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Joint named entity recognition and relation extraction is an essential natural language processing task that aims to identify entities and extract the corresponding relations in an end-to-end manner. At present, compared with the named entity recognition task, the relation extraction task performs poorly on complex text. To solve this problem, we proposed a novel joint model named extracting Entity-Relations viaImproved Graph Attention networks (ERIGAT), which enhances the ability of the relation extraction task. In our proposed model, we introduced the graph attention network to extract entities and relations after graph embedding based on constructing symmetry relations. To mitigate the over-smoothing problem of graph convolutional networks, inspired by matrix factorization, we improved the graph attention network by designing a new multi-head attention mechanism and sharing attention parameters. To enhance the model robustness, we adopted the adversarial training to generate adversarial samples for training by adding tiny perturbations. Comparing with typical baseline models, we comprehensively evaluated our model by conducting experiments on an open domain dataset (CoNLL04) and a medical domain dataset (ADE). The experimental results demonstrate the effectiveness of ERIGAT in extracting entity and relation information.