One of the most serious and unexpected risks to contemporary cybersecurity is zero-day vulnerabilities. Before updates or fixes are provided, attackers can use software defects to construct weapons that no one is aware of. Static severity indicators and rule-based scoring systems are two prevalent ways to prioritize vulnerabilities. However, neither technique accurately forecasts which vulnerabilities would be used most frequently in the field. This study suggests a new method for discovering zero-day vulnerabilities utilizing graph-based deep learning on vulnerability and threat intelligence data. We construct a diversified cybersecurity knowledge graph that demonstrates how vulnerabilities (CVE), weaknesses (CWE), software products, exploit data, threat actors, and intelligence indicators are all linked. In order to find connections and hints that conventional flat-feature models miss, the suggested approach makes use of Graph Neural Networks (GNNs), specifically Graph Convolutional Networks (GCN) and Graph Attention Networks (GAT). The technique enhances forecasts by leveraging temporal data, publishing trends, semantic embeddings of vulnerability descriptions, and intelligence-driven risk signals. The graph-based approach outperforms baseline machine learning algorithms in terms of AUC-ROC, F1-score, and early risk detection using historical vulnerability datasets. Statistics demonstrate that identifying relationships is an effective method to prevent cyberattacks. It supports security teams in selecting which patching options to utilize initially and how to best focus their resources. In situations where threats are constantly changing, this study suggests a scalable and flexible substitute for predictive cybersecurity analytics.