Analysis and Probability seminar

An intersection graph is constructed by assigning each vertex a subset of some auxiliary set and then connecting two vertices if their subsets intersect. The model type has been popular in network modeling to describe networks arising from bipartite structures, for instance individuals who are connected if they share a social group, communication units connected via cell towers and scientists related through joint papers. We study a spatial version of the model type where both the vertex set and the auxiliary set are represented by Poisson processes on R^d, giving rise to a variation of the random connection model. Our results concern local quantities (e.g. the degree distribution) and percolation properties of the resulting graph.