Topological Data Analysis (TDA) has proved to be a very powerful tool for the analysis of the structure of the Cosmic Web. In our recent work “Topological bias: how haloes trace structural patterns in the cosmic web”, we report a remarkable linear relationship between halo masses and topology: haloes of different mass trace environments with different topological signature. This allows to determine the overall connectivity from a limited sample of galaxies and can be of particular relevance for the large upcoming galaxy surveys such as DESI, Euclid, and the Vera Rubin telescope surveys. This work has now appeared in the Monthly Notices of the Royal Astronomical Society and more details can be found here.