We consider a population of N interacting neurons, represented by a multivariate Hawkes process : the firing rate of each neuron depends on the history of the connected neurons. Contrary to the mean-field framework where the interaction occurs on the complete graph, the connectivity between particles is given by a random possibly diluted and inhomogeneous graphs where the probability of presence of each edge depends on the spatial position of its vertices. We address the well-posedness of this system and the behaviour as N → ∞. A crucial issue will be to understand how spatial inhomogeneity influences the large time behaviour of the system.