White matter fibers transfer the information between brain regions with delays that are measurable with magnetoencephalography and electroencephalography (M/EEG). In the context of regularizing the dynamics of M/EEG and recovering electrical activity of the brain from M/EEG measurements, this article proposes a graph representation-based framework to solve the M/EEG inverse problem, where prior information about transmission delays supported by diffusion MRI (dMRI) are included to enforce temporal smoothness. Results of the reconstruction of brain activity from simulated MEG measurements are compared to MNE, LORETA and CGS methods and we show that our approach improves MEG source localization when compared to these three state-of-theart approaches. In addition, we show preliminary qualitative results of the proposed reconstruction method on real MEG data for a sensory-motor task.