I am currently trying to write a program, which creates a simplicial complex, plots the persistence diagram and outputs the Betti numbers. I completed the first two steps using GUDHI, but I am not sure how can I compute Betti numbers using GUDHI or any other library.
I do realize that Betti numbers will be the number of points on the persistence diagram, which are far from the diagonal, but I am not sure if that is useful for an efficient computation. Any advice is greatly appreciated.