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Financial institutions operate within densely interconnected networks of accounts, transactions, and counterparties, making them highly susceptible to systemic cyber threats that propagate across entities in ways that conventional, feature-isolated machine-learning models cannot adequately model. This paper presents FIN-GNN, a unified framework that applies Graph Neural Networks (GNNs) to the problem of cyber threat prediction in financial networks. We model financial ecosystems as heterogeneous, temporal graphs in which nodes represent accounts, institutions, or transactions, and directed edges encode monetary flows, ownership, or trust relationships. FIN-GNN integrates a multi-relational message-passing layer with temporal evolution via recurrent GNN components to detect both static anomalies and dynamically propagating attack patterns. We evaluate the proposed framework on two publicly available benchmarks the Elliptic Bitcoin Transaction dataset and the IEEE-CIS Fraud Detection dataset, comparing it against logistic regression, random forests, XGBoost, and three canonical GNN baselines (GCN, GAT, GraphSAGE). FIN-GNN achieves an AUC-ROC of 0.94 and an F1-score of 0.89 on the primary benchmark, outperforming the strongest non-graph baseline by 8–12 percentage points across all metrics. Our results demonstrate that relational and temporal inductive biases embedded in GNNs are essential for capturing networked threat propagation. This work contributes (i) a principled graph-theoretic formulation of financial cyber risk, (ii) the FIN-GNN architecture with ablation analysis, and (iii) a discussion of deployment considerations for risk-management practitioners.