Code clone detection is a fundamental task in software engineering that underpins refactoring, debugging, plagiarism detection, and vulnerability analysis. Existing methods often rely on singular representations such as abstract syntax trees (ASTs), control flow graphs (CFGs), and data flow graphs (DFGs), which capture only partial aspects of code semantics. Hybrid approaches have emerged, but their fusion strategies are typically handcrafted and ineffective. In this study, we propose MAGNET, a multi-graph attentional framework that jointly leverages AST, CFG, and DFG representations to capture syntactic and semantic features of source code. MAGNET integrates residual graph neural networks with node-level self-attention to learn both local and long-range dependencies, introduces a gated cross-attention mechanism for fine-grained inter-graph interactions, and employs Set2Set pooling to fuse multi-graph embeddings into unified program-level representations. Extensive experiments on BigCloneBench and Google Code Jam demonstrate that MAGNET achieves state-of-the-art performance with an overall F1 score of 96.5\% and 99.2\% on the two datasets, respectively. Ablation studies confirm the critical contributions of multi-graph fusion and each attentional component. Our code is available at https://github.com/ZixianReid/Multigraph_match