Daniel Král: lecture „Models of large networks“
Models of large networks
A graph is a mathematical model of a network of nodes, which can be, e.g., a computer network or a social network. Problems concerning networks of enormous sizes, which more and more often arise in computer science applications, led to a need to find new mathematical tools to represent and analyze large graphs. The theory of graph limits, whose foundations were laid at Microsoft Research about a decade ago, has responded to these challenges by developing analytic models of large graphs.
We will provide a brief self-contained introduction to the theory of graph limits, which will be followed by the exposition of the most major lines of research. We will conclude with presenting solutions of some of the most significant open problems in the area.