With the increasing use of RDF graphs, storing and querying such data using SPARQL remains a critical problem. Current mainstream solutions rely on cloud-based data management architectures, but often suffer from performance bottlenecks in environments with limited bandwidth or high system load. To address this issue, this paper explores for the first time the integration of edge computing to move graph data storage and processing to edge environments, thereby improving query performance. This approach requires offloading query processing to edge servers, which involves addressing two challenges: data localization and network scheduling. First, the data localization challenge lies in computing the subgraphs maintained on edge servers to quickly identify the servers that can handle specific queries. To address this challenge, we introduce a new concept of pattern-induced subgraphs. Second, the network scheduling challenge involves efficiently assigning queries to edge and cloud servers to optimize overall system performance. We tackle this by constructing a overall system model that jointly captures data distribution, query characteristics, network communication, and computational resources. Accordingly, we further propose a joint formulation of query assignment and computational resource allocation, modeling it as a Mixed Integer Nonlinear Programming (MINLP) problem and solve this problem using a modified branch-and-bound algorithm. Experimental results on real datasets under a real cloud platform demonstrate that our proposed method outperforms the state-of-the-art baseline methods in terms of efficiency. The codes are available on GitHub