Abstract: Efficient structure encoding for graphs with labeled edges is an important yet challenging point in many graph-based models. This work focuses on AMR-to-text generation -- A graph-to-sequence task aiming to recover natural language from Abstract Meaning Representations (AMR). Existing graph-to-sequence approaches generally utilize graph neural networks as their encoders, which have two limitations: 1) The message propagation process in AMR graphs is only guided by the first-order adjacency information. 2) The relationships between labeled edges are not fully considered. In this work, we propose a novel graph encoding framework which can effectively explore the edge relations. We also adopt graph attention networks with higher-order neighborhood information to encode the rich structure in AMR graphs. Experiment results show that our approach obtains new state-of-the-art performance on English AMR benchmark datasets. The ablation analyses also demonstrate that both edge relations and higher-order information are beneficial to graph-to-sequence modeling.