The human brain relies upon the dynamic formation and dissolution of a hierarchy of functional networks to support ongoing cognition. However, how functional connectivities underlying such networks are supported by cortical microstructure remains poorly understood. Recent animal work has demonstrated that electrical activity promotes myelination. Inspired by this, we test a hypothesis that gray-matter myelin is related to electrophysiological connectivity. Using ultra-high field MRI and the principle of structural covariance, we derive a structural network showing how myelin density differs across cortical regions and how separate regions can exhibit similar myeloarchitecture. Building upon recent evidence that neural oscillations mediate connectivity, we use magnetoencephalography to elucidate networks that represent the major electrophysiological pathways of communication in the brain. Finally, we show that a significant relationship exists between our functional and structural networks; this relationship differs as a function of neural oscillatory frequency and becomes stronger when integrating oscillations over frequency bands. Our study sheds light on the way in which cortical microstructure supports functional networks. Further, it paves the way for future investigations of the gray-matter structure/function relationship and its breakdown in pathology.