This paper presents a network science approach to investigate a health information dataset, the Sexual Acquisition and Transmission of HIV Cooperative Agreement Program (SATHCAP), to uncover hidden relationships that can be used to suggest targeted health interventions. From the data, four key target variables are chosen: HIV status, injecting drug use, homelessness, and insurance status. These target variables are converted to a graph format using four separate graph inference techniques: graphical lasso, Meinshausen Bühlmann (MB), k-Nearest Neighbors (kNN), and correlation thresholding (CT). The graphs are then clustered using four clustering methods: Louvain, Leiden, and NBR-Clust with VAT and integrity. Promising clusters are chosen using internal evaluation measures and are visualized and analyzed to identify marker attributes and key relationships. The kNN and CT inference methods are shown to give useful results when combined with NBR-Clust clustering. Examples of cluster analysis indicate that the methodology produces results that will be relevant to the public health community.