Sponsored search ads appear next to search results when people look for products and services on search engines. In recent years, they have become one of the most lucrative channels for marketing. As the fundamental basis of search ads, relevance modeling has attracted increasing attention due to the significant research challenges and tremendous practical value. Most existing approaches solely rely on the semantic information in the input query-ad pair, while the pure semantic information in the short ads data is not sufficient to fully identify user's search intents. Our motivation lies in incorporating the tremendous amount of unsupervised user behavior data from the historical search logs as the complementary graph to facilitate relevance modeling. In this paper, we extensively investigate how to naturally fuse the semantic textual information with the user behavior graph, and further propose three novel AdsGNN models to aggregate topological neighborhood from the perspectives of nodes, edges and tokens. Furthermore, two critical but rarely investigated problems, domain-specific pre-training and long-tail ads matching, are studied thoroughly. Empirically, we evaluate the AdsGNN models over the large industry dataset, and the experimental results of online/offline tests consistently demonstrate the superiority of our proposal.