I can use software to calculate the Betti numbers $\beta_0,\beta_1,\beta_2,\dots$ of a finite simplicial complex.
This is prohibitive for large complexes, built on say > 100,000 nodes.
Is there some way to computationally approximate the ranks of the first $n$ homology groups? Results e.g. Carlson here seem to work only for data points in Euclidean space, where the relations on which the complex is built are interpretations of the data (i.e. persistent homology). I have a set of fixed, deterministic relations on a set of vertices i.e. a graph, and the corresponding clique complex.