Respondent-Driven Sampling method and sparse graph convergence

Respondent-Driven Sampling (RDS) is a sampling method used to sample from hard-to-reach populations such as drugs users, people of HIV, etc. We consider a particular RDS procedure governed by a graphon. Using a specific clumping procedure of sampled vertices, we construct a sequence of sparse graph. If the sequence of vertex-sets is stationary, the sequence of sparse graphs converges to the governing graphon in the cut-metric.