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 Nervous systems are complex networks with a topology governed by the pattern of axonal connections linking distinct neural elements. Highly connected and topologically central elements are thought to play an important role in meditating the flow of information across different parts of the system. However, it is unclear how the intrinsic dynamics of a given neuronal population relates to the pattern of connections that population shares with other network nodes. In this work, we show that there is a strong and robust correlation between the structural connectivity properties of a brain region and its blood-oxygenation-level-dependent (BOLD) signal dynamics, as measured with resting-state fMRI (rs-fMRI) in the mouse. The strongest relationship is found with the total weight of incoming connections to a brain region, or weighted in-degree, which is associated with longer dynamical timescales of rs-fMRI dynamics. Our findings indicate that structural connection weights convey important information about neural activity, and that the aggregate strength of incoming projections to a brain region is closely related to its BOLD signal dynamics.