Enhanced detectability of community structure in multilayer networks through layer aggregation

TL;DR

This paper investigates how aggregating layers in multilayer networks affects the ability to detect community structures, revealing that certain aggregation methods improve detectability as the number of layers increases.

Contribution

It introduces a random matrix theory analysis of detectability limits in multilayer stochastic block models and explores how layer aggregation impacts community detection.

Findings

Detectability limit vanishes as O(L^{-1/2}) with more layers when summing adjacency matrices.

Optimal thresholding during summation maintains similar scaling, aiding sparse network analysis.

Layer aggregation can significantly enhance community detectability in multilayer networks.

Abstract

Many systems are naturally represented by a multilayer network in which edges exist in multiple layers that encode different, but potentially related, types of interactions, and it is important to understand limitations on the detectability of community structure in these networks. Using random matrix theory, we analyze detectability limitations for multilayer (specifically, multiplex) stochastic block models (SBMs) in which L layers are derived from a common SBM. We study the effect of layer aggregation on detectability for several aggregation methods, including summation of the layers' adjacency matrices for which we show the detectability limit vanishes as O(L^{-1/2}) with increasing number of layers, L. Importantly, we find a similar scaling behavior when the summation is thresholded at an optimal value, providing insight into the common - but not well understood - practice of thresholding pairwise-interaction data to obtain sparse network representations.