Do the rich get richer? Mathematical models for real-world networks

Abstract

Networks can be found all around us. From the friendships we form, both in person and online, to the websites we visit on the Internet, and the telephones we use to send messages and make phone calls. Understanding the behavior and structure of these networks can be a difficult task. Mathematicians use models of such complex real-world networks to provide novel insights from an analytical point of view. In this snapshot, we take a look at why mathematics can be useful in understanding networks and discuss interesting recent developments in the study of a popular class of models known as preferential attachment models, which try to explain why the rich get richer.