Creating human-like large language model (LLM) agents is crucial for faithful social simulation. Having LLMs role-play based on demographic information sometimes improves human likeness but often does not. This study assessed whether LLM alignment with human behavior can be improved by integrating information from empirically-derived human belief networks. Using data from a human survey, we estimated a belief network encompassing 64 topics loading on nine non-overlapping latent factors. We then seeded LLM-based agents with an opinion on one topic, and assessed the alignment of its expressed opinions on remaining test topics with corresponding human data. Role-playing based on demographic information alone did not align LLM and human opinions, but seeding the agent with a single belief greatly improved alignment for topics related in the belief network, and not for topics outside the network. These results suggest a novel path for human-LLM belief alignment in work seeking to simulate and understand patterns of belief distributions in society.