Abstract: Brain networks are complicated. Scientists usually apply statistical models from connectomics to try to unravel what brain connections hide. However, these approaches are only able to see macroscopic properties of such networks. Using Topological Data Analysis permits to go one level deeper in the structure of networks. I will provide an intuitive introduction to the topic of Topology in graphs and go through a case-study in subjects injected with psilocybin and their potential usage in longitudinal studies.