Graph Theory is a central subject of Discrete Mathematics, important both for theoretical reasons and in view of its wide applicability. It models patterns (and strength) of connections between the components of complex systems. Investigation of very large graphs usually require special mathematical tools.
The most widely known example for very large graphs is the connection structure of the Internet, where various parts differ substantially. Breaking up such large graphs to a small number of more homogeneous and thus more manageable pieces is the core of the PI's current research.
