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

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 Cech closure structure, have the same homotopy type that the realization of their Vietoris Rips complex.