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
Incorporating uncertainty in graph embeddings through REGE
Graph machine learning models face uncertainties from noisy data, model output, and adversarial attacks. We introduce Radius Enhanced Graph Embeddings (REGE), a method that encodes uncertainty into embeddings using radius values. REGE leverages curriculum learning to address data uncertainty and conformal learning for output uncertainty. Experiments show that REGE improves robustness under adversarial attacks, achieving an average 1.5% accuracy gain compared to state-of-the-art approaches.
Navigation in Networks
Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of distributed computation. However, in many real networks nodes communicate efficiently even without such global intelligence. We have shown that latent network geometry can guide the routing process, leading to efficient communication without global knowledge of the network structure in arbitrarily large networks as soon as their structure is similar to the structure of many large real networks. Therefore neuronal firing in the brain, signaling pathways in gene-regulatory networks, routing in the Internet, and search patterns in social networks may all be driven by properties of latent geometric spaces underlying these systems.
Higher-order contagion
Beyond simple pairwise connections, many real-world processes involve group interactions. We study how contagion unfolds in higher-order networks, such as hypergraphs and simplicial complexes, where the spread of diseases or ideas depends on collective behaviors within groups rather than just pair interactions. This approach reveals new mechanisms that shape how information and diseases propagate.
