Knowledge graphs (KGs) are vital for knowledge-intensive tasks and have shown promise in reducing hallucinations in large language models (LLMs). However, constructing high-quality KGs remains difficult, requiring accurate information extraction and structured representations that support interpretability and downstream utility. Existing LLM-based approaches often focus narrowly on entity and relation extraction, limiting coverage to sentence-level contexts or relying on predefined schemas. We propose a hierarchical extraction framework that organizes information at multiple levels, enabling the creation of semantically rich and well-structured KGs. Using state-of-the-art LLMs, we extract and construct knowledge graphs and evaluate them comprehensively from both structural and semantic perspectives. Our results highlight the strengths and shortcomings of current LLMs in KG construction and identify key challenges for future work. To advance research in this area, we also release a curated dataset of LLM-generated KGs derived from research papers on children's mental well-being. This resource aims to foster more transparent, reliable, and impactful applications in high-stakes domains such as healthcare.