Mind mapping is a popular way to explore a design space in creative thinking exercises, allowing users to form associations between concepts. Yet, most existing digital tools for mind mapping focus on authoring and organization, with little support for addressing the challenges of mind mapping such as stagnation and design fixation. We present Spinneret, a functional approach to aid mind mapping by providing suggestions based on a knowledge graph. Spinneret uses biased random walks to explore the knowledge graph in the neighborhood of an existing concept node in the mind map, and provides "suggestions" for the user to add to the mind map. A comparative study with a baseline mind-mapping tool reveals that participants created more diverse and distinct concepts with Spinneret, and reported that the suggestions inspired them to think of ideas they would otherwise not have explored.