Kernel-based random graphs (KBRGs) are a class of random graph models that account for inhomogeneity among  vertices. We consider KBRGs on a discrete d-dimensional torus. Conditionally on an i.i.d. sequence of Pareto weights, we connect any two points independently with a probability that increases in the points' weights and decreases in the distance between the points. We focus on the adjacency matrix of this graph and study its empirical spectral distribution. In the dense regime we show that a limiting distribution with non-trivial second moment exists as the size of the torus goes to infinity, and that the corresponding measure is absolutely continuous with respect to the Lebesgue measure. We also derive a fixed-point equation for its Stieltjes transform in an appropriate Banach space. In the case corresponding to so-called scale-free percolation we can explicitly describe the limiting measure and study its tail. Based on a joint work with R. S. Hazra, N. Malhotra and M. Salvi.