# permaviss.simplicial_complexes.vietoris_rips¶

vietoris_rips.py

Functions

 `vietoris_rips`(Dist, max_r, max_dim) This computes the Vietoris-Rips complex with simplexes of dimension less or equal to max_dim, and with maximum radius specified by max_r
`permaviss.simplicial_complexes.vietoris_rips.``_lower_neighbours`(G, u)[source]

Given a graph G and a vertex u in G, we return a list with the vertices in G that are lower than u and are connected to u by an edge in G.

Parameters: G (`Numpy Array(no. of edges, 2)`) – Matrix storing the edges of the graph. u (int) – Vertex of the graph. lower_neighbours – List of lower neighbours of u in G. `list`
`permaviss.simplicial_complexes.vietoris_rips.``vietoris_rips`(Dist, max_r, max_dim)[source]

This computes the Vietoris-Rips complex with simplexes of dimension less or equal to max_dim, and with maximum radius specified by max_r

Parameters: Dist (`Numpy Array(no. of points, no. of points)`) – Distance matrix of points. max_r (float) – Maximum radius of filtration. max_dim (int) – Maximum dimension of computed Rips complex. C (`list(Numpy Array)`) – Vietoris Rips complex generated for the given parameters. List where the first entry stores the number of vertices, and all other entries contain a `Numpy Array` with the list of simplices in C. R (`list(Numpy Array)`) – List with radius of birth for the simplices in C. The i entry contains a 1D `Numpy Array` containing each of the birth radii for each i simplex in C.