Reeb-Graph

The Reeb graph is a topological graph named after the French mathematician Georges Reeb ( 1920-1993 ). It has its origin in the Morse theory.

Definition

Let be a continuous scalar function on the compact manifold. Reeb the graph of with regard to the space ratio of which is induced by the equivalent ratio. This holds if and only if

  • And
  • And lie in the same connected component of.

That is, nodes occur at points where the topology changes of regard. These are also referred to as the critical points. Edges indicate topological consistency in the relevant area.

  • Graph Theory
Topology (disambiguation) Critical point (mathematics)
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