Reeb graphs and Mapper graphs are widely used in topological data analysis to summarize the evolution of connected components of level sets of a scalar function. However, using these summaries in practice requires principled methods for parameter selection and uncertainty quantification under sampling assumptions. In this talk, I will present a framework for building confidence regions for Reeb graphs using the interleaving distance. The key advantage of this metric viewpoint is that zero distance corresponds to isomorphism of the underlying Reeb-type objects, so confidence balls provide object-level guarantees rather than guarantees only on persistence signatures.

Starting from a finite sample, we define intrinsic and extrinsic Mapper-type cosheaf estimators and prove stability bounds comparing them to the target Reeb cosheaf. These bounds lead to confidence regions once the sampling scale is controlled, either through standard sampling assumptions or via subsampling-based estimates. I will also explain how these interleaving bounds relate to classical persistence-based guarantees: in particular, we prove that the extended-persistence pseudometric is controlled by the interleaving distance, with sharp constant 1 for the $H_0$-related components and global constant 2. This provides a direct bridge with previous Mapper confidence frameworks, while giving stronger, metric-level control of the underlying Reeb graph.