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Independent brain regions in neuroanatomy achieve a specific function through connections. As one of the significant morphological features of the cerebral cortex, previous studies have found significant differences in the structure and function of the cerebral gyri and sulci, which provides a basis for us to study the functional connectivity differences between these two anatomic parts. Previous studies using fully connected functional connectivity (FC) and structural connectivity (SC) matrices found significant differences in the perspective of region or connection in gyri and sulci. However, a clear issue is that previous studies have only analyzed the differences through either FC or SC, without effectively integrating both. Meanwhile, another nonnegligible issue is that the subcortical areas, involved in various tasks, have not been systematically explored with cortical regions. Due to the strong coupling between FC and SC, we use SC-informed FC to systematically explore the functional characteristics of gyri/sulci and subcortical regions by combining deep learning method with magnetic resonance imaging (MRI) technology. Specifically, we use graph attention network (GAT) to explore the important connections in the SC-informed FC through the Human Connectome Project (HCP) dataset. With high classification results of above 99%, we have successfully discovered important connections under different tasks. We have successfully explored the importance of different types of connections. In low threshold, gyri-gyri are the most important connections. With the threshold increasing, sub-sub become the most important. Gyri have a higher importance in functional connectivity than sulci. In the seven task states, these connections are mainly distributed among the front, subcortical, and occipital. This study provides a novel way to explore the characteristics of functional connectivity at the whole brain scale.