The poultry meat supply chain is complex and therefore vulnerable to many potential contaminations that may occur. To ensure a safe product for the consumer, an efficient traceability system is required that enables a quick and efficient identification of the potential sources of contamination and proper implementation of mitigation actions. In this study, we explored the use of graph theory to construct a food supply chain network for the broiler meat supply chain in the Netherlands and tested it as a traceability system. To build the graph, we first identified the main actors in the supply chain such as broiler breeder farms, broiler farms, slaughterhouses, processors, and retailers. The capacity data of each supply chain actor, represented by its production or trade volumes, were gathered from various sources. The trade relationships between the supply chain actors were collected and the missing relationships were estimated using the gravity model. Once the network was modeled, we computed degree centrality and betweenness centrality to identify critical nodes in the network. In addition, we computed trade density to get insight into the complexity of sub-networks. We identified the critical nodes at each stage of the Dutch broiler meat supply chain and verified our results with a domain expert of the Dutch poultry industry and literature. The results showed that processors with own slaughtering facility were the most critical points in the broiler meat supply chain.