This mapping pattern appears in many graph problems where you need to convert or copy structure while preserving relationships.
The critical technique: add nodes to your map before processing their connections. This handles cycles gracefully. If node A points to node B, and B points back to A, the second visit finds A already in the map and uses the existing copy.
You'll see this pattern in problems involving graph serialization, graph isomorphism, and converting between graph representations. The hash map acts as your bridge between the old structure and the new one.
Next problem: detecting cycles in graphs.