Credit Default Swap (CDS) spreads exhibit network effects due to firms' default interdependence. This paper employs Graph Neural Networks (GNNs) to predict CDS spreads by modeling firms as nodes and idiosyncratic volatility spillover measures as directed edges. GNNs capture inter-firm network dynamics, improving prediction accuracy by over 50% compared to traditional models without edge features. We enhance the GNN with node- and edge-attention layers, identifying key nodes (e.g., manufacturing and intermediary firms) and edges (e.g., connections between intermediary, retail trade, or information firms and other firms) as critical to CDS spread prediction.