Mark Newman
MATHEMATICS COLLOQUIUM
Speaker: Mark Newman Abstract. Many systems of scientific interest take the form of networks, including the Internet, the World Wide Web, social networks, metabolic networks, food webs, and others. To help us understand the structure of these networks and the effect that structure has on function, we build network models, typically defined as probability distributions over possible network topologies. The first and best-studied such model is the random graph of Erdos and Renyi, but the random graph turns out to be a poor guide to the properties of real networks for a number of reasons. In this talk I will discuss some of the experimental data on the topology of real-world networks and then present a selection of network models of increasing sophistication and show how, despite their complexity, many of these models can be solved exactly for a range of interesting properties, at least in the limit of large network size. |