Percolation phase transition in weight-dependent random connection models

Abstract We investigate spatial random graphs defined on the points of a Poisson process in d -dimensional space, which combine scale-free degree distributions and long-range effects. Every point is assigned an independent weight. Given weight position points, we form edge between any pair independently with probability depending two weights their distance. Preference given to short edges connections vertices large weights. characterize parameter regime where there non-trivial percolation phase transition show that it depends not only power-law exponent distribution but also geometric model parameter. apply this result robustness age-based preferential attachment networks.