In Morse theory, a branch of mathematics, a Reeb graph of a scalar function describes the connectivity of its level sets.[1]Reeb graphs are named after Georges Reeb.
If the function is defined over a vector space rather than over a more general manifold, the Reeb graph forms a polytree (a directed graph formed by assigning orientations to the edges of an undirected forest). In this special case, it is also called a contour tree.[2]
Reeb graphs and contour trees have a wide variety of applications including computer aided geometric design, topology-based shape matching [3], topological simplification and cleaning, surface segmentation and parametrization, and efficient computation of level sets.