Persistent Betti numbers form a key tool in topological data analysis as they track the appearance and disappearance of topological features in a sample. In this talk, we derive a goodness of fit test of point patterns and random networks based on the persistence diagram in large volumes. On the conceptual side, the tests rely on functional central limit theorems for the sub-level filtration in cylindrical networks and for bounded-size features of the Čech-complex of planar point patterns. The proof is based on methods from a recently developed framework for CLTs on point processes with fast decay of correlations. We analyze the power of tests derived from this statistic on simulated point patterns and apply the tests to a point pattern from an application context in neuroscience.