Recent advancements in large language models have demonstrated significant potential in the automated construction of knowledge graphs from unstructured text. This paper builds upon our previous work [16], which evaluated various models using metrics like precision, recall, F1 score, triple matching, and graph matching, and introduces a refined approach to address the critical issues of hallucination and omission. We propose an enhanced evaluation framework incorporating BERTScore for graph similarity, setting a practical threshold of 95% for graph matching. Our experiments focus on the Mistral model, comparing its original and fine-tuned versions in zero-shot and few-shot settings. We further extend our experiments using examples from the KELM-sub training dataset, illustrating that the fine-tuned model significantly improves knowledge graph construction accuracy while reducing the exact hallucination and omission. However, our findings also reveal that the fine-tuned models perform worse in generalization tasks on the KELM-sub dataset. This study underscores the importance of comprehensive evaluation metrics in advancing the state-of-the-art in knowledge graph construction from textual data.