'Networks: the Science of Interconnected Systems' Keith Levin, 04/20/2022

What do social media, food webs, brains and the highway system all have in common? They are described by networks-- systems of interacting entities, pairs of whom form relations. For example, a social network like Facebook or Twitter can be described by a collection of users, and pairs of these users form friendship or following relationships. In ecology, pairs of species engage in predator-prey relationships. The structure of the brain can be described by which pairs of neurons form synapses with one another. The US highway system can be described by pairs of interchanges connected by roadway.

In the past fifty years, scientists in a wide range of disciplines have come to recognize the importance of networks in describing a wide range of systems in our world, and the field of network science has emerged to provide the tools necessary to investigate the properties of these systems. In this talk, I will give an overview of this exciting and still (comparatively) new field and discuss some of the exciting work in this area currently happening here at UW-Madison. We will begin with a whirlwind tour of some basic discoveries in network science to date, including the "six degrees of separation" phenomenon (made famous by the game "six degrees of Kevin Bacon"). Finally, we will discuss some of the work done by my group and by some of my colleagues here at UW-Madison developing statistical methods for rigorously describing and comparing the basic properties of networks.