The relationship between structural and functional brain networks is still highly debated. Most previous studies have used a single functional imaging modality to analyze this relationship. In this work, we use multimodal data, from functional MRI, magnetoencephalography, and diffusion tensor imaging, and assume that there exists a mapping between the connectivity matrices of the resting-state functional and structural networks. We investigate this mapping employing group averaged as well as individual data. We indeed find a significantly high goodness of fit level for this structure-function mapping. Our analysis suggests that a functional connection is shaped by all walks up to the diameter in the structural network in both modality cases. When analyzing the inverse mapping, from function to structure, longer walks in the functional network also seem to possess minor influence on the structural connection strengths. Even though similar overall properties for the structure-function mapping are found for different functional modalities, our results indicate that the structure-function relationship is modality dependent.

Neuronal oscillations exist across a broad frequency spectrum, and are thought to provide a mechanism of interaction between spatially separated brain regions. Since ongoing mental activity necessitates the simultaneous formation of multiple networks, it seems likely that the brain employs interactions within multiple frequency bands, as well as cross-frequency coupling, to support such networks. Here, we propose a multi-layer network framework that elucidates this pan-spectral picture of network interactions. Our network consists of multiple layers (frequency-band specific networks) that influence each other via inter-layer (cross-frequency) coupling. Applying this model to MEG resting-state data and using envelope correlations as connectivity metric, we demonstrate strong dependency between within layer structure and inter-layer coupling, indicating that networks obtained in different frequency bands do not act as independent entities. More specifically, our results suggest that frequency band specific networks are characterised by a common structure seen across all layers, superimposed by layer specific connectivity, and inter-layer coupling is most strongly associated with this common mode. Finally, using a biophysical model, we demonstrate that there are two regimes of multi-layer network behaviour; one in which different layers are independent and a second in which they operate highly dependent. Results suggest that the healthy human brain operates at the transition point between these regimes, allowing for integration and segregation between layers. Overall, our observations show that a complete picture of global brain network connectivity requires integration of connectivity patterns across the full frequency spectrum.