  We study the exploration of an Erd\"os-R\'enyi random graph by a
respondent-driven sampling method, where discovered vertices reveal their
neighbours. Some of them receive coupons to reveal in their turn their own
neighbourhood. This leads to the study of a Markov chain on the random graph
that we study. For sparse Erd\"os-R\'enyi graphs of large sizes, this process
correctly renormalized converges to the solution of a deterministic curve,
solution of a system of ODEs absorbed on the abscissa axis. The associated
fluctuation process is also studied, providing a functional central limit
theorem, with a Gaussian limiting process. Simulations and numerical
computation illustrate the study.
