In this study, we investigate if phase-locking of fast oscillatory activity relies on the anatomical skeleton and if simple computational models informed by structural connectivity can help further to explain missing links in the structure-function relationship. We use diffusion tensor imaging data and alpha band-limited EEG signal recorded in a group of healthy individuals. Our results show that about 23.4% of the variance in empirical networks of resting-state functional connectivity is explained by the underlying white matter architecture. Simulating functional connectivity using a simple computational model based on the structural connectivity can increase the match to 45.4%. In a second step, we use our modeling framework to explore several technical alternatives along the modeling path. First, we find that an augmentation of homotopic connections in the structural connectivity matrix improves the link to functional connectivity while a correction for fiber distance slightly decreases the performance of the model. Second, a more complex computational model based on Kuramoto oscillators leads to a slight improvement of the model fit. Third, we show that the comparison of modeled and empirical functional connectivity at source level is much more specific for the underlying structural connectivity. However, different source reconstruction algorithms gave comparable results. Of note, as the fourth finding, the model fit was much better if zero-phase lag components were preserved in the empirical functional connectome, indicating a considerable amount of functionally relevant synchrony taking place with near zero or zero-phase lag. The combination of the best performing alternatives at each stage in the pipeline results in a model that explains 54.4% of the variance in the empirical EEG functional connectivity. Our study shows that large-scale brain circuits of fast neural network synchrony strongly rely upon the structural connectome and simple computational models of neural activity can explain missing links in the structure-function relationship.