We present a model to describe spatial random graphs, exploiting the so called "graphex" setting embedded in a Bayesian nonparametric framework, that allows for flexibility and interpretable parameters. We provide a number of asymptotic results, namely that the model is able describe both sparse and dense networks (with various levels of sparsity), is equipped with positive global and local clustering coefficients and can have a power-law degree distribution whose exponent is easily tuned. We offer a way to perform posterior inference through an MCMC algorithm. We show the results of the estimation obtained on simulated and real data from airports connections. Finally, we discuss how our proposal relates to other spatial network models in the literature.