Graphs and Their Vietoris-Rips Complexes Have the Same Pseudotopological Weak Homotopy Type

Abstract

In this document, we propose a bridge between the graphs and the geometric realizations of their Vietoris Rips complexes, i.e. Graphs, with their canonical \v{C}ech closure structure, have the same homotopy type that the realization of their Vietoris Rips complex.