Title: Improving Abstractive Dialogue Summarization with Conversational Structure and Factual Knowledge. Abstract: Recently, people have been paying more attention to the abstractive dialogue summarization task. Compared with news text, the information flows of the dialogue exchange between at least two interlocutors, which leads to the necessity of capturing long-distance cross-sentence relations. In addition, the generated summaries commonly suffer from fake facts because the key elements of dialogues often scatter in multiple utterances. However, the existing sequence-to-sequence models are difficult to address these issues. Therefore, it is necessary for researchers to explore the implicit conversational structure to ensure the richness and faithfulness of generated contents. In this paper, we present a Knowledge Graph Enhanced Dual-Copy network (KGEDC), a novel framework for abstractive dialogue summarization with conversational structure and factual knowledge. We use a sequence encoder to draw local features and a graph encoder to integrate global features via the sparse relational graph self-attention network, complementing each other. Besides, a dual-copy mechanism is also designed in decoding process to force the generation conditioned on both the source text and extracted factual knowledge. The experimental results show that our method produces significantly higher ROUGE scores than most of the baselines on both SAMSum corpus and Automobile Master corpus. Human judges further evaluate that outputs of our model contain more richer and faithful information.