Here, we view the mental lexicon as a semantic network where words are connected if they are semantically related. Steyvers and Tenenbaum (Cognitive Science, 29, 41–78, 2005) proposed that the growth of semantic networks follows preferential attachment, the observation that new nodes are more likely to connect to preexisting nodes that are more well connected (i.e., the rich get richer). If this is the case, well-connected known words should be better at acquiring new links than poorly connected words. We tested this prediction in three paired-associate learning (PAL) experiments in which participants memorized arbitrary cue–response word pairs. We manipulated the semantic connectivity of the cue words, indexed by the words’ free associative degree centrality. Experiment 1 is a reanalysis of the PAL data from Qiu and Johns (Psychonomic Bulletin & Review, 27, 114–121, 2020), in which young adults remembered 40 cue–response word pairs (e.g., nature–chain) and completed a cued recall task. Experiment 2 is a preregistered replication of Qiu and Johns. Experiment 3 addressed some limitations in Qiu and Johns’s design by using pseudowords as the response items (e.g., boot–arruity). The three experiments converged to show that cue words of higher degree centrality facilitated the recall/recognition of the response items, providing support for the notion that better-connected words have a greater ability to acquire new links (i.e., the rich do get richer). Importantly, while degree centrality consistently accounted for significant portions of variance in PAL accuracy, other psycholinguistic variables (e.g., concreteness, contextual diversity) did not, suggesting that degree centrality is a distinct variable that affects the ease of verbal associative learning.