Any Graph is a Mapper Graph

Enrique G. Alvarado, Robin Belton, Kang-Ju Lee, Sourabh Palande, Sarah Percival, Emilie Purvine, Sarah Tymochko

Abstract: The Mapper algorithm is a popular tool for visualization and data exploration in topological data analysis. We investigate an inverse problem for the Mapper algorithm: Given a dataset $X$ and a graph $G$, does there exist a set of Mapper parameters such that the output Mapper graph of $X$ is isomorphic to $G$? We provide constructions that affirmatively answer this question. Our results demonstrate that it is possible to engineer Mapper parameters to generate a desired graph.