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.
Our focus
Network Geometry
Latent hyperbolic geometry naturally explains the heterogeneous degree distributions and strong clustering observed in many real networks. We want to understand how latent geometry shapes topological properties of evolving networks and to devise efficient methods to uncover latent geometries of real networks. Hyperbolic methods have proven to be extremely useful in machine learning and data mining dealing with heterogeneous data in a variety of applications including developing better recommendation systems, estimating biases associated with incomplete data, identification of disease mechanisms, understanding human communication patterns, and signaling in the brain.
Quantum Gravity
Causal set theory is an approach to quantum gravity that proposes that spacetime at the Planck scale consists of nodes (spacetime quanta) connected by causal relationships, forming a network structure. Our research shows that this causal network representing our accelerating universe exhibits scale-free properties with strong clustering, resembling many real-world networks. This connection suggests that equations similar to Einstein equations might govern complex network evolution, with significant implications for cosmology and quantum gravity.
Graph Mining
Real-world networks, including social systems and biological interactions, are highly complex and intricate. They contain rich patterns, are often noisy or incomplete, and often display irregular structures that challenge traditional analytical methods. Our research focuses on machine learning algorithms for extracting structure, meaning, and reliable information from these large-scale systems. The focus is on developing learning systems that maintain robustness to noise, while also offering interpretability in their predictions. The work advances graph embeddings, graph distance measures, and uncertainty-aware representations, establishing principled methodologies for comparing, compressing, and analyzing graphs at scale.


