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Understanding the relationship between the dynamics of neural processes and the anatomical substrate of the brain is a central question in neuroscience. On the one hand, modern neuroimaging technologies, such as diffusion tensor imaging, can be used to construct structural graphs representing the architecture of white matter streamlines linking cortical and subcortical structures. On the other hand, temporal patterns of neural activity can be used to construct functional graphs representing temporal correlations between brain regions. Although some studies provide evidence that whole-brain functional connectivity is shaped by the underlying anatomy, the observed relationship between function and structure is weak, and the rules by which anatomy constrains brain dynamics remain elusive. In this article, we introduce a methodology to predict with high accuracy the functional connectivity of a subject at rest from his or her structural graph. Using our methodology, we are able to systematically unveil the role of structural paths in the formation of functional correlations. Furthermore, in our empirical evaluations, we observe that the eigen-modes of the predicted functional connectivity are aligned with activity patterns associated with different cognitive systems. Our work offers the potential to infer properties of brain dynamics in clinical or developmental populations with low tolerance for functional neuroimaging.