Prof Ton Coolen, King's College London (profile)
Title: Counting and generating tailored random graphs
Abstract: Ensembles of tailored random graphs with controlled topological properties are a natural language for describing real-world networks. They suggest precise definitions of structural features, they allow us to classify networks and obtain precise measures of complexity and (dis)similarity, they provide ‘null models’ for hypothesis testing, and they serve as efficient proxies for real networks in process modelling. In this seminar I explain the connection between networks and tailored random graphs, show how this connection can be exploited using tools from statistical mechanics and information theory, and I discuss exact algorithms for generating such graphs numerically. I end with a description of ongoing research and open problems, such as the analysis of ensembles of graphs with many short loops.