models to uncover the layered interaction structure in complex networks from aggregate data, addressing the challenge of unknown layer interactions.

Contribution

It generalizes single-layer SBMs to multilayer systems and provides a probabilistic solution and approximation method for identifying layers in observed networks.

Findings

Multilayer SBMs better predict network structure in real systems.

The proposed approximation makes layer inference computationally feasible.

Multilayer models outperform single-layer models in capturing network complexity.

Abstract

In complex systems, the network of interactions we observe between system's components is the aggregate of the interactions that occur through different mechanisms or layers. Recent studies reveal that the existence of multiple interaction layers can have a dramatic impact in the dynamical processes occurring on these systems. However, these studies assume that the interactions between systems components in each one of the layers are known, while typically for real-world systems we do not have that information. Here, we address the issue of uncovering the different interaction layers from aggregate data by introducing multilayer stochastic block models (SBMs), a generalization of single-layer SBMs that considers different mechanisms of layer aggregation. First, we find the complete probabilistic solution to the problem of finding the optimal multilayer SBM for a given aggregate observed network. Because this solution is computationally intractable, we propose an approximation that enables us to verify that multilayer SBMs are more predictive of network structure in real-world complex systems.