Abstract: Event-event temporal relation extraction aims to extract the temporal order between a pair of event mentions, which is usually used to construct temporal event graphs. However, event graphs generated by existing methods are usually globally inconsistent (event graphs containing cycles), semantically irrelevant (two unrelated events having temporal links), and context unaware (neglecting neighborhood information of an event node). In this paper, we propose a novel event-event temporal relation extraction method to address these limitations. Our model combines a pretrained language model and a graph neural network to output event embeddings, which captures the contextual information of event graphs. Moreover, to achieve global consistency and semantic relevance, (1) event temporal order should be in accordance with the norm of their embeddings, and (2) two events have temporal relation only if their embeddings are close enough. Experimental results on a real-world event dataset demonstrate that our method achieves state-of-the-art performance and generates high-quality event graphs.