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Title: Sparse spatial random graphs Authors:  Francesca Panero - University of Oxford (United Kingdom) [presenting]
Francois Caron - University of Oxford (United Kingdom)
Judith Rousseau - University of Oxford (United Kingdom)
Abstract: A model is presented to describe spatial random graphs, exploiting the graphex setting in a Bayesian nonparametric framework that allows us flexibility and interpretable parameters. We provide several asymptotic results, namely that the model can describe both sparse and dense networks, is equipped with positive global and local clustering coefficients and can have power-law or double power-law degree distributions whose exponents are easily tuned. We also offer an efficient way to simulate from the model and perform posterior inference through an MCMC algorithm, and we show the results obtained on simulated and real data. Finally, we show that our proposal generalises several other spatial models, for example, the homogeneous random geometric graph and the hyperbolic random graph, and explain the relations with other proposals such as the scale-free percolation and the sparse latent space models.