Dr Mason Porter, Mathematical Institute, University of Oxford

Abstract: Whether they come from the realm of biology, physics, technology, or the social sciences, real-world networks are typically neither fully ordered nor fully random but instead share properties with both structured and random graphs. Such "complex networks" tend to live in small worlds (their diameters are small), yet most of them can also be decomposed into interconnected modules or "communities." In this talk, I'll discuss some research that my collaborators and I have done using network models to rank United States college football teams and uncover the community structure of the United States Congress (in terms of both committee assignments and legislation cosponsorship). I will also show how the concept of modularity can be used to examine partisan polarization and realignments in voting and legislation networks. I will end with a brief discussion of some current projects.