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Various relations existing in Electroencephalogram (EEG) data are significant for EEG feature representation. Thus, studies on the graph-based method focus on extracting relevancy between EEG channels. The shortcoming of existing graph studies is that they only consider a single relationship of EEG electrodes, which results an incomprehensive representation of EEG data and relatively low accuracy of emotion recognition. In this paper, we propose a fusion graph convolutional network (FGCN) to extract various relations existing in EEG data and fuse these extracted relations to represent EEG data more comprehensively for emotion recognition. First, the FGCN mines brain connection features on topology, causality, and function. Then, we propose a local fusion strategy to fuse these three graphs to fully utilize the valuable channels with strong topological, causal, and functional relations. Finally, the graph convolutional neural network is adopted to represent EEG data for emotion recognition better. Experiments on SEED and SEED-IV demonstrate that fusing different relation graphs are effective for improving the ability in emotion recognition. Furthermore, the emotion recognition accuracy of 3-class and 4-class is higher than that of other state-of-the-art methods.