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Comparing multilayer brain networks between groups: Introducing graph metrics and recommendations

Mandke, Kanad; Meier, Jil; Brookes, Matthew J.; O'Dea, Reuben D.; Van Mieghem, P.; Stam, Cornelis J.; Hillebrand, A.; Tewarie, Prejaas K.


Kanad Mandke

Jil Meier

P. Van Mieghem

Cornelis J. Stam

A. Hillebrand

Prejaas K. Tewarie


There is an increasing awareness of the advantages of multi-modal neuroimaging. Networks obtained from different modalities are usually treated in isolation, which is however contradictory to accumulating evidence that these networks show non-trivial interdependencies. Even networks obtained from a single modality, such as frequency-band specific functional networks measured from magnetoencephalography (MEG) are often treated independently. Here, we discuss how a multilayer network framework allows for integration of multiple networks into a single network description and how graph metrics can be applied to quantify multilayer network organisation for group comparison. We analyse how well-known biases for single layer networks, such as effects of group differences in link density and/or average connectivity, influence multilayer networks, and we compare four schemes that aim to correct for such biases: the minimum spanning tree (MST), effective graph resistance cost minimisation, efficiency cost optimisation (ECO) and a normalisation scheme based on singular value decomposition (SVD). These schemes can be applied to the layers independently or to the multilayer network as a whole. For correction applied to whole multilayer networks, only the SVD showed sufficient bias correction. For correction applied to individual layers, three schemes (ECO, MST, SVD) could correct for biases. By using generative models as well as empirical MEG and functional magnetic resonance imaging (fMRI) data, we further demonstrated that all schemes were sensitive to identify network topology when the original networks were perturbed. In conclusion, uncorrected multilayer network analysis leads to biases. These biases may differ between centres and studies and could consequently lead to unreproducible results in a similar manner as for single layer networks. We therefore recommend using correction schemes prior to multilayer network analysis for group comparisons.


Mandke, K., Meier, J., Brookes, M. J., O'Dea, R. D., Van Mieghem, P., Stam, C. J., …Tewarie, P. K. (2018). Comparing multilayer brain networks between groups: Introducing graph metrics and recommendations. NeuroImage, 166,

Journal Article Type Article
Acceptance Date Nov 8, 2017
Online Publication Date Nov 11, 2017
Publication Date Feb 1, 2018
Deposit Date Nov 20, 2017
Publicly Available Date Nov 12, 2018
Journal NeuroImage
Print ISSN 1053-8119
Electronic ISSN 1053-8119
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 166
Keywords Functional connectivity; Functional networks; Structural networks; Multilayer networks; Graph theory; Multi-modal imaging; Minimum spanning tree; Network comparison
Public URL
Publisher URL


accepted_multilayer_compare_KM.pdf (1.9 Mb)

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