An ensemble perspective on multi-layer networks

TL;DR

This paper introduces an ensemble-based framework for analyzing multi-layer networks, focusing on how diffusion speed relates to aggregate intra- and inter-layer connectivity, useful when only partial network information is available.

Contribution

It develops a mean-field approach and block-matrix model to estimate properties of multi-layer networks from aggregate statistics, addressing partial information scenarios.

Findings

Diffusion speed depends on intra- and inter-layer connectivity.

Ensemble averages can be estimated using aggregate layer statistics.

Conditions identified for estimating properties with partial network data.

Abstract

We study properties of multi-layered, interconnected networks from an ensemble perspective, i.e. we analyze ensembles of multi-layer networks that share similar aggregate characteristics. Using a diffusive process that evolves on a multi-layer network, we analyze how the speed of diffusion depends on the aggregate characteristics of both intra- and inter-layer connectivity. Through a block-matrix model representing the distinct layers, we construct transition matrices of random walkers on multi-layer networks, and estimate expected properties of multi-layer networks using a mean-field approach. In addition, we quantify and explore conditions on the link topology that allow to estimate the ensemble average by only considering aggregate statistics of the layers. Our approach can be used when only partial information is available, like it is usually the case for real-world multi-layer complex systems.