Any Graph is a Mapper Graph
<|reference_start|>Any Graph is a Mapper Graph: 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.<|reference_end|>
@article{alvarado2024any,
    title={Any Graph is a Mapper Graph},
    author={Enrique G Alvarado, Robin Belton, Kang-Ju Lee, Sourabh Palande, Sarah
  Percival, Emilie Purvine, and Sarah Tymochko},
    journal={arXiv preprint arXiv:2408.11180},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.11180},
    primaryClass={math.AT cs.CG}
}