The network science perspective on vocabulary development emphasizes the structured relationships between words and how they can influence learning. Words that appear in many contexts and thus develop associations with many other words tend to be learned earlier---a growth model called preferential acquisition. Likewise, children appear to have a bias towards learning new words associated with many known words---a growth model called lure of the associates. Although both are statistically related to age of acquisition estimates, much variance remains unexplained, and it is unknown what structures these models promote within the developing vocabulary. We simulated vocabulary growth strictly adhering to preferential acquisition and lure of the associates and found that they promote similar structures: more connectivity, more clustering, and much shorter path lengths than random growth would achieve. They clearly promote small-world structure, consistent with that seen in young children’s vocabularies.