The spectacular rise of money laundering poses a significant challenge to global financial institutions. Traditional machine learning-based anti-money laundering (AML) methods are unable to detect it owing to the increasing complexity of criminal activities, necessitating proposal of innovative methods. In this study, we propose a novel and generic framework for anti-money laundering by hybridizing graph convolutional neural networks (GCN) separately with probabilistic neural networks (PNN), wavelet neural networks (WNN), and radial basis function neural networks (RBFN). We demonstrate their effectiveness on the benchmark Elliptic dataset, which contains over 200,000 bitcoin transactions. All the three shallow networks are chosen based on their proven performance as classifiers. This study contributes significantly to the banking sector by presenting an efficient method for identifying money laundering operations, thereby enhancing the security and integrity of financial institutions and markets. GCN + PNN turned out to be the statistically significant hybrid with a very high F1 score. Finally, the proposed hybrids can be applied to any classification problem in banking, finance, and insurance where graphical data is present.