Emotion recognition is essential in the diagnosis and rehabilitation of various mental diseases. In the last decade, electroencephalogram (EEG)-based emotion recognition has been intensively investigated due to its prominative accuracy and reliability, and graph convolutional network (GCN) has become a mainstream model to decode emotions from EEG signals. However, the electrode relationship, especially long-range electrode dependencies across the scalp, may be underutilized by GCNs, although such relationships have been proven to be important in emotion recognition. The small receptive field makes shallow GCNs only aggregate local nodes. On the other hand, stacking too many layers leads to over-smoothing. To solve these problems, we propose the pyramidal graph convolutional network (PGCN), which aggregates features at three levels: local, mesoscopic, and global. First, we construct a vanilla GCN based on the 3D topological relationships of electrodes, which is used to integrate two-order local features; Second, we construct several mesoscopic brain regions based on priori knowledge and employ mesoscopic attention to sequentially calculate the virtual mesoscopic centers to focus on the functional connections of mesoscopic brain regions; Finally, we fuse the node features and their 3D positions to construct a numerical relationship adjacency matrix to integrate structural and functional connections from the global perspective. Experimental results on three public datasets indicate that PGCN enhances the relationship modelling across the scalp and achieves state-of-the-art performance in both subject-dependent and subject-independent scenarios. Meanwhile, PGCN makes an effective trade-off between enhancing network depth and receptive fields while suppressing the ensuing over-smoothing. Our codes are publicly accessible at https://github.com/Jinminbox/PGCN.