The Fundamental Network Theory research area develops core theoretical frameworks, probabilistic models, and computational methods for understanding the structure, function, and dynamics of complex networks. This includes advancements in theoretical network science via maximum entropy random graphs, models of physical and temporal networks, latent network geometry, graphons and graph limits, topological data analysis, higher-order interactions, graph embedding, and scalable graph mining algorithms. Albeit primarily being of a theoretical nature, research results are often systematically validated against real-world network data across diverse applications, ensuring that theoretical insights translate into practical methodologies for complex networked systems.
Fundamental Network Theory
Featured projects
Higher-order Laplacian renormalization
Renormalization group theory underpins scaling and universality, but its adaptation to networks has focused mainly on pairwise interactions. As polyadic interactions grow in importance, extending these methods to higher-order networks is essential. This study introduces a Laplacian renormalization group scheme for arbitrary higher-order networks, enabled by cross-order Laplacians that model diffusion across hyperedges of any order. This framework reveals order-specific scale invariance, supports coarse-graining, and is validated on synthetic and real higher-order systems.
Center for Complex Particle Systems
The Center for Complex Particle Systems (COMPASS), supported by the National Science Foundation, is a multi-university collaboration advancing a network-science approach to small particles and novel materials. COMPASS develops methodologies for describing particles with complex geometries and internal architectures, enabling their use in modeling and designing next-generation materials. By representing diverse particle shapes—from spheroids to fibers—through graph-based frameworks that capture imperfections and polydispersity, the center aims to engineer complex materials with mission-critical combinations of properties once considered impossible to achieve.
