##  [Vietoris–Rips Complex](/index.php/vietoris-rips-complex) 

  ##  [Vietoris–Rips Complex](https://puremath.quantumdictionary.io/vietoris-rips-complex-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A simplicial complex constructed from a metric space X and a scale parameter r ≥ 0 by declaring a finite subset {x0,...,xk} to span a k-simplex exactly when every pairwise distance d(xi,xj) ≤ r; used to convert metric/point-cloud data into combinatorial topological objects.