In this paper, we introduce a post-hoc and local explainable AI method tailored for Knowledge Graph Embedding (KGE) models. These models are essential to Knowledge Graph Completion yet criticized for their black-box nature. Despite their success in capturing the semantics of knowledge graphs through high-dimensional latent representations, their inherent complexity poses substantial challenges to explainability. While existing methods like Kelpie use resource-intensive perturbation to explain KGE models, our approach directly decodes the latent representations encoded by KGE models, leveraging the smoothness of the embeddings, which follows the principle that similar embeddings reflect similar behaviours within the Knowledge Graph, meaning that nodes are similarly embedded because their graph neighbourhood looks similar. This principle is commonly referred to as smoothness. By identifying symbolic structures, in the form of triples, within the subgraph neighborhoods of similarly embedded entities, our method identifies the statistical regularities on which the models rely and translates these insights into human-understandable symbolic rules and facts. This bridges the gap between the abstract representations of KGE models and their predictive outputs, providing clear and interpretable insights. The contributions include a novel post-hoc and local explainable AI method for KGE models, which provides immediate and faithful explanations without retraining, thereby facilitating real-time application on large-scale knowledge graphs. The method’s flexibility enables the generation of rule-based, instance-based, and analogy-based explanations, meeting diverse user needs. Extensive evaluations show the effectiveness of our approach in delivering faithful and well-localized explanations, enhancing the transparency and trustworthiness of KGE models.