The associative theory of creativity has long held that creative thinking involves connecting remote concepts in semantic memory. Network science tools have recently been applied to map the organization of concepts in semantic memory, and to study the link between semantic memory and creativity. Yet such work has largely overlooked the domain of convergent thinking, despite the theoretical importance of semantic memory networks for facilitating associative processes relevant for convergent problem solving (e.g., spreading activation). Convergent thinking problems, such as the Compound Remote Associates (CRA) test, can be solved with insight (the sudden “aha” experience) or analysis (deliberately and incrementally working towards the solution). In a sample of 477 participants, we adopted network science methods to compare semantic memory structure across two grouping variables: 1) convergent thinking ability (i.e., CRA accuracy), and 2) the self-reported tendency to solve problems with insight or analysis. Semantic memory networks were constructed from a semantic fluency task, and problem solving style (insight or analysis) was determined from judgments provided during solving of CRAs. We found that, compared to the low-convergent thinking group, the high-convergent thinking group exhibited a more flexible and interconnected semantic network—with short paths and many connections between concepts. Moreover, participants who primarily solved problems with insight (compared to analysis) showed shorter average path distances between concepts, even after controlling for accuracy. Our results extend the literature on semantic memory and creativity, and suggest that the organization of semantic memory plays a key role in convergent thinking, including insight problem solving.