Time: 21 November 2018, 1 - 2 pm

Place: B705

### Abstract

An important problem in network modelling is that of generating graphs with a given degree distribution, for instance one that has been observed in an empirical network. We will consider a spatial version of this problem, where the vertices have positions in continuum space. How should one go about to obtain a random graph with a given distribution for the degrees on such a vertex set? When is the resulting graph well connected in the sense that it contains an infinite component? One natural way of constructing the graph is based on the Gale-Shapley stable marriage, and the component structure has then turned out to be surprisingly difficult to understand. I will describe some existing results - including a "statistical" proof of the existence of an infinite component - and a number of open problems.