Estimation On the Basis of Snowball Samples: How To Weight?

What are the possibilities of snowball sampling, if one desires valid statistical inference without making probabilistic assumptions on the network structure? In a critical review of the possibilities of snowball sampling for a population of vertices connected by a network of arcs, it is argued that the snowball method is much more suitable for the estimation of parameters of the network structure (or parameters of the population of arcs) than to estimate parameters of the population of vertices. Further work needs to be done to relax the assumption of randomness of the initial sample of the snowball.