Connectivity between different brain regions is one of the most important properties for classification of brain signals including electroencephalography (EEG). However, how to define the connectivity structure for a given task is still an open problem, because there is no ground truth about how the connectivity structure should be in order to maximize the performance. In this paper, we propose an end-to-end neural network model for EEG classification, which can extract an appropriate multi-layer graph structure and signal features directly from a set of raw EEG signals and perform classification. Experimental results demonstrate that our method yields improved performance in comparison to the existing approaches where manually defined connectivity structures and signal features are used. Furthermore, we show that the graph structure extraction process is reliable in terms of consistency, and the learned graph structures make much sense in the neuroscientific viewpoint.