N edges are selected at random from the graph. Nodes connected by those edges are included in the resulting network.
Pros & Cons
Because this algorithm focuses on the edges, it is more sensitive to the structure of the graph than the node sampler, which samples nodes indiscriminate of network structure (except in that it discards unattached nodes in the result). That is, since higher degree nodes have more neighboring edges (by definition), they are more likely to be in the output graph than lower degree nodes.
S. H. Lee, P-J. Kim, and H. Jeong. (2006) Statistical properties of sampled networks. Physical Review E 73.