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Reeb graph

A Reeb graph (named after Georges Reeb by René Thom) is a mathematical object reflecting the evolution of the level sets of a real-valued function on a manifold. A similar concept was introduced by G.M. Adelson-Velskii and A.S. Kronrod and applied to analysis of Hilbert's thirteenth problem. Proposed by G. Reeb as a tool in Morse theory, Reeb graphs are…

Formal definition, Structure of the Reeb graph defined by a smooth function & Overview

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Formal definition

Topological spaceContinuous functionEquivalence relationConnected componentLevel set
13 related topics

Structure of the Reeb graph defined by a smooth function

Smooth functionsClosed manifoldBetti numberCycle rankCo-rank
12 related topics

Overview

Georges ReebRené ThomMathematicalLevel setsFunction
27 related topics

Description for Morse functions

Critical valuesSaddle point
2 related topics

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Overview

Formal definition

Structure of the Reeb graph defined by a smooth function

Description for Morse functions

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Map overview Semantic statistics

Reeb graph

Nodes59
Edges58
Triples25
Avg. degree1.97
Density0.033898
Components1

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Reeb graph

Top relations

related to Description for Morse functions · 6
Reeb graph → For, If, Its, Morse, Reeb, The
related to Formal definition · 6
Reeb graph → Even, Generally, Given, Hausdorff, Reeb, The Reeb
related to Leaf blocks of the Reeb graph · 5
Reeb graph → Bott, If, Morse, Reeb, This
related to The first Betti number of the Reeb graph · 4
Reeb graph → An, Betti, Reeb, Since
related to Structure of the Reeb graph defined by a smooth function · 3
Reeb graph → Let, Reeb, The
is a · 1
Reeb graph → quotient space X

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Important terminology

reeb graph function displaystyle morse manifold level functions structure smooth finite graphs closed space analysis degree sets also number first

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Reeb graphis aquotient space X0.90text
Reeb graphrelated to Description for Morse functionsIf0.60section
Reeb graphrelated to Description for Morse functionsMorse0.60section
Reeb graphrelated to Description for Morse functionsReeb0.60section
Reeb graphrelated to Description for Morse functionsIts0.60section
Reeb graphrelated to Description for Morse functionsThe0.60section
Reeb graphrelated to Description for Morse functionsFor0.60section
Reeb graphrelated to Formal definitionGiven0.60section
Reeb graphrelated to Formal definitionThe Reeb0.60section
Reeb graphrelated to Formal definitionGenerally0.60section
Reeb graphrelated to Formal definitionEven0.60section
Reeb graphrelated to Formal definitionReeb0.60section

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