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Visual exploration of large and complex 3D steady and unsteady flow fields is critically important in many areas of science and engineering. In this paper, we introduce FlowGraph, a novel compound graph representation that organizes field line clusters and spatiotemporal regions hierarchically for occlusion-free and controllable visual exploration. It works with any seeding strategy as long as the domain is well covered and important flow features are captured. By transforming a flow field to a graph representation, we enable observation