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Vietoris–Rips complex

In topology, the Vietoris–Rips complex, also called the Vietoris complex or Rips complex, is a way of forming a topological space from distances in a set of points. It is an abstract simplicial complex that can be defined from any metric space M and distance δ by forming a simplex for every finite set of points that has diameter no more than δ. That is…

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Overview

History

Relation to Čech complex

Relation to hyperbolic groups

Relation to unit disk graphs and clique complexes

Other results

Applications

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Vietoris–Rips complex

Nodes52
Edges51
Triples38
Avg. degree1.96
Density0.038462
Components1

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Vietoris–Rips complex

Top relations

related to Relation to Čech complex · 10
Vietoris–Rips complex → As, Euclidean, However, If, In, M3, Rips, The Vietoris, Thus, Vietoris
related to history · 8
Vietoris–Rips complex → After Eliyahu Rips, Jean-ClaudeHausmann, Leopold Vietoris, MikhailGromov, Rips, The, The Vietoris, Vietoris
related to Other results · 8
Vietoris–Rips complex → Chambers, Erickson, Euclidean, If, Riemannian, Rips, Vietoris, Worah
has application · 6
Vietoris–Rips complex → An, As, One, Rips, TDAstats, Vietoris
related to Relation to unit disk graphs and clique complexes · 6
Vietoris–Rips complex → As, It, More, Rips, The Vietoris, Vietoris

Important terminology Word statistics

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Important terminology

complex rips vietoris points space metric čech set balls distance finite every simplex unit complexes forming m3 triangle three disk

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Vietoris–Rips complexhas applicationAs0.60section
Vietoris–Rips complexhas applicationVietoris0.60section
Vietoris–Rips complexhas applicationRips0.60section
Vietoris–Rips complexhas applicationOne0.60section
Vietoris–Rips complexhas applicationAn0.60section
Vietoris–Rips complexhas applicationTDAstats0.60section
Vietoris–Rips complexrelated to historyThe Vietoris0.60section
Vietoris–Rips complexrelated to historyRips0.60section
Vietoris–Rips complexrelated to historyVietoris0.60section
Vietoris–Rips complexrelated to historyLeopold Vietoris0.60section
Vietoris–Rips complexrelated to historyAfter Eliyahu Rips0.60section
Vietoris–Rips complexrelated to historyMikhailGromov0.60section

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