Brain dynamics unfold on a network determined by the pattern of axonal connections linking pairs of neuronal populations; the so-called connectome. Prior work has indicated that structural brain connectivity constrains pairwise correlations in brain dynamics (also called functional connectivity), but it is not known whether brain network structure is related to the intrinsic dynamics of individual brain regions. In this study, we investigate the relationship between a brain region's inter-regional axonal connectivity and its dynamics using a weighted, directed mesoscale mouse connectome from the Allen Mouse Brain Connectivity Atlas and resting state functional MRI (rs-fMRI) time-series data measured in 184 brain regions in eighteen anesthetized mice. Three properties of a brain region's structural network connectivity were measured - degree, betweenness, and clustering coeﬃcient - from weighted and unweighted, and directed and undirected versions of the connectome. We then characterised the univariate rs-fMRI dynamics at each brain region by computing 6930 time-series properties using recently developed highly comparative time-series analysis software, hctsa. We found that strong and robust relationships between the inter-regional axonal connectivity of a brain region and its intrinsic fMRI dynamics were mediated by the weighted in-degree, the total weight of incoming connections to a brain region, emphasizing the importance of measuring weight and directionality of network connections. Brain regions with increased weighted in-degree exhibit rs-fMRI dynamics with reduced variance (correlation to standard deviation, ρ = −0.62), and slower correlation timescales (correlation to relative high frequency power, f ≥ 0.375Hz, ρ = -0.58), relationships that were reproduced in each of the eighteen individual mice that underwent rs-fMRI. Our results indicate that the topology of inter-regional axonal connections of the mouse brain is closely related to the intrinsic, spontaneous dynamics occurring within a region and that variations in the aggregate strength of incoming projections to a region are associated with both the variability and timescales of that region's activity ﬂuctuations.