Supply chain networks are critical to the operational efficiency of industries, yet their increasing complexity presents significant challenges in mapping relationships and identifying the roles of various entities. Traditional methods for constructing supply chain networks rely heavily on structured datasets and manual data collection, limiting their scope and efficiency. In contrast, recent advancements in Natural Language Processing (NLP) and large language models (LLMs) offer new opportunities for discovering and analyzing supply chain networks using unstructured text data. This paper proposes a novel approach that leverages LLMs to extract and process raw textual information from publicly available sources to construct a comprehensive supply chain graph. We focus on the civil engineering sector as a case study, demonstrating how LLMs can uncover hidden relationships among companies, projects, and other entities. Additionally, we fine-tune an LLM to classify entities within the supply chain graph, providing detailed insights into their roles and relationships. The results show that domain-specific fine-tuning improves classification accuracy, highlighting the potential of LLMs for industry-specific supply chain analysis. Our contributions include the development of a supply chain graph for the civil engineering sector, as well as a fine-tuned LLM model that enhances entity classification and understanding of supply chain networks.