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In shaping the Internet of Money, the application of blockchain and distributed ledger technologies (DLTs) to the financial sector triggered regulatory concerns. Notably, while the user anonymity enabled in this field may safeguard privacy and data protection, the lack of identifiability hinders accountability and challenges the fight against money laundering and the financing of terrorism and proliferation (AML/CFT). As law enforcement agencies and the private sector apply forensics to track crypto transfers across ecosystems that are socio-technical in nature, this paper focuses on the growing relevance of these techniques in a domain where their deployment impacts the traits and evolution of the sphere. In particular, this work offers contextualized insights into the application of methods of machine learning and transaction graph analysis. Namely, it analyzes a real-world dataset of Bitcoin transactions represented as a directed graph network through various techniques. The modeling of blockchain transactions as a complex network suggests that the use of graph-based data analysis methods can help classify transactions and identify illicit ones. Indeed, this work shows that the neural network types known as Graph Convolutional Networks (GCN) and Graph Attention Networks (GAT) are a promising AML/CFT solution. Notably, in this scenario GCN outperform other classic approaches and GAT are applied for the first time to detect anomalies in Bitcoin. Ultimately, the paper upholds the value of public–private synergies to devise forensic strategies conscious of the spirit of explainability and data openness.