This $350,000 National Science Foundation project grant supports statistical modeling research for complex networks at the University of Michigan from September 2022 through August 2025. Funded through the NSF's Mathematical and Physical Sciences program (CFDA 47.049), the award aims to develop new statistical methodologies and theory to incorporate higher-order structures into network modeling. Specifically, the investigators will study leveraging subgraphs and other higher-order structures to improve community detection methods for networks with dependent edges; develop latent space models accommodating balance theory for signed networks; and create new latent space models for polyadic relations involving more than two nodes simultaneously. In addition to advancing scientific knowledge, the project is expected to contribute to fields including biology, computer science, healthcare, engineering, medicine, physics, psychology and sociology.