In this paper, we propose a novel graph-based methodology to evaluate the functional correctness of SQL generation. Conventional metrics for assessing SQL code generation, such as matching-based and execution-based methods (e.g., exact set match and execution accuracy), are subject to two primary limitations. Firstly, the former fails to effectively assess functional correctness, as different SQL queries may possess identical functionalities. Secondly, the latter is susceptible to producing false positive samples in evaluations. Our proposed evaluation method, \texttt{FuncEvalGMN}, does not depend on the sufficient preparation of the test data, and it enables precise testing of the functional correctness of the code. Firstly, we parse SQL using a relational operator tree (ROT) called \textit{Relnode}, which contains rich semantic information from the perspective of logical execution.Then, we introduce a GNN-based approach for predicting the functional correctness of generated SQL. This approach incorporates global positional embeddings to address the limitations with the loss of topological information in conventional graph matching frameworks. As an auxiliary contribution, we propose a rule-based matching algorithm, Relnode Partial Matching (\texttt{RelPM}) as a baseline. Finally, we contribute a dataset, \texttt{Pair-Aug-Spider} with a training set and two testing sets, each comprising pairs of SQL codes to simulate various SQL code evaluation scenarios. The training set and one testing dataset focus on code generation using large language models (LLMs), while the other emphasizes SQL equivalence rewriting.