The supplement materials include the following: 1. A supplement proof.pdf file for the proof of the main results in the paper, 2. A data_generation.py file for the data generation of the simulation study, 3. A hypergraph_fun.py file for various hypergraph community detection algorithms, 4. A simulation.py file for the implementation of the simulation study. The MEDLINE database is publicly available at https://www.nlm.nih.gov/medline/medline_overview.html, and the processed dataset is provided by Dr. Dong Xia. The SPECT dataset is publicly available at https://archive.ics.uci.edu/ml/datasets/spect+heart.