Brain dynamics are thought to unfold on a network determined by the pattern of axonal connections linking pairs of neuronal elements; the so-called connectome. Prior work has indicated that structural brain connectivity constrains pairwise correlations of brain dynamics ("functional connectivity"), but it is not known whether inter-regional axonal connectivity is related to the intrinsic dynamics of individual brain areas. Here we investigate this relationship 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. For each brain region, we measured degree, betweenness, and clustering coefficient from weighted and unweighted, and directed and undirected versions of the connectome. We then characterized the univariate rs-fMRI dynamics in each brain region by computing 6930 time-series properties using the time-series analysis toolbox, hctsa. After correcting for regional volume variations, strong and robust correlations between structural connectivity properties and rs-fMRI dynamics were found only when edge weights were accounted for, and were associated with variations in the autocorrelation properties of the rs-fMRI signal. The strongest relationships were found for weighted in-degree, which was positively correlated to the autocorrelation of fMRI time series at time lag τ = 34 s (partial Spearman correlation ρ=0.58), as well as a range of related measures such as relative high frequency power (f > 0.4 Hz: ρ=-0.43). Our results indicate that the topology of inter-regional axonal connections of the mouse brain is closely related to intrinsic, spontaneous dynamics such that regions with a greater aggregate strength of incoming projections display longer timescales of activity fluctuations.