  In this article, we study the large-population limit of interacting particle
systems posed on weighted random graphs. In that aim, we introduce a general
framework for the construction of weighted random graphs, generalizing the
concept of graphons. We prove that as the number of particles tends to
infinity, the finite-dimensional particle system converges in probability to
the solution of a deterministic graph-limit equation, in which the graphon
prescribing the interaction is given by the first moment of the weighted random
graph law. We also study interacting particle systems posed on switching
weighted random graphs, which are obtained by resetting the weighted random
graph at regular time intervals. We show that these systems converge to the
same graph-limit equation, in which the interaction is prescribed by a
constant-in-time graphon.
