The Snowball sampler picks a random starting node, then all nodes connected to that node, then all nodes connected to those nodes, and so on until n nodes are picked. If not all nodes in a particular iteration are needed to reach n nodes, the needed number of nodes is chosen at random.
All edges among the selected nodes are included in the resulting graph.
This is the most naive form of snowball sampling and doesn't have some nice properties achieved by snowball sampling in the experimental sense.
It is, however, simple and easy to understand.
Snowball sampling can be used to simulate experimental sampling techniques on a large (preferably complete) dataset, perhaps to compare the resulting network properties to those of actual experimental sample properties.
S. H. Lee, P-J. Kim, and H. Jeong. (2006) Statistical properties of sampled networks. Physical Review E 73.