In the talk I will present the class of random graphs based on exchangeable random measures. Such class allows to model networks which are either dense or sparse, that is where the number of edges scales subquadratically with the number of nodes. For some values of its parameters, it generates scale-free networks with power-law exponent between 1 and 2. I will present the general construction, a representation theorem for such construction due to Kallenberg, and discuss its sparsity, power-law and transitivity properties. Then I will introduce a specific model within this framework that allows to capture sparsity/heavy-tailed degree distributions as well as latent overlapping community structure, and a Markov chain Monte Carlo algorithm for posterior inference with this model. Experiments are done on two real-world networks, showing the usefulness of the approach for network analysis.

Based on joint work with Emily Fox, Adrien Todeschini, Xenia Miscouridou, Judith Rousseau, Francesca Panero.

**Date**: 11 November 2019, 12:00 (Monday, 5th week, Michaelmas 2019)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Details**: L4**Speaker**: François Caron (Department of Statistics, University of Oxford)**Organising department**: Department of Statistics**Organisers**: Christina Goldschmidt (Department of Statistics, University of Oxford), James Martin (Department of Statistics, University of Oxford)**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Public- Editor: Christina Goldschmidt