High Quality Content by WIKIPEDIA articles! In topology, the Vietoris–Rips complex, also called the Vietoris complex or Rips complex, is an abstract simplicial complex that can be defined from any metric space M and distance ? by forming a simplex for every finite set of points that has diameter at most ?. That is, it is a family of finite subsets of M, in which we think of a subset of k points as forming a (k ? 1)-dimensional simplex (an edge for two points, a triangle for three points, a tetrahedron for four points, etc.); if a finite set S has the property that the distance between every pair of points in S is at most ?, then we include S as a simplex in the complex.

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