Recent work has attempted to characterize the structure of semantic memory and the search algorithms which, together, best approximate human patterns of search revealed in a semantic fluency task. There are a number of models that seek to capture semantic search processes over networks, but they vary in the cognitive plausibility of their implementation. Existing work has also neglected to consider the constraints that the incremental process of language acquisition must place on the structure of semantic memory. Here we present a model that incrementally updates a semantic network, with limited computational steps, and replicates many patterns found in human semantic fluency using a simple random walk. We also perform thorough analyses showing that a combination of both structural and semantic features are correlated with human performance patterns.