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It has increasingly become a useful data structure that supports topological feature\u2010directed visualization of 2D\/3D scalar fields, and enables dimensionality reduction together with exploratory analysis of high\u2010dimensional scalar fields. Current methods that employ the extremum graph compute it either using a simple sequential algorithm for computing the Morse decomposition or by computing the more detailed Morse\u2013Smale complex. Both approaches are typically limited to two and three\u2010dimensional scalar fields. We describe a GPU\u2013CPU hybrid parallel algorithm for computing the extremum graph of scalar fields in all dimensions. The proposed shared memory algorithm utilizes both fine\u2010grained parallelism and task parallelism to achieve efficiency. 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