Frequency-based brain networks: From a multiplex framework to a full multilayer description

• Main Authors: Javier M. Buldú, Mason A. Porter
• Format: Article
• Language: English
• Published: The MIT Press 2018-10-01
• Series: Network Neuroscience
• Subjects: Functional brain networks; Magnetoencephalography; Multilayer networks; Multiplex networks; Algebraic connectivity
• Online Access: https://www.mitpressjournals.org/doi/pdf/10.1162/netn_a_00033

We explore how to study dynamical interactions between brain regions by using functional multilayer networks whose layers represent different frequency bands at which a brain operates. Specifically, we investigate the consequences of considering the brain as (i) a multilayer network, in which all brain regions can interact with each other at different frequency bands; and as (ii) a multiplex network, in which interactions between different frequency bands are allowed only within each brain region and not between them. We study the second-smallest eigenvalue λ2 of the combinatorial supra-Laplacian matrix of both the multiplex and multilayer networks, as λ2 has been used previously as an indicator of network synchronizability and as a biomarker for several brain diseases. We show that the heterogeneity of interlayer edge weights and, especially, the fraction of missing edges crucially modify the value of λ2, and we illustrate our results with both synthetic network models and real data obtained from resting-state magnetoencephalography. Our work highlights the differences between using a multiplex approach and a full multilayer approach when studying frequency-based multilayer brain networks. For more than a decade, network analysis has been used to investigate the organization and function of the human brain. However, applications of multilayer network analysis to neuronal networks are still at a preliminary stage, in part because of the difficulties of adequately representing brain-imaging data in the form of multilayer networks. In this study, we investigate the main differences in using multiplex networks versus more general multilayer networks when constructing frequency-based brain networks. Specifically, we are concerned with the differences for estimating the algebraic connectivity λ2, which has been related to structural, diffusion, and synchronization properties of networks. Using synthetic network models and real data, we show how edge-weight heterogeneity and missing interlayer edges crucially influence the value of λ2.